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		<updated>2015-12-05T23:50:20Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* Contact Interactions */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;__NOTOC__&lt;br /&gt;
Welcome to the Georgia Tech Wiki for Intro Physics.  This resources was created so that students can contribute and curate content to help those with limited or no access to a textbook.  When reading this website, please correct any errors you may come across. If you read something that isn&#039;t clear, please consider revising it!&lt;br /&gt;
&lt;br /&gt;
Looking to make a contribution?&lt;br /&gt;
#Pick a specific topic from intro physics&lt;br /&gt;
#Add that topic, as a link to a new page, under the appropriate category listed below by editing this page.&lt;br /&gt;
#Copy and paste the default [[Template]] into your new page and start editing.&lt;br /&gt;
&lt;br /&gt;
Please remember that this is not a textbook and you are not limited to expressing your ideas with only text and equations.  Whenever possible embed: pictures, videos, diagrams, simulations, computational models (e.g. Glowscript), and whatever content you think makes learning physics easier for other students.&lt;br /&gt;
&lt;br /&gt;
== Source Material ==&lt;br /&gt;
All of the content added to this resource must be in the public domain or similar free resource.  If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web.  Here is an incomplete list of intro physics resources (please update as needed).&lt;br /&gt;
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]&lt;br /&gt;
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]&lt;br /&gt;
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]&lt;br /&gt;
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]&lt;br /&gt;
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]&lt;br /&gt;
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]&lt;br /&gt;
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]&lt;br /&gt;
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]&lt;br /&gt;
&lt;br /&gt;
== Organizing Categories ==&lt;br /&gt;
These are the broad, overarching categories, that we cover in two semester of introductory physics.  You can add subcategories or make a new category as needed.  A single topic should direct readers to a page in one of these catagories.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
===Interactions===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[Kinds of Matter]]&lt;br /&gt;
**[[Ball and Spring Model of Matter]]&lt;br /&gt;
*[[Detecting Interactions]]&lt;br /&gt;
*[[Escape Velocity]]&lt;br /&gt;
*[[Fundamental Interactions]]&lt;br /&gt;
*[[Determinism]]&lt;br /&gt;
*[[System &amp;amp; Surroundings]] &lt;br /&gt;
*[[Free Body Diagram]]&lt;br /&gt;
*[[Newton&#039;s First Law of Motion]]&lt;br /&gt;
*[[Newton&#039;s Second Law of Motion]]&lt;br /&gt;
*[[Newton&#039;s Third Law of Motion]]&lt;br /&gt;
*[[Gravitational Force]]&lt;br /&gt;
*[[Electric Force]]&lt;br /&gt;
*[[Conservation of Energy]]&lt;br /&gt;
*[[Conservation of Charge]]&lt;br /&gt;
*[[Terminal Speed]]&lt;br /&gt;
*[[Simple Harmonic Motion]]&lt;br /&gt;
*[[Speed and Velocity]]&lt;br /&gt;
*[[Electric Polarization]]&lt;br /&gt;
*[[Perpetual Freefall (Orbit)]]&lt;br /&gt;
*[[2-Dimensional Motion]]&lt;br /&gt;
*[[Center of Mass]]&lt;br /&gt;
*[[Reaction Time]]&lt;br /&gt;
*[[Time Dilation]]&lt;br /&gt;
*[[Pauli exclusion principle]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Modeling with VPython===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[VPython]]&lt;br /&gt;
*[[VPython basics]]&lt;br /&gt;
*[[VPython Common Errors and Troubleshooting]]&lt;br /&gt;
*[[VPython Functions]]&lt;br /&gt;
*[[VPython Lists]]&lt;br /&gt;
*[[VPython Multithreading]]&lt;br /&gt;
*[[VPython Animation]]&lt;br /&gt;
*[[VPython 3D Objects]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Theory===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[Einstein&#039;s Theory of Special Relativity]]&lt;br /&gt;
*[[Einstein&#039;s Theory of General Relativity]]&lt;br /&gt;
*[[Quantum Theory]]&lt;br /&gt;
*[[Maxwell&#039;s Electromagnetic Theory]]&lt;br /&gt;
*[[Atomic Theory]]&lt;br /&gt;
*[[String Theory]]&lt;br /&gt;
*[[Elementary Particles and Particle Physics Theory]]&lt;br /&gt;
*[[Law of Gravitation]]&lt;br /&gt;
*[[Newton&#039;s Laws]]&lt;br /&gt;
*[[Higgs field]]&lt;br /&gt;
*[[Supersymmetry]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Notable Scientists===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[Alexei Alexeyevich Abrikosov]]&lt;br /&gt;
*[[Christian Doppler]]&lt;br /&gt;
*[[Albert Einstein]]&lt;br /&gt;
*[[Ernest Rutherford]]&lt;br /&gt;
*[[Joseph Henry]]&lt;br /&gt;
*[[Michael Faraday]]&lt;br /&gt;
*[[J.J. Thomson]]&lt;br /&gt;
*[[James Maxwell]]&lt;br /&gt;
*[[Robert Hooke]]&lt;br /&gt;
*[[Carl Friedrich Gauss]]&lt;br /&gt;
*[[Nikola Tesla]]&lt;br /&gt;
*[[Andre Marie Ampere]]&lt;br /&gt;
*[[Sir Isaac Newton]]&lt;br /&gt;
*[[J. Robert Oppenheimer]]&lt;br /&gt;
*[[Oliver Heaviside]]&lt;br /&gt;
*[[Rosalind Franklin]]&lt;br /&gt;
*[[Enrico Fermi]]&lt;br /&gt;
*[[Robert J. Van de Graaff]]&lt;br /&gt;
*[[Charles de Coulomb]]&lt;br /&gt;
*[[Hans Christian Ørsted]]&lt;br /&gt;
*[[Philo Farnsworth]]&lt;br /&gt;
*[[Niels Bohr]]&lt;br /&gt;
*[[Georg Ohm]]&lt;br /&gt;
*[[Galileo Galilei]]&lt;br /&gt;
*[[Gustav Kirchhoff]]&lt;br /&gt;
*[[Max Planck]]&lt;br /&gt;
*[[Heinrich Hertz]]&lt;br /&gt;
*[[Edwin Hall]]&lt;br /&gt;
*[[James Watt]]&lt;br /&gt;
*[[Count Alessandro Volta]]&lt;br /&gt;
*[[Josiah Willard Gibbs]]&lt;br /&gt;
*[[Richard Phillips Feynman]]&lt;br /&gt;
*[[Sir David Brewster]]&lt;br /&gt;
*[[Daniel Bernoulli]]&lt;br /&gt;
*[[William Thomson]]&lt;br /&gt;
*[[Leonhard Euler]]&lt;br /&gt;
*[[Robert Fox Bacher]]&lt;br /&gt;
*[[Stephen Hawking]]&lt;br /&gt;
*[[Amedeo Avogadro]]&lt;br /&gt;
*[[Wilhelm Conrad Roentgen]]&lt;br /&gt;
*[[Pierre Laplace]]&lt;br /&gt;
*[[Thomas Edison]]&lt;br /&gt;
*[[Hendrik Lorentz]]&lt;br /&gt;
*[[Jean-Baptiste Biot]]&lt;br /&gt;
*[[Lise Meitner]]&lt;br /&gt;
*[[Lisa Randall]]&lt;br /&gt;
*[[Felix Savart]]&lt;br /&gt;
*[[Heinrich Lenz]]&lt;br /&gt;
*[[Max Born]]&lt;br /&gt;
*[[Archimedes]]&lt;br /&gt;
*[[Jean Baptiste Biot]]&lt;br /&gt;
*[[Carl Sagan]]&lt;br /&gt;
*[[Eugene Wigner]]&lt;br /&gt;
*[[Marie Curie]]&lt;br /&gt;
*[[Pierre Curie]]&lt;br /&gt;
*[[Werner Heisenberg]]&lt;br /&gt;
*[[Johannes Diderik van der Waals]]&lt;br /&gt;
*[[Louis de Broglie]]&lt;br /&gt;
*[[Aristotle]]&lt;br /&gt;
*[[Émilie du Châtelet]]&lt;br /&gt;
*[[Blaise Pascal]]&lt;br /&gt;
*[[Siméon Denis Poisson]]&lt;br /&gt;
*[[Benjamin Franklin]]&lt;br /&gt;
*[[James Chadwick]]&lt;br /&gt;
*[[Henry Cavendish]]&lt;br /&gt;
*[[Thomas Young]]&lt;br /&gt;
*[[James Prescott Joule]]&lt;br /&gt;
*[[John Bardeen]]&lt;br /&gt;
*[[Leo Baekeland]]&lt;br /&gt;
*[[Alhazen]]&lt;br /&gt;
*[[Willebrord Snell]]&lt;br /&gt;
*[[Fritz Walther Meissner]]&lt;br /&gt;
*[[Johannes Kepler]]&lt;br /&gt;
*[[Johann Wilhelm Ritter]]&lt;br /&gt;
*[[Philipp Lenard]]&lt;br /&gt;
*[[Robert A. Millikan]]&lt;br /&gt;
*[[Joseph Louis Gay-Lussac]]&lt;br /&gt;
*[[Guglielmo Marconi]]&lt;br /&gt;
*[[William Lawrence Bragg]]&lt;br /&gt;
*[[Robert Goddard]]&lt;br /&gt;
*[[Léon Foucault]]&lt;br /&gt;
*[[Henri Poincaré]]&lt;br /&gt;
*[[Steven Weinberg]]&lt;br /&gt;
*[[Arthur Compton]]&lt;br /&gt;
*[[Pythagoras of Samos]]&lt;br /&gt;
*[[Subrahmanyan Chandrasekhar]]&lt;br /&gt;
*[[Wilhelm Eduard Weber]]&lt;br /&gt;
*[[Edmond Becquerel]]&lt;br /&gt;
*[[Joseph Rotblat]]&lt;br /&gt;
*[[Carl David Anderson]]&lt;br /&gt;
*[[Hermann von Helmholtz]]&lt;br /&gt;
*[[Nicolas Leonard Sadi Carnot]]&lt;br /&gt;
*[[Wallace Carothers]]&lt;br /&gt;
*[[David J. Wineland]]&lt;br /&gt;
*[[Rudolf Clausius]]&lt;br /&gt;
*[[Edward L. Norton]]&lt;br /&gt;
*[[Shuji Nakamura]]&lt;br /&gt;
*[[Pierre Laplace Pt. 2]]&lt;br /&gt;
*[[William B. Shockley]]&lt;br /&gt;
*[[Osborne Reynolds]]&lt;br /&gt;
*[[Alexander Graham Bell]]&lt;br /&gt;
*[[Hans Bethe]]&lt;br /&gt;
*[[Erwin Schrodinger]]&lt;br /&gt;
*[[Wolfgang Pauli]]&lt;br /&gt;
*[[Paul Dirac]]&lt;br /&gt;
*[[Bill Nye]]&lt;br /&gt;
*[[Arnold Sommerfeld]]&lt;br /&gt;
*[[Albert A. Micheleson and Edward W. Morley]]&lt;br /&gt;
*[[James Franck]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Properties of Matter===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[Mass]]&lt;br /&gt;
*[[Velocity]]&lt;br /&gt;
*[[Relative Velocity]]&lt;br /&gt;
*[[Density]]&lt;br /&gt;
*[[Charge]]&lt;br /&gt;
*[[Spin]]&lt;br /&gt;
*[[SI Units]]&lt;br /&gt;
*[[Heat Capacity]]&lt;br /&gt;
*[[Specific Heat]]&lt;br /&gt;
*[[Wavelength]]&lt;br /&gt;
*[[Conductivity]]&lt;br /&gt;
*[[Malleability]]&lt;br /&gt;
*[[Ductility]]&lt;br /&gt;
*[[Weight]]&lt;br /&gt;
*[[Boiling Point]]&lt;br /&gt;
*[[Melting Point]]&lt;br /&gt;
*[[Inertia]]&lt;br /&gt;
*[[Non-Newtonian Fluids]]&lt;br /&gt;
*[[Ferrofluids]]&lt;br /&gt;
*[[Color]]&lt;br /&gt;
*[[Temperature]]&lt;br /&gt;
*[[Plasma]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Contact Interactions===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
* [[Young&#039;s Modulus]]&lt;br /&gt;
* [[Friction]]&lt;br /&gt;
* [[Static Friction]]&lt;br /&gt;
* [[Tension]]&lt;br /&gt;
* [[Hooke&#039;s Law]]&lt;br /&gt;
*[[Centripetal Force and Curving Motion]]&lt;br /&gt;
*[[Compression or Normal Force]]&lt;br /&gt;
* [[Length and Stiffness of an Interatomic Bond]]&lt;br /&gt;
* [[Speed of Sound in Solids]]&lt;br /&gt;
* [[Iterative Prediction of Spring-Mass System]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Momentum===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
* [[Vectors]]&lt;br /&gt;
* [[Kinematics]]&lt;br /&gt;
* [[Conservation of Momentum]]&lt;br /&gt;
* [[Predicting Change in multiple dimensions]]&lt;br /&gt;
* [[Derivation of the Momentum Principle]]&lt;br /&gt;
* [[Momentum Principle]]&lt;br /&gt;
* [[Impulse Momentum]]&lt;br /&gt;
* [[Curving Motion]]&lt;br /&gt;
* [[Projectile Motion]]&lt;br /&gt;
* [[Multi-particle Analysis of Momentum]]&lt;br /&gt;
* [[Iterative Prediction]]&lt;br /&gt;
* [[Analytical Prediction]]&lt;br /&gt;
* [[Newton&#039;s Laws and Linear Momentum]]&lt;br /&gt;
* [[Net Force]]&lt;br /&gt;
* [[Center of Mass]]&lt;br /&gt;
* [[Momentum at High Speeds]]&lt;br /&gt;
* [[Change in Momentum in Time for Curving Motion]]&lt;br /&gt;
* [[Momentum with respect to external Forces]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Angular Momentum===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
* [[The Moments of Inertia]]&lt;br /&gt;
* [[Moment of Inertia for a cylinder]]&lt;br /&gt;
* [[Rotation]]&lt;br /&gt;
* [[Torque]]&lt;br /&gt;
* [[Systems with Zero Torque]]&lt;br /&gt;
* [[Systems with Nonzero Torque]]&lt;br /&gt;
* [[Torque vs Work]]&lt;br /&gt;
* [[Angular Impulse]]&lt;br /&gt;
* [[Right Hand Rule]]&lt;br /&gt;
* [[Angular Velocity]]&lt;br /&gt;
* [[Predicting the Position of a Rotating System]]&lt;br /&gt;
* [[Translational Angular Momentum]]&lt;br /&gt;
* [[The Angular Momentum Principle]]&lt;br /&gt;
* [[Angular Momentum of Multiparticle Systems]]&lt;br /&gt;
* [[Rotational Angular Momentum]]&lt;br /&gt;
* [[Total Angular Momentum]]&lt;br /&gt;
* [[Gyroscopes]]&lt;br /&gt;
* [[Angular Momentum Compared to Linear Momentum]]&lt;br /&gt;
*[[Torque 2]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Energy===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[The Photoelectric Effect]]&lt;br /&gt;
*[[Photons]]&lt;br /&gt;
*[[The Energy Principle]]&lt;br /&gt;
*[[Predicting Change]]&lt;br /&gt;
*[[Rest Mass Energy]]&lt;br /&gt;
*[[Kinetic Energy]]&lt;br /&gt;
*[[Potential Energy]]&lt;br /&gt;
**[[Potential Energy for a Magnetic Dipole]]&lt;br /&gt;
**[[Potential Energy of a Multiparticle System]]&lt;br /&gt;
*[[Work]]&lt;br /&gt;
**[[Work Done By A Nonconstant Force]]&lt;br /&gt;
*[[Work and Energy for an Extended System]]&lt;br /&gt;
*[[Thermal Energy]]&lt;br /&gt;
*[[Conservation of Energy]]&lt;br /&gt;
*[[Electric Potential]]&lt;br /&gt;
*[[Energy Transfer due to a Temperature Difference]]&lt;br /&gt;
*[[Gravitational Potential Energy]]&lt;br /&gt;
*[[Point Particle Systems]]&lt;br /&gt;
*[[Real Systems]]&lt;br /&gt;
*[[Spring Potential Energy]]&lt;br /&gt;
**[[Ball and Spring Model]]&lt;br /&gt;
*[[Internal Energy]]&lt;br /&gt;
**[[Potential Energy of a Pair of Neutral Atoms]]&lt;br /&gt;
*[[Translational, Rotational and Vibrational Energy]]&lt;br /&gt;
*[[Franck-Hertz Experiment]]&lt;br /&gt;
*[[Power (Mechanical)]]&lt;br /&gt;
*[[Transformation of Energy]]&lt;br /&gt;
&lt;br /&gt;
*[[Energy Graphs]]&lt;br /&gt;
**[[Energy graphs and the Bohr model]]&lt;br /&gt;
*[[Air Resistance]]&lt;br /&gt;
*[[Electronic Energy Levels]]&lt;br /&gt;
*[[Second Law of Thermodynamics and Entropy]]&lt;br /&gt;
*[[Specific Heat Capacity]]&lt;br /&gt;
*[[The Maxwell-Boltzmann Distribution]]&lt;br /&gt;
*[[Electronic Energy Levels and Photons]]&lt;br /&gt;
*[[Energy Density]]&lt;br /&gt;
*[[Bohr Model]]&lt;br /&gt;
*[[Quantized energy levels]]&lt;br /&gt;
**[[Spontaneous Photon Emission]]&lt;br /&gt;
*[[Path Independence of Electric Potential]]&lt;br /&gt;
*[[Energy in a Circuit]]&lt;br /&gt;
*[[The Photovoltaic Effect]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Collisions===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
[[File:opener.png]]&lt;br /&gt;
&lt;br /&gt;
*[[Collisions]] &lt;br /&gt;
Collisions are events that happen very frequently in our day-to-day world. In the realm of Physics, a collision is defined as any sort of process in which before and after a short time interval there is little interaction, but during that short time interval there are large interactions. When looking at collisions, it is first important to understand two very important principles: the Momentum Principle and the Energy Principle. Both principles serve use when talking of collisions because they provide a way in which to analyze these collisions. Collisions themselves can be categorized into 3 main different types: elastic collisions, inelastic collisions, maximally inelastic collisions. All 3 collisions will get touched on in more detail further on.&lt;br /&gt;
   [[File:pe.png]]&lt;br /&gt;
 &lt;br /&gt;
*[[Elastic Collisions]]&lt;br /&gt;
A collision is deemed &amp;quot;elastic&amp;quot; when the internal energy of the objects in the system does not change (in other words, change in internal energy equals 0). Because in an elastic collision no kinetic energy is converted over to internal energy, in any elastic collision Kfinal always equals Kinitial.&lt;br /&gt;
   [[File:Elco.png]]&lt;br /&gt;
&lt;br /&gt;
*[[Inelastic Collisions]]&lt;br /&gt;
A collision is said to be &amp;quot;inelastic&amp;quot; when it is not elastic; therefore, an inelastic collision is an interaction in which some change in internal energy occurs between the colliding objects (in other words, change in internal energy does not equal 0). Examples of such changes that occur between colliding objects include, but are not limited to, things like they get hot, or they vibrate/rotate, or they deform. Because some of the kinetic energy is converted to internal energy during an inelastic collision, Kfinal does not equal Kinitial.&lt;br /&gt;
There are a few characteristics that one can search for when identifying inelasticity. These indications include things such as:&lt;br /&gt;
*Objects stick together after the collision&lt;br /&gt;
*An object is in an excited state after the collision&lt;br /&gt;
*An object becomes deformed after the collision&lt;br /&gt;
*The objects become hotter after the collision&lt;br /&gt;
*There exists more vibration or rotation after the collision&lt;br /&gt;
   [[File:inve.gif]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*[[Maximally Inelastic Collision]] &lt;br /&gt;
Maximally inelastic collisions, also known as &amp;quot;sticking collisions&amp;quot;, are the most extreme kinds of inelastic collisions. Just as its secondary name implies, a maximally inelastic collision is one in which the colliding objects stick together creating maximum dissipation. This does not automatically mean that the colliding objects stop dead because the law of conservation of momentum. In a maximally inelastic collision, the remaining kinetic energy is present only because total momentum can&#039;t change and must be conserved.&lt;br /&gt;
   [[File:inel.gif]]&lt;br /&gt;
&lt;br /&gt;
*[[Head-on Collision of Equal Masses]]&lt;br /&gt;
The easiest way to understand this phenomenon is to look at it through an example. In this case, we can analyze it through the common game of billiards. Taking the two, equally massed billiard balls as the system, we can neglect the small frictional force exerted on the balls by the billiard table. The Momentum Principle states that in this head-on collision of billiard balls the total final momentum in the x direction must equal the total initial momentum. However, this alone does not give us the knowledge to know how the momentum will be divided up between the two balls. Considering the law of conservation of energy, we can more accurately depict what will happen. This will also allow for one to identify what kind of collision occurs (elastic, inelastic, or maximally inelastic). It is important to know that head-on collisions of equal masses do not have a definite type of collision associated with it.&lt;br /&gt;
   [[File:momentum-real-life-applications-2895.jpg]]   [[File:8ball.gif]]&lt;br /&gt;
&lt;br /&gt;
*[[Head-on Collision of Unequal Masses]]&lt;br /&gt;
Just as with head-on collisions of equal masses, it is easy to understand head-on collisions of unequal masses by viewing it through an example. Let&#039;s take for example two balls of unequal masses like a ping-pong ball and a bowling ball. For the purpose of this example (so as to allow for no friction and no other significant external forces), let&#039;s imagine these objects collide in outer space inside an orbiting spacecraft. If there were to be a collision between the two, what would one expect to happen? One could expect to see the ping-pong ball collide with the bowling ball and bounce straight back with a very small change of speed. What one might not expect as much is that the bowling ball also moves, just very slowly. Again, this can all be explained through the conservation of momentum and the conservation of energy.&lt;br /&gt;
   [[File:mi3e.jpg]]&lt;br /&gt;
&lt;br /&gt;
*[[Frame of Reference]]&lt;br /&gt;
In the world of Physics, a frame of reference is the perspective from which a system is observed. It can be stationary or sometimes it can even be moving at a constant velocity. In some rare cases, the frame of reference moves at an nonconstant velocity and is deemed &amp;quot;noninertial&amp;quot; meaning the basic laws of physics do not apply. Continuing with the trend of examples, pretend you are at a train station observing trains as they pass by. From your stationary frame of reference, you observe that the passenger on the train is moving at the same velocity as the train. However, from a moving frame of reference, say from the eyes of the train conductor, he would view the train passengers as &amp;quot;anchored&amp;quot; to the train.&lt;br /&gt;
   [[File:train.png]]&lt;br /&gt;
&lt;br /&gt;
*[[Scattering: Collisions in 2D and 3D]]&lt;br /&gt;
Experiments that involve scattering are often used to study the structure and behavior of atoms, nuclei, as well as of other small particles. In an experiment like such, a beam of particles collides with other particles. If it is an atomic or nuclear collision, we are unable to observe the curving trajectories inside the tiny region of interaction. Instead, we can only truly observe the trajectories before and after the collision. This is only possible because the particles are at a farther distance apart and have a very weak mutual interaction; this essentially means that the particles are moving almost in a straight line. A good example which demonstrates scattering is the collision between an alpha particle (the nucleus of a helium atom) and the nucleus of a gold atom. One will understand this phenomenon more in depth after first understanding the Rutherford Experiment which will get touched on later.&lt;br /&gt;
&lt;br /&gt;
*[[Rutherford Experiment and Atomic Collisions]]&lt;br /&gt;
In England in 1911, a famous experiment was performed by a group of scientists led by Mr. Ernest Rutherford. This experiment, later known as &amp;quot;The Rutherford Experiment&amp;quot;, was a tremendous breakthrough for its time because it led to the discovery of the nucleus inside the atom. Rutherford&#039;s experiment involved the scattering of a high-speed alpha particle (now known as a helium nuclei - 2 protons and 2 neutrons) as it was shot at a thin gold foil (consisting of a nuclei with 79 protons and 118 neutrons). In the experiment, Rutherford and his team discovered that the velocity of the alpha particles was not high enough to allow the particles to make actual contact with the gold nucleus. Although they never actually made contact, it is still deemed a collision because there exists a sizable force between the alpha particle and the gold nucleus over a very short period of time. In conclusion, we say the alpha particle is &amp;quot;scattered&amp;quot; by its interaction with the nucleus of a gold atom and experiments like such are called &amp;quot;scattering&amp;quot; experiments.&lt;br /&gt;
   [[File:ruthef.jpg]]&lt;br /&gt;
&lt;br /&gt;
*[[Coefficient of Restitution]]&lt;br /&gt;
The coefficient of restitution is a measure of the elasticity in a collision. It is the ratio of the differences in velocities before and after the collision. The coefficient is evaluated by taking the difference in the velocities of the colliding objects after the collision and dividing by the difference in the velocities of the colliding objects before the collision.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
All of the following information was collected from the Matter and Interactions 4th Edition physics textbook. The book is cited as follows...&lt;br /&gt;
&lt;br /&gt;
Chabay, Ruth W., and Bruce A. Sherwood. &amp;quot;Chapter 10: Collisions.&amp;quot; Matter &amp;amp; Interactions. Fourth Edition ed. Wiley, 2015. 383-409. Print.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Fields===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
* [[Electric Field]] of a&lt;br /&gt;
** [[Point Charge]]&lt;br /&gt;
** [[Electric Dipole]]&lt;br /&gt;
** [[Capacitor]]&lt;br /&gt;
** [[Charged Rod]]&lt;br /&gt;
** [[Charged Ring]]&lt;br /&gt;
** [[Charged Disk]]&lt;br /&gt;
** [[Charged Spherical Shell]]&lt;br /&gt;
** [[Charged Cylinder]]&lt;br /&gt;
**[[A Solid Sphere Charged Throughout Its Volume]]&lt;br /&gt;
*[[Charge Density]]&lt;br /&gt;
*[[Superposition Principle]]&lt;br /&gt;
*[[Electric Potential]] &lt;br /&gt;
**[[Potential Difference Path Independence]]&lt;br /&gt;
**[[Potential Difference in a Uniform Field]]&lt;br /&gt;
**[[Potential Difference of point charge in a non-Uniform Field]]&lt;br /&gt;
**[[Potential Difference at One Location]]&lt;br /&gt;
**[[Sign of Potential Difference]]&lt;br /&gt;
**[[Potential Difference in an Insulator]]&lt;br /&gt;
**[[Energy Density and Electric Field]]&lt;br /&gt;
** [[Systems of Charged Objects]]&lt;br /&gt;
*[[Electric Force]]&lt;br /&gt;
*[[Polarization]]&lt;br /&gt;
**[[Polarization of an Atom]]&lt;br /&gt;
**[[Charged Conductor and Charged Insulator]]&lt;br /&gt;
*[[Charge Motion in Metals]]&lt;br /&gt;
*[[Charge Transfer]]&lt;br /&gt;
*[[Magnetic Field]]&lt;br /&gt;
**[[Right-Hand Rule]]&lt;br /&gt;
**[[Direction of Magnetic Field]]&lt;br /&gt;
**[[Magnetic Field of a Long Straight Wire]]&lt;br /&gt;
**[[Magnetic Field of a Loop]]&lt;br /&gt;
**[[Magnetic Field of a Solenoid]]&lt;br /&gt;
**[[Bar Magnet]]&lt;br /&gt;
**[[Magnetic Dipole Moment]]&lt;br /&gt;
***[[Stern-Gerlach Experiment]]&lt;br /&gt;
**[[Magnetic Torque]]&lt;br /&gt;
**[[Magnetic Force]]&lt;br /&gt;
***[[Applying Magnetic Force to Currents]]&lt;br /&gt;
**[[Earth&#039;s Magnetic Field]]&lt;br /&gt;
**[[Atomic Structure of Magnets]]&lt;br /&gt;
*[[Combining Electric and Magnetic Forces]]&lt;br /&gt;
**[[Hall Effect]]&lt;br /&gt;
**[[Lorentz Force]]&lt;br /&gt;
**[[Biot-Savart Law]]&lt;br /&gt;
**[[Biot-Savart Law for Currents]]&lt;br /&gt;
**[[Integration Techniques for Magnetic Field]]&lt;br /&gt;
**[[Sparks in Air]]&lt;br /&gt;
**[[Motional Emf]]&lt;br /&gt;
**[[Detecting a Magnetic Field]]&lt;br /&gt;
**[[Moving Point Charge]]&lt;br /&gt;
**[[Non-Coulomb Electric Field]]&lt;br /&gt;
**[[Electric Motors]]&lt;br /&gt;
**[[Solenoid Applications]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Simple Circuits===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[Components]]&lt;br /&gt;
*[[Steady State]]&lt;br /&gt;
*[[Non Steady State]]&lt;br /&gt;
*[[Charging and Discharging a Capacitor]]&lt;br /&gt;
*[[Work and Power In A Circuit]]&lt;br /&gt;
*[[Thin and Thick Wires]]&lt;br /&gt;
*[[Node Rule]]&lt;br /&gt;
*[[Loop Rule]]&lt;br /&gt;
*[[Resistivity]]&lt;br /&gt;
*[[Power in a circuit]]&lt;br /&gt;
*[[Ammeters,Voltmeters,Ohmmeters]]&lt;br /&gt;
*[[Current]]&lt;br /&gt;
**[[AC]]&lt;br /&gt;
*[[Ohm&#039;s Law]]&lt;br /&gt;
*[[Series Circuits]]&lt;br /&gt;
*[[Parallel Circuits]]&lt;br /&gt;
*[[RC]]&lt;br /&gt;
*[[Parallel Circuits vs. Series Circuits]]&lt;br /&gt;
*[[AC vs DC]]&lt;br /&gt;
**[[Rectification (Converting AC to DC)]]&lt;br /&gt;
*[[Charge in a RC Circuit]]&lt;br /&gt;
*[[Current in a RC circuit]]&lt;br /&gt;
*[[Circular Loop of Wire]]&lt;br /&gt;
*[[Current in a RL Circuit]]&lt;br /&gt;
*[[RL Circuit]]&lt;br /&gt;
*[[Feedback]]&lt;br /&gt;
*[[Transformers (Circuits)]]&lt;br /&gt;
*[[Resistors and Conductivity]]&lt;br /&gt;
*[[Semiconductor Devices]]&lt;br /&gt;
*[[Insulators]]&lt;br /&gt;
*[[Voltage]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Maxwell&#039;s Equations===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[Gauss&#039;s Flux Theorem]]&lt;br /&gt;
**[[Electric Fields]]&lt;br /&gt;
***[[Examples of Flux Through Surfaces and Objects]]&lt;br /&gt;
**[[Magnetic Fields]]&lt;br /&gt;
**[[Proof of Gauss&#039;s Law]]&lt;br /&gt;
*[[Ampere&#039;s Law]]&lt;br /&gt;
**[[Magnetic Field of Coaxial Cable Using Ampere&#039;s Law]]&lt;br /&gt;
**[[Magnetic Field of a Long Thick Wire Using Ampere&#039;s Law]]&lt;br /&gt;
**[[Magnetic Field of a Toroid Using Ampere&#039;s Law]]&lt;br /&gt;
*[[Faraday&#039;s Law]]&lt;br /&gt;
**[[Curly Electric Fields]]&lt;br /&gt;
**[[Inductance]]&lt;br /&gt;
***[[Transformers (Physics)]]&lt;br /&gt;
***[[Energy Density]]&lt;br /&gt;
**[[Lenz&#039;s Law]]&lt;br /&gt;
***[[Lenz Effect and the Jumping Ring]]&lt;br /&gt;
**[[Lenz&#039;s Rule]]&lt;br /&gt;
**[[Motional Emf using Faraday&#039;s Law]]&lt;br /&gt;
*[[Ampere-Maxwell Law]]&lt;br /&gt;
*[[Superconductors]]&lt;br /&gt;
**[[Meissner effect]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Radiation===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[Producing a Radiative Electric Field]]&lt;br /&gt;
*[[Sinusoidal Electromagnetic Radiaton]]&lt;br /&gt;
*[[Lenses]]&lt;br /&gt;
*[[Energy and Momentum Analysis in Radiation]]&lt;br /&gt;
**[[Poynting Vector]]&lt;br /&gt;
*[[Electromagnetic Propagation]]&lt;br /&gt;
**[[Wavelength and Frequency]]&lt;br /&gt;
*[[Snell&#039;s Law]]&lt;br /&gt;
*[[Effects of Radiation on Matter]]&lt;br /&gt;
*[[Light Propagation Through a Medium]]&lt;br /&gt;
*[[Light Scaterring: Why is the Sky Blue]]&lt;br /&gt;
*[[Light Refraction: Bending of light]]&lt;br /&gt;
*[[Cherenkov Radiation]]&lt;br /&gt;
*[[Rayleigh Effect]]&lt;br /&gt;
*[[Image Formation]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Sound===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[Doppler Effect]]&lt;br /&gt;
*[[Nature, Behavior, and Properties of Sound]]&lt;br /&gt;
*[[Speed of Sound]]&lt;br /&gt;
*[[Resonance]]&lt;br /&gt;
*[[Sound Barrier]]&lt;br /&gt;
*[[Sound Rarefaction]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Waves===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[Bragg&#039;s Law]]&lt;br /&gt;
*[[Standing waves]]&lt;br /&gt;
*[[Gravitational waves]]&lt;br /&gt;
*[[Plasma waves]]&lt;br /&gt;
*[[Wave-Particle Duality]]&lt;br /&gt;
*[[Electromagnetic Spectrum]]&lt;br /&gt;
*[[Color Light Wave]]&lt;br /&gt;
*[[The Wave Equation]]&lt;br /&gt;
*[[Pendulum Motion]]&lt;br /&gt;
*[[Transverse and Longitudinal Waves]]&lt;br /&gt;
*[[Planck&#039;s Relation]]&lt;br /&gt;
*[[interference]]&lt;br /&gt;
*[[Polarization of Waves]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Real Life Applications of Electromagnetic Principles===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[Electromagnetic Junkyard Cranes]]&lt;br /&gt;
*[[Maglev Trains]]&lt;br /&gt;
*[[Spark Plugs]]&lt;br /&gt;
*[[Metal Detectors]]&lt;br /&gt;
*[[Speakers]]&lt;br /&gt;
*[[Radios]]&lt;br /&gt;
*[[Ampullae of Lorenzini]]&lt;br /&gt;
*[[Electrocytes]]&lt;br /&gt;
*[[Generator]]&lt;br /&gt;
*[[Using Capacitors to Measure Fluid Level]]&lt;br /&gt;
*[[Cyclotron]]&lt;br /&gt;
*[[Railgun]]&lt;br /&gt;
*[[Magnetic Resonance Imaging]]&lt;br /&gt;
*[[Electric Eels]]&lt;br /&gt;
*[[Windshield Wipers]]&lt;br /&gt;
*[[Galvanic Cells]]&lt;br /&gt;
*[[Magnetoreception]]&lt;br /&gt;
*[[Memory Storage Devices]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Optics===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[Mirrors]]&lt;br /&gt;
*[[Refraction]]&lt;br /&gt;
*[[Quantum Properties of Light]]&lt;br /&gt;
*[[Lasers]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
== Resources ==&lt;br /&gt;
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]&lt;br /&gt;
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]&lt;br /&gt;
* A page to keep track of all the physics [[Constants]]&lt;br /&gt;
* A page for review of [[Vectors]] and vector operations&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Main_Page&amp;diff=13281</id>
		<title>Main Page</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Main_Page&amp;diff=13281"/>
		<updated>2015-12-05T03:41:09Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* Collisions */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;__NOTOC__&lt;br /&gt;
Welcome to the Georgia Tech Wiki for Intro Physics.  This resources was created so that students can contribute and curate content to help those with limited or no access to a textbook.  When reading this website, please correct any errors you may come across. If you read something that isn&#039;t clear, please consider revising it!&lt;br /&gt;
&lt;br /&gt;
Looking to make a contribution?&lt;br /&gt;
#Pick a specific topic from intro physics&lt;br /&gt;
#Add that topic, as a link to a new page, under the appropriate category listed below by editing this page.&lt;br /&gt;
#Copy and paste the default [[Template]] into your new page and start editing.&lt;br /&gt;
&lt;br /&gt;
Please remember that this is not a textbook and you are not limited to expressing your ideas with only text and equations.  Whenever possible embed: pictures, videos, diagrams, simulations, computational models (e.g. Glowscript), and whatever content you think makes learning physics easier for other students.&lt;br /&gt;
&lt;br /&gt;
== Source Material ==&lt;br /&gt;
All of the content added to this resource must be in the public domain or similar free resource.  If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web.  Here is an incomplete list of intro physics resources (please update as needed).&lt;br /&gt;
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]&lt;br /&gt;
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]&lt;br /&gt;
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]&lt;br /&gt;
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]&lt;br /&gt;
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]&lt;br /&gt;
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]&lt;br /&gt;
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]&lt;br /&gt;
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]&lt;br /&gt;
&lt;br /&gt;
== Organizing Categories ==&lt;br /&gt;
These are the broad, overarching categories, that we cover in two semester of introductory physics.  You can add subcategories or make a new category as needed.  A single topic should direct readers to a page in one of these catagories.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
===Interactions===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[Kinds of Matter]]&lt;br /&gt;
**[[Ball and Spring Model of Matter]]&lt;br /&gt;
*[[Detecting Interactions]]&lt;br /&gt;
*[[Fundamental Interactions]]&lt;br /&gt;
*[[Determinism]]&lt;br /&gt;
*[[System &amp;amp; Surroundings]] &lt;br /&gt;
*[[Free Body Diagram]]&lt;br /&gt;
*[[Newton&#039;s First Law of Motion]]&lt;br /&gt;
*[[Newton&#039;s Second Law of Motion]]&lt;br /&gt;
*[[Newton&#039;s Third Law of Motion]]&lt;br /&gt;
*[[Gravitational Force]]&lt;br /&gt;
*[[Electric Force]]&lt;br /&gt;
*[[Conservation of Energy]]&lt;br /&gt;
*[[Conservation of Charge]]&lt;br /&gt;
*[[Terminal Speed]]&lt;br /&gt;
*[[Simple Harmonic Motion]]&lt;br /&gt;
*[[Speed and Velocity]]&lt;br /&gt;
*[[Electric Polarization]]&lt;br /&gt;
*[[Perpetual Freefall (Orbit)]]&lt;br /&gt;
*[[2-Dimensional Motion]]&lt;br /&gt;
*[[Center of Mass]]&lt;br /&gt;
*[[Reaction Time]]&lt;br /&gt;
*[[Time Dilation]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Modeling with VPython===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[VPython]]&lt;br /&gt;
*[[VPython basics]]&lt;br /&gt;
*[[VPython Common Errors and Troubleshooting]]&lt;br /&gt;
*[[VPython Functions]]&lt;br /&gt;
*[[VPython Lists]]&lt;br /&gt;
*[[VPython Multithreading]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Theory===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[Einstein&#039;s Theory of Special Relativity]]&lt;br /&gt;
*[[Einstein&#039;s Theory of General Relativity]]&lt;br /&gt;
*[[Quantum Theory]]&lt;br /&gt;
*[[Maxwell&#039;s Electromagnetic Theory]]&lt;br /&gt;
*[[Atomic Theory]]&lt;br /&gt;
*[[String Theory]]&lt;br /&gt;
*[[Elementary Particles and Particle Physics Theory]]&lt;br /&gt;
*[[Law of Gravitation]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Notable Scientists===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[Alexei Alexeyevich Abrikosov]]&lt;br /&gt;
*[[Christian Doppler]]&lt;br /&gt;
*[[Albert Einstein]]&lt;br /&gt;
*[[Ernest Rutherford]]&lt;br /&gt;
*[[Joseph Henry]]&lt;br /&gt;
*[[Michael Faraday]]&lt;br /&gt;
*[[J.J. Thomson]]&lt;br /&gt;
*[[James Maxwell]]&lt;br /&gt;
*[[Robert Hooke]]&lt;br /&gt;
*[[Carl Friedrich Gauss]]&lt;br /&gt;
*[[Nikola Tesla]]&lt;br /&gt;
*[[Andre Marie Ampere]]&lt;br /&gt;
*[[Sir Isaac Newton]]&lt;br /&gt;
*[[J. Robert Oppenheimer]]&lt;br /&gt;
*[[Oliver Heaviside]]&lt;br /&gt;
*[[Rosalind Franklin]]&lt;br /&gt;
*[[Erwin Schrödinger]]&lt;br /&gt;
*[[Enrico Fermi]]&lt;br /&gt;
*[[Robert J. Van de Graaff]]&lt;br /&gt;
*[[Charles de Coulomb]]&lt;br /&gt;
*[[Hans Christian Ørsted]]&lt;br /&gt;
*[[Philo Farnsworth]]&lt;br /&gt;
*[[Niels Bohr]]&lt;br /&gt;
*[[Georg Ohm]]&lt;br /&gt;
*[[Galileo Galilei]]&lt;br /&gt;
*[[Gustav Kirchhoff]]&lt;br /&gt;
*[[Max Planck]]&lt;br /&gt;
*[[Heinrich Hertz]]&lt;br /&gt;
*[[Edwin Hall]]&lt;br /&gt;
*[[James Watt]]&lt;br /&gt;
*[[Count Alessandro Volta]]&lt;br /&gt;
*[[Josiah Willard Gibbs]]&lt;br /&gt;
*[[Richard Phillips Feynman]]&lt;br /&gt;
*[[Sir David Brewster]]&lt;br /&gt;
*[[Daniel Bernoulli]]&lt;br /&gt;
*[[William Thomson]]&lt;br /&gt;
*[[Leonhard Euler]]&lt;br /&gt;
*[[Robert Fox Bacher]]&lt;br /&gt;
*[[Stephen Hawking]]&lt;br /&gt;
*[[Amedeo Avogadro]]&lt;br /&gt;
*[[Wilhelm Conrad Roentgen]]&lt;br /&gt;
*[[Pierre Laplace]]&lt;br /&gt;
*[[Thomas Edison]]&lt;br /&gt;
*[[Hendrik Lorentz]]&lt;br /&gt;
*[[Jean-Baptiste Biot]]&lt;br /&gt;
*[[Lise Meitner]]&lt;br /&gt;
*[[Lisa Randall]]&lt;br /&gt;
*[[Felix Savart]]&lt;br /&gt;
*[[Heinrich Lenz]]&lt;br /&gt;
*[[Max Born]]&lt;br /&gt;
*[[Archimedes]]&lt;br /&gt;
*[[Jean Baptiste Biot]]&lt;br /&gt;
*[[Carl Sagan]]&lt;br /&gt;
*[[Eugene Wigner]]&lt;br /&gt;
*[[Marie Curie]]&lt;br /&gt;
*[[Pierre Curie]]&lt;br /&gt;
*[[Werner Heisenberg]]&lt;br /&gt;
*[[Johannes Diderik van der Waals]]&lt;br /&gt;
*[[Louis de Broglie]]&lt;br /&gt;
*[[Aristotle]]&lt;br /&gt;
*[[Émilie du Châtelet]]&lt;br /&gt;
*[[Blaise Pascal]]&lt;br /&gt;
*[[Benjamin Franklin]]&lt;br /&gt;
*[[James Chadwick]]&lt;br /&gt;
*[[Henry Cavendish]]&lt;br /&gt;
*[[Thomas Young]]&lt;br /&gt;
*[[James Prescott Joule]]&lt;br /&gt;
*[[John Bardeen]]&lt;br /&gt;
*[[Leo Baekeland]]&lt;br /&gt;
*[[Alhazen]]&lt;br /&gt;
*[[Willebrod Snell]]&lt;br /&gt;
*[[Fritz Walther Meissner]]&lt;br /&gt;
*[[Johannes Kepler]]&lt;br /&gt;
*[[Johann Wilhelm Ritter]]&lt;br /&gt;
*[[Philipp Lenard]]&lt;br /&gt;
*[[Robert A. Millikan]]&lt;br /&gt;
*[[Joseph Louis Gay-Lussac]]&lt;br /&gt;
*[[Guglielmo Marconi]]&lt;br /&gt;
*[[William Lawrence Bragg]]&lt;br /&gt;
*[[Robert Goddard]]&lt;br /&gt;
*[[Léon Foucault]]&lt;br /&gt;
*[[Henri Poincaré]]&lt;br /&gt;
*[[Steven Weinberg]]&lt;br /&gt;
*[[Arthur Compton]]&lt;br /&gt;
*[[Pythagoras of Samos]]&lt;br /&gt;
*[[Subrahmanyan Chandrasekhar]]&lt;br /&gt;
*[[Wilhelm Eduard Weber]]&lt;br /&gt;
*[[Edmond Becquerel]]&lt;br /&gt;
*[[Joseph Rotblat]]&lt;br /&gt;
*[[Carl David Anderson]]&lt;br /&gt;
*[[Hermann von Helmholtz]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Properties of Matter===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[Mass]]&lt;br /&gt;
*[[Velocity]]&lt;br /&gt;
*[[Relative Velocity]]&lt;br /&gt;
*[[Density]]&lt;br /&gt;
*[[Charge]]&lt;br /&gt;
*[[Spin]]&lt;br /&gt;
*[[SI Units]]&lt;br /&gt;
*[[Heat Capacity]]&lt;br /&gt;
*[[Specific Heat]]&lt;br /&gt;
*[[Wavelength]]&lt;br /&gt;
*[[Conductivity]]&lt;br /&gt;
*[[Malleability]]&lt;br /&gt;
*[[Weight]]&lt;br /&gt;
*[[Boiling Point]]&lt;br /&gt;
*[[Melting Point]]&lt;br /&gt;
*[[Inertia]]&lt;br /&gt;
*[[Non-Newtonian Fluids]]&lt;br /&gt;
*[[Color]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Contact Interactions===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
* [[Young&#039;s Modulus]]&lt;br /&gt;
* [[Friction]]&lt;br /&gt;
* [[Tension]]&lt;br /&gt;
* [[Hooke&#039;s Law]]&lt;br /&gt;
*[[Centripetal Force and Curving Motion]]&lt;br /&gt;
*[[Compression or Normal Force]]&lt;br /&gt;
* [[Length and Stiffness of an Interatomic Bond]]&lt;br /&gt;
* [[Speed of Sound in a Solid]]&lt;br /&gt;
* [[Iterative Prediction of Spring-Mass System]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Momentum===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
* [[Vectors]]&lt;br /&gt;
* [[Kinematics]]&lt;br /&gt;
* [[Conservation of Momentum]]&lt;br /&gt;
* [[Predicting Change in multiple dimensions]]&lt;br /&gt;
* [[Derivation of the Momentum Principle]]&lt;br /&gt;
* [[Momentum Principle]]&lt;br /&gt;
* [[Impulse Momentum]]&lt;br /&gt;
* [[Curving Motion]]&lt;br /&gt;
* [[Projectile Motion]]&lt;br /&gt;
* [[Multi-particle Analysis of Momentum]]&lt;br /&gt;
* [[Iterative Prediction]]&lt;br /&gt;
* [[Analytical Prediction]]&lt;br /&gt;
* [[Newton&#039;s Laws and Linear Momentum]]&lt;br /&gt;
* [[Net Force]]&lt;br /&gt;
* [[Center of Mass]]&lt;br /&gt;
* [[Momentum at High Speeds]]&lt;br /&gt;
* [[Change in Momentum in Time for Curving Motion]]&lt;br /&gt;
* [[Momentum with respect to external Forces]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Angular Momentum===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
* [[The Moments of Inertia]]&lt;br /&gt;
* [[Moment of Inertia for a ring]]&lt;br /&gt;
* [[Rotation]]&lt;br /&gt;
* [[Torque]]&lt;br /&gt;
* [[Systems with Zero Torque]]&lt;br /&gt;
* [[Systems with Nonzero Torque]]&lt;br /&gt;
* [[Angular Impulse &amp;amp; Torque vs Energy]]&lt;br /&gt;
* [[Right Hand Rule]]&lt;br /&gt;
* [[Angular Velocity]]&lt;br /&gt;
* [[Predicting the Position of a Rotating System]]&lt;br /&gt;
* [[Translational Angular Momentum]]&lt;br /&gt;
* [[The Angular Momentum Principle]]&lt;br /&gt;
* [[Angular Momentum of Multiparticle Systems]]&lt;br /&gt;
* [[Rotational Angular Momentum]]&lt;br /&gt;
* [[Total Angular Momentum]]&lt;br /&gt;
* [[Gyroscopes]]&lt;br /&gt;
* [[Angular Momentum Compared to Linear Momentum]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Energy===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[The Photoelectric Effect]]&lt;br /&gt;
*[[Photons]]&lt;br /&gt;
*[[The Energy Principle]]&lt;br /&gt;
*[[Predicting Change]]&lt;br /&gt;
*[[Rest Mass Energy]]&lt;br /&gt;
*[[Kinetic Energy]]&lt;br /&gt;
*[[Potential Energy]]&lt;br /&gt;
**[[Potential Energy for a Magnetic Dipole]]&lt;br /&gt;
**[[Potential Energy of a Multiparticle System]]&lt;br /&gt;
*[[Work]]&lt;br /&gt;
**[[Work Done By A Nonconstant Force]]&lt;br /&gt;
*[[Work and Energy for an Extended System]]&lt;br /&gt;
*[[Thermal Energy]]&lt;br /&gt;
*[[Conservation of Energy]]&lt;br /&gt;
*[[Electric Potential]]&lt;br /&gt;
*[[Energy Transfer due to a Temperature Difference]]&lt;br /&gt;
*[[Gravitational Potential Energy]]&lt;br /&gt;
*[[Point Particle Systems]]&lt;br /&gt;
*[[Real Systems]]&lt;br /&gt;
*[[Spring Potential Energy]]&lt;br /&gt;
**[[Ball and Spring Model]]&lt;br /&gt;
*[[Internal Energy]]&lt;br /&gt;
**[[Potential Energy of a Pair of Neutral Atoms]]&lt;br /&gt;
*[[Translational, Rotational and Vibrational Energy]]&lt;br /&gt;
*[[Franck-Hertz Experiment]]&lt;br /&gt;
*[[Power (Mechanical)]]&lt;br /&gt;
*[[Transformation of Energy]]&lt;br /&gt;
&lt;br /&gt;
*[[Energy Graphs]]&lt;br /&gt;
**[[Energy graphs and the Bohr model]]&lt;br /&gt;
*[[Air Resistance]]&lt;br /&gt;
*[[Electronic Energy Levels]]&lt;br /&gt;
*[[Second Law of Thermodynamics and Entropy]]&lt;br /&gt;
*[[Specific Heat Capacity]]&lt;br /&gt;
*[[The Maxwell-Boltzmann Distribution]]&lt;br /&gt;
*[[Electronic Energy Levels and Photons]]&lt;br /&gt;
*[[Energy Density]]&lt;br /&gt;
*[[Bohr Model]]&lt;br /&gt;
*[[Quantized energy levels]]&lt;br /&gt;
**[[Spontaneous Photon Emission]]&lt;br /&gt;
*[[Path Independence of Electric Potential]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Collisions===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[Collisions]] &lt;br /&gt;
Collisions are events that happen very frequently in our day-to-day world. In the realm of Physics, a collision is defined as any sort of process in which before and after a short time interval there is little interaction, but during that short time interval there are large interactions. When looking at collisions, it is first important to understand two very important principles: the Momentum Principle and the Energy Principle. Both principles serve use when talking of collisions because they provide a way in which to analyze these collisions. Collisions themselves can be categorized into 3 main different types: elastic collisions, inelastic collisions, maximally inelastic collisions. All 3 collisions will get touched on in more detail further on. &lt;br /&gt;
*[[Elastic Collisions]]&lt;br /&gt;
A collision is deemed &amp;quot;elastic&amp;quot; when the internal energy of the objects in the system does not change (in other words, change in internal energy equals 0). Because in an elastic collision no kinetic energy is converted over to internal energy, in any elastic collision Kfinal always equals Kinitial.&lt;br /&gt;
*[[Inelastic Collisions]]&lt;br /&gt;
A collision is said to be &amp;quot;inelastic&amp;quot; when it is not elastic; therefore, an inelastic collision is an interaction in which some change in internal energy occurs between the colliding objects (in other words, change in internal energy does not equal 0). Examples of such changes that occur between colliding objects include, but are not limited to, things like they get hot, or they vibrate/rotate, or they deform. Because some of the kinetic energy is converted to internal energy during an inelastic collision, Kfinal does not equal Kinitial.&lt;br /&gt;
*[[Maximally Inelastic Collision]] &lt;br /&gt;
*[[Head-on Collision of Equal Masses]]&lt;br /&gt;
*[[Head-on Collision of Unequal Masses]]&lt;br /&gt;
*[[Frame of Reference]]&lt;br /&gt;
*[[Scattering: Collisions in 2D and 3D]]&lt;br /&gt;
*[[Rutherford Experiment and Atomic Collisions]]&lt;br /&gt;
*[[Coefficient of Restitution]]&lt;br /&gt;
*[[testing123]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Fields===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
* [[Electric Field]] of a&lt;br /&gt;
** [[Point Charge]]&lt;br /&gt;
** [[Electric Dipole]]&lt;br /&gt;
** [[Capacitor]]&lt;br /&gt;
** [[Charged Rod]]&lt;br /&gt;
** [[Charged Ring]]&lt;br /&gt;
** [[Charged Disk]]&lt;br /&gt;
** [[Charged Spherical Shell]]&lt;br /&gt;
** [[Charged Cylinder]]&lt;br /&gt;
** [[Charge Density]]&lt;br /&gt;
**[[A Solid Sphere Charged Throughout Its Volume]]&lt;br /&gt;
*[[Electric Potential]] &lt;br /&gt;
**[[Potential Difference Path Independence]]&lt;br /&gt;
**[[Potential Difference in a Uniform Field]]&lt;br /&gt;
**[[Potential Difference of point charge in a non-Uniform Field]]&lt;br /&gt;
**[[Sign of Potential Difference]]&lt;br /&gt;
**[[Potential Difference in an Insulator]]&lt;br /&gt;
**[[Energy Density and Electric Field]]&lt;br /&gt;
** [[Systems of Charged Objects]]&lt;br /&gt;
*[[Electric Force]]&lt;br /&gt;
*[[Polarization]]&lt;br /&gt;
**[[Polarization of an Atom]]&lt;br /&gt;
*[[Charge Motion in Metals]]&lt;br /&gt;
*[[Charge Transfer]]&lt;br /&gt;
*[[Magnetic Field]]&lt;br /&gt;
**[[Right-Hand Rule]]&lt;br /&gt;
**[[Direction of Magnetic Field]]&lt;br /&gt;
**[[Magnetic Field of a Long Straight Wire]]&lt;br /&gt;
**[[Magnetic Field of a Loop]]&lt;br /&gt;
**[[Magnetic Field of a Solenoid]]&lt;br /&gt;
**[[Bar Magnet]]&lt;br /&gt;
**[[Magnetic Dipole Moment]]&lt;br /&gt;
***[[Stern-Gerlach Experiment]]&lt;br /&gt;
**[[Magnetic Torque]]&lt;br /&gt;
**[[Magnetic Force]]&lt;br /&gt;
**[[Earth&#039;s Magnetic Field]]&lt;br /&gt;
**[[Atomic Structure of Magnets]]&lt;br /&gt;
*[[Combining Electric and Magnetic Forces]]&lt;br /&gt;
**[[Hall Effect]]&lt;br /&gt;
**[[Lorentz Force]]&lt;br /&gt;
**[[Biot-Savart Law]]&lt;br /&gt;
**[[Biot-Savart Law for Currents]]&lt;br /&gt;
**[[Integration Techniques for Magnetic Field]]&lt;br /&gt;
**[[Sparks in Air]]&lt;br /&gt;
**[[Motional Emf]]&lt;br /&gt;
**[[Detecting a Magnetic Field]]&lt;br /&gt;
**[[Moving Point Charge]]&lt;br /&gt;
**[[Non-Coulomb Electric Field]]&lt;br /&gt;
**[[Motors and Generators]]&lt;br /&gt;
**[[Solenoid Applications]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Simple Circuits===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[Components]]&lt;br /&gt;
*[[Steady State]]&lt;br /&gt;
*[[Non Steady State]]&lt;br /&gt;
*[[Charging and Discharging a Capacitor]]&lt;br /&gt;
*[[Thin and Thick Wires]]&lt;br /&gt;
*[[Node Rule]]&lt;br /&gt;
*[[Loop Rule]]&lt;br /&gt;
*[[Resistivity]]&lt;br /&gt;
*[[Power in a circuit]]&lt;br /&gt;
*[[Ammeters,Voltmeters,Ohmmeters]]&lt;br /&gt;
*[[Current]]&lt;br /&gt;
**[[AC]]&lt;br /&gt;
*[[Ohm&#039;s Law]]&lt;br /&gt;
*[[Series Circuits]]&lt;br /&gt;
*[[Parallel Circuits]]&lt;br /&gt;
*[[RC]]&lt;br /&gt;
*[[AC vs DC]]&lt;br /&gt;
*[[Charge in a RC Circuit]]&lt;br /&gt;
*[[Current in a RC circuit]]&lt;br /&gt;
*[[Circular Loop of Wire]]&lt;br /&gt;
*[[Current in a RL Circuit]]&lt;br /&gt;
*[[RL Circuit]]&lt;br /&gt;
*[[Surface Charge Distributions]]&lt;br /&gt;
*[[Feedback]]&lt;br /&gt;
*[[Transformers (Circuits)]]&lt;br /&gt;
*[[Resistors and Conductivity]]&lt;br /&gt;
*[[Semiconductor Devices]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Maxwell&#039;s Equations===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[Gauss&#039;s Flux Theorem]]&lt;br /&gt;
**[[Electric Fields]]&lt;br /&gt;
***[[Examples of Flux Through Surfaces and Objects]]&lt;br /&gt;
**[[Magnetic Fields]]&lt;br /&gt;
*[[Ampere&#039;s Law]]&lt;br /&gt;
**[[Magnetic Field of Coaxial Cable Using Ampere&#039;s Law]]&lt;br /&gt;
**[[Magnetic Field of a Long Thick Wire Using Ampere&#039;s Law]]&lt;br /&gt;
**[[Magnetic Field of a Toroid Using Ampere&#039;s Law]]&lt;br /&gt;
*[[Faraday&#039;s Law]]&lt;br /&gt;
**[[Curly Electric Fields]]&lt;br /&gt;
**[[Inductance]]&lt;br /&gt;
***[[Transformers (Physics)]]&lt;br /&gt;
***[[Energy Density]]&lt;br /&gt;
**[[Lenz&#039;s Law]]&lt;br /&gt;
***[[Lenz Effect and the Jumping Ring]]&lt;br /&gt;
**[[Lenz&#039;s Rule]]&lt;br /&gt;
**[[Motional Emf using Faraday&#039;s Law]]&lt;br /&gt;
*[[Ampere-Maxwell Law]]&lt;br /&gt;
*[[Superconductors]]&lt;br /&gt;
**[[Meissner effect]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Radiation===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[Producing a Radiative Electric Field]]&lt;br /&gt;
*[[Sinusoidal Electromagnetic Radiaton]]&lt;br /&gt;
*[[Lenses]]&lt;br /&gt;
*[[Energy and Momentum Analysis in Radiation]]&lt;br /&gt;
**[[Poynting Vector]]&lt;br /&gt;
*[[Electromagnetic Propagation]]&lt;br /&gt;
**[[Wavelength and Frequency]]&lt;br /&gt;
*[[Snell&#039;s Law]]&lt;br /&gt;
*[[Effects of Radiation on Matter]]&lt;br /&gt;
*[[Light Propagation Through a Medium]]&lt;br /&gt;
*[[Light Scaterring: Why is the Sky Blue]]&lt;br /&gt;
*[[Light Refraction: Bending of light]]&lt;br /&gt;
*[[Cherenkov Radiation]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Sound===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[Doppler Effect]]&lt;br /&gt;
*[[Nature, Behavior, and Properties of Sound]]&lt;br /&gt;
*[[Resonance]]&lt;br /&gt;
*[[Sound Barrier]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Waves===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[Bragg&#039;s Law]]&lt;br /&gt;
*[[Multisource Interference: Diffraction]]&lt;br /&gt;
*[[Standing waves]]&lt;br /&gt;
*[[Gravitational waves]]&lt;br /&gt;
*[[Plasma waves]]&lt;br /&gt;
*[[Wave-Particle Duality]]&lt;br /&gt;
*[[Electromagnetic Waves]]&lt;br /&gt;
*[[Electromagnetic Spectrum]]&lt;br /&gt;
*[[Color Light Wave]]&lt;br /&gt;
*[[Mechanical Waves]]&lt;br /&gt;
*[[Pendulum Motion]]&lt;br /&gt;
*[[Transverse and Longitudinal Waves]]&lt;br /&gt;
*[[Planck&#039;s Relation]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Real Life Applications of Electromagnetic Principles===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[Electromagnetic Junkyard Cranes]]&lt;br /&gt;
*[[Maglev Trains]]&lt;br /&gt;
*[[Spark Plugs]]&lt;br /&gt;
*[[Metal Detectors]]&lt;br /&gt;
*[[Speakers]]&lt;br /&gt;
*[[Radios]]&lt;br /&gt;
*[[Ampullae of Lorenzini]]&lt;br /&gt;
*[[Electrocytes]]&lt;br /&gt;
*[[Generator]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Optics===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[Mirrors]]&lt;br /&gt;
*[[Refraction]]&lt;br /&gt;
*[[Quantum Properties of Light]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
== Resources ==&lt;br /&gt;
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]&lt;br /&gt;
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]&lt;br /&gt;
* A page to keep track of all the physics [[Constants]]&lt;br /&gt;
* A page for review of [[Vectors]] and vector operations&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Main_Page&amp;diff=13279</id>
		<title>Main Page</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Main_Page&amp;diff=13279"/>
		<updated>2015-12-05T03:40:48Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* Collisions */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;__NOTOC__&lt;br /&gt;
Welcome to the Georgia Tech Wiki for Intro Physics.  This resources was created so that students can contribute and curate content to help those with limited or no access to a textbook.  When reading this website, please correct any errors you may come across. If you read something that isn&#039;t clear, please consider revising it!&lt;br /&gt;
&lt;br /&gt;
Looking to make a contribution?&lt;br /&gt;
#Pick a specific topic from intro physics&lt;br /&gt;
#Add that topic, as a link to a new page, under the appropriate category listed below by editing this page.&lt;br /&gt;
#Copy and paste the default [[Template]] into your new page and start editing.&lt;br /&gt;
&lt;br /&gt;
Please remember that this is not a textbook and you are not limited to expressing your ideas with only text and equations.  Whenever possible embed: pictures, videos, diagrams, simulations, computational models (e.g. Glowscript), and whatever content you think makes learning physics easier for other students.&lt;br /&gt;
&lt;br /&gt;
== Source Material ==&lt;br /&gt;
All of the content added to this resource must be in the public domain or similar free resource.  If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web.  Here is an incomplete list of intro physics resources (please update as needed).&lt;br /&gt;
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]&lt;br /&gt;
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]&lt;br /&gt;
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]&lt;br /&gt;
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]&lt;br /&gt;
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]&lt;br /&gt;
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]&lt;br /&gt;
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]&lt;br /&gt;
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]&lt;br /&gt;
&lt;br /&gt;
== Organizing Categories ==&lt;br /&gt;
These are the broad, overarching categories, that we cover in two semester of introductory physics.  You can add subcategories or make a new category as needed.  A single topic should direct readers to a page in one of these catagories.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
===Interactions===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[Kinds of Matter]]&lt;br /&gt;
**[[Ball and Spring Model of Matter]]&lt;br /&gt;
*[[Detecting Interactions]]&lt;br /&gt;
*[[Fundamental Interactions]]&lt;br /&gt;
*[[Determinism]]&lt;br /&gt;
*[[System &amp;amp; Surroundings]] &lt;br /&gt;
*[[Free Body Diagram]]&lt;br /&gt;
*[[Newton&#039;s First Law of Motion]]&lt;br /&gt;
*[[Newton&#039;s Second Law of Motion]]&lt;br /&gt;
*[[Newton&#039;s Third Law of Motion]]&lt;br /&gt;
*[[Gravitational Force]]&lt;br /&gt;
*[[Electric Force]]&lt;br /&gt;
*[[Conservation of Energy]]&lt;br /&gt;
*[[Conservation of Charge]]&lt;br /&gt;
*[[Terminal Speed]]&lt;br /&gt;
*[[Simple Harmonic Motion]]&lt;br /&gt;
*[[Speed and Velocity]]&lt;br /&gt;
*[[Electric Polarization]]&lt;br /&gt;
*[[Perpetual Freefall (Orbit)]]&lt;br /&gt;
*[[2-Dimensional Motion]]&lt;br /&gt;
*[[Center of Mass]]&lt;br /&gt;
*[[Reaction Time]]&lt;br /&gt;
*[[Time Dilation]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Modeling with VPython===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[VPython]]&lt;br /&gt;
*[[VPython basics]]&lt;br /&gt;
*[[VPython Common Errors and Troubleshooting]]&lt;br /&gt;
*[[VPython Functions]]&lt;br /&gt;
*[[VPython Lists]]&lt;br /&gt;
*[[VPython Multithreading]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Theory===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[Einstein&#039;s Theory of Special Relativity]]&lt;br /&gt;
*[[Einstein&#039;s Theory of General Relativity]]&lt;br /&gt;
*[[Quantum Theory]]&lt;br /&gt;
*[[Maxwell&#039;s Electromagnetic Theory]]&lt;br /&gt;
*[[Atomic Theory]]&lt;br /&gt;
*[[String Theory]]&lt;br /&gt;
*[[Elementary Particles and Particle Physics Theory]]&lt;br /&gt;
*[[Law of Gravitation]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Notable Scientists===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[Alexei Alexeyevich Abrikosov]]&lt;br /&gt;
*[[Christian Doppler]]&lt;br /&gt;
*[[Albert Einstein]]&lt;br /&gt;
*[[Ernest Rutherford]]&lt;br /&gt;
*[[Joseph Henry]]&lt;br /&gt;
*[[Michael Faraday]]&lt;br /&gt;
*[[J.J. Thomson]]&lt;br /&gt;
*[[James Maxwell]]&lt;br /&gt;
*[[Robert Hooke]]&lt;br /&gt;
*[[Carl Friedrich Gauss]]&lt;br /&gt;
*[[Nikola Tesla]]&lt;br /&gt;
*[[Andre Marie Ampere]]&lt;br /&gt;
*[[Sir Isaac Newton]]&lt;br /&gt;
*[[J. Robert Oppenheimer]]&lt;br /&gt;
*[[Oliver Heaviside]]&lt;br /&gt;
*[[Rosalind Franklin]]&lt;br /&gt;
*[[Erwin Schrödinger]]&lt;br /&gt;
*[[Enrico Fermi]]&lt;br /&gt;
*[[Robert J. Van de Graaff]]&lt;br /&gt;
*[[Charles de Coulomb]]&lt;br /&gt;
*[[Hans Christian Ørsted]]&lt;br /&gt;
*[[Philo Farnsworth]]&lt;br /&gt;
*[[Niels Bohr]]&lt;br /&gt;
*[[Georg Ohm]]&lt;br /&gt;
*[[Galileo Galilei]]&lt;br /&gt;
*[[Gustav Kirchhoff]]&lt;br /&gt;
*[[Max Planck]]&lt;br /&gt;
*[[Heinrich Hertz]]&lt;br /&gt;
*[[Edwin Hall]]&lt;br /&gt;
*[[James Watt]]&lt;br /&gt;
*[[Count Alessandro Volta]]&lt;br /&gt;
*[[Josiah Willard Gibbs]]&lt;br /&gt;
*[[Richard Phillips Feynman]]&lt;br /&gt;
*[[Sir David Brewster]]&lt;br /&gt;
*[[Daniel Bernoulli]]&lt;br /&gt;
*[[William Thomson]]&lt;br /&gt;
*[[Leonhard Euler]]&lt;br /&gt;
*[[Robert Fox Bacher]]&lt;br /&gt;
*[[Stephen Hawking]]&lt;br /&gt;
*[[Amedeo Avogadro]]&lt;br /&gt;
*[[Wilhelm Conrad Roentgen]]&lt;br /&gt;
*[[Pierre Laplace]]&lt;br /&gt;
*[[Thomas Edison]]&lt;br /&gt;
*[[Hendrik Lorentz]]&lt;br /&gt;
*[[Jean-Baptiste Biot]]&lt;br /&gt;
*[[Lise Meitner]]&lt;br /&gt;
*[[Lisa Randall]]&lt;br /&gt;
*[[Felix Savart]]&lt;br /&gt;
*[[Heinrich Lenz]]&lt;br /&gt;
*[[Max Born]]&lt;br /&gt;
*[[Archimedes]]&lt;br /&gt;
*[[Jean Baptiste Biot]]&lt;br /&gt;
*[[Carl Sagan]]&lt;br /&gt;
*[[Eugene Wigner]]&lt;br /&gt;
*[[Marie Curie]]&lt;br /&gt;
*[[Pierre Curie]]&lt;br /&gt;
*[[Werner Heisenberg]]&lt;br /&gt;
*[[Johannes Diderik van der Waals]]&lt;br /&gt;
*[[Louis de Broglie]]&lt;br /&gt;
*[[Aristotle]]&lt;br /&gt;
*[[Émilie du Châtelet]]&lt;br /&gt;
*[[Blaise Pascal]]&lt;br /&gt;
*[[Benjamin Franklin]]&lt;br /&gt;
*[[James Chadwick]]&lt;br /&gt;
*[[Henry Cavendish]]&lt;br /&gt;
*[[Thomas Young]]&lt;br /&gt;
*[[James Prescott Joule]]&lt;br /&gt;
*[[John Bardeen]]&lt;br /&gt;
*[[Leo Baekeland]]&lt;br /&gt;
*[[Alhazen]]&lt;br /&gt;
*[[Willebrod Snell]]&lt;br /&gt;
*[[Fritz Walther Meissner]]&lt;br /&gt;
*[[Johannes Kepler]]&lt;br /&gt;
*[[Johann Wilhelm Ritter]]&lt;br /&gt;
*[[Philipp Lenard]]&lt;br /&gt;
*[[Robert A. Millikan]]&lt;br /&gt;
*[[Joseph Louis Gay-Lussac]]&lt;br /&gt;
*[[Guglielmo Marconi]]&lt;br /&gt;
*[[William Lawrence Bragg]]&lt;br /&gt;
*[[Robert Goddard]]&lt;br /&gt;
*[[Léon Foucault]]&lt;br /&gt;
*[[Henri Poincaré]]&lt;br /&gt;
*[[Steven Weinberg]]&lt;br /&gt;
*[[Arthur Compton]]&lt;br /&gt;
*[[Pythagoras of Samos]]&lt;br /&gt;
*[[Subrahmanyan Chandrasekhar]]&lt;br /&gt;
*[[Wilhelm Eduard Weber]]&lt;br /&gt;
*[[Edmond Becquerel]]&lt;br /&gt;
*[[Joseph Rotblat]]&lt;br /&gt;
*[[Carl David Anderson]]&lt;br /&gt;
*[[Hermann von Helmholtz]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Properties of Matter===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[Mass]]&lt;br /&gt;
*[[Velocity]]&lt;br /&gt;
*[[Relative Velocity]]&lt;br /&gt;
*[[Density]]&lt;br /&gt;
*[[Charge]]&lt;br /&gt;
*[[Spin]]&lt;br /&gt;
*[[SI Units]]&lt;br /&gt;
*[[Heat Capacity]]&lt;br /&gt;
*[[Specific Heat]]&lt;br /&gt;
*[[Wavelength]]&lt;br /&gt;
*[[Conductivity]]&lt;br /&gt;
*[[Malleability]]&lt;br /&gt;
*[[Weight]]&lt;br /&gt;
*[[Boiling Point]]&lt;br /&gt;
*[[Melting Point]]&lt;br /&gt;
*[[Inertia]]&lt;br /&gt;
*[[Non-Newtonian Fluids]]&lt;br /&gt;
*[[Color]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Contact Interactions===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
* [[Young&#039;s Modulus]]&lt;br /&gt;
* [[Friction]]&lt;br /&gt;
* [[Tension]]&lt;br /&gt;
* [[Hooke&#039;s Law]]&lt;br /&gt;
*[[Centripetal Force and Curving Motion]]&lt;br /&gt;
*[[Compression or Normal Force]]&lt;br /&gt;
* [[Length and Stiffness of an Interatomic Bond]]&lt;br /&gt;
* [[Speed of Sound in a Solid]]&lt;br /&gt;
* [[Iterative Prediction of Spring-Mass System]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Momentum===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
* [[Vectors]]&lt;br /&gt;
* [[Kinematics]]&lt;br /&gt;
* [[Conservation of Momentum]]&lt;br /&gt;
* [[Predicting Change in multiple dimensions]]&lt;br /&gt;
* [[Derivation of the Momentum Principle]]&lt;br /&gt;
* [[Momentum Principle]]&lt;br /&gt;
* [[Impulse Momentum]]&lt;br /&gt;
* [[Curving Motion]]&lt;br /&gt;
* [[Projectile Motion]]&lt;br /&gt;
* [[Multi-particle Analysis of Momentum]]&lt;br /&gt;
* [[Iterative Prediction]]&lt;br /&gt;
* [[Analytical Prediction]]&lt;br /&gt;
* [[Newton&#039;s Laws and Linear Momentum]]&lt;br /&gt;
* [[Net Force]]&lt;br /&gt;
* [[Center of Mass]]&lt;br /&gt;
* [[Momentum at High Speeds]]&lt;br /&gt;
* [[Change in Momentum in Time for Curving Motion]]&lt;br /&gt;
* [[Momentum with respect to external Forces]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Angular Momentum===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
* [[The Moments of Inertia]]&lt;br /&gt;
* [[Moment of Inertia for a ring]]&lt;br /&gt;
* [[Rotation]]&lt;br /&gt;
* [[Torque]]&lt;br /&gt;
* [[Systems with Zero Torque]]&lt;br /&gt;
* [[Systems with Nonzero Torque]]&lt;br /&gt;
* [[Angular Impulse &amp;amp; Torque vs Energy]]&lt;br /&gt;
* [[Right Hand Rule]]&lt;br /&gt;
* [[Angular Velocity]]&lt;br /&gt;
* [[Predicting the Position of a Rotating System]]&lt;br /&gt;
* [[Translational Angular Momentum]]&lt;br /&gt;
* [[The Angular Momentum Principle]]&lt;br /&gt;
* [[Angular Momentum of Multiparticle Systems]]&lt;br /&gt;
* [[Rotational Angular Momentum]]&lt;br /&gt;
* [[Total Angular Momentum]]&lt;br /&gt;
* [[Gyroscopes]]&lt;br /&gt;
* [[Angular Momentum Compared to Linear Momentum]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Energy===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[The Photoelectric Effect]]&lt;br /&gt;
*[[Photons]]&lt;br /&gt;
*[[The Energy Principle]]&lt;br /&gt;
*[[Predicting Change]]&lt;br /&gt;
*[[Rest Mass Energy]]&lt;br /&gt;
*[[Kinetic Energy]]&lt;br /&gt;
*[[Potential Energy]]&lt;br /&gt;
**[[Potential Energy for a Magnetic Dipole]]&lt;br /&gt;
**[[Potential Energy of a Multiparticle System]]&lt;br /&gt;
*[[Work]]&lt;br /&gt;
**[[Work Done By A Nonconstant Force]]&lt;br /&gt;
*[[Work and Energy for an Extended System]]&lt;br /&gt;
*[[Thermal Energy]]&lt;br /&gt;
*[[Conservation of Energy]]&lt;br /&gt;
*[[Electric Potential]]&lt;br /&gt;
*[[Energy Transfer due to a Temperature Difference]]&lt;br /&gt;
*[[Gravitational Potential Energy]]&lt;br /&gt;
*[[Point Particle Systems]]&lt;br /&gt;
*[[Real Systems]]&lt;br /&gt;
*[[Spring Potential Energy]]&lt;br /&gt;
**[[Ball and Spring Model]]&lt;br /&gt;
*[[Internal Energy]]&lt;br /&gt;
**[[Potential Energy of a Pair of Neutral Atoms]]&lt;br /&gt;
*[[Translational, Rotational and Vibrational Energy]]&lt;br /&gt;
*[[Franck-Hertz Experiment]]&lt;br /&gt;
*[[Power (Mechanical)]]&lt;br /&gt;
*[[Transformation of Energy]]&lt;br /&gt;
&lt;br /&gt;
*[[Energy Graphs]]&lt;br /&gt;
**[[Energy graphs and the Bohr model]]&lt;br /&gt;
*[[Air Resistance]]&lt;br /&gt;
*[[Electronic Energy Levels]]&lt;br /&gt;
*[[Second Law of Thermodynamics and Entropy]]&lt;br /&gt;
*[[Specific Heat Capacity]]&lt;br /&gt;
*[[The Maxwell-Boltzmann Distribution]]&lt;br /&gt;
*[[Electronic Energy Levels and Photons]]&lt;br /&gt;
*[[Energy Density]]&lt;br /&gt;
*[[Bohr Model]]&lt;br /&gt;
*[[Quantized energy levels]]&lt;br /&gt;
**[[Spontaneous Photon Emission]]&lt;br /&gt;
*[[Path Independence of Electric Potential]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Collisions===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[Collisions]] &lt;br /&gt;
Collisions are events that happen very frequently in our day-to-day world. In the realm of Physics, a collision is defined as any sort of process in which before and after a short time interval there is little interaction, but during that short time interval there are large interactions. When looking at collisions, it is first important to understand two very important principles: the Momentum Principle and the Energy Principle. Both principles serve use when talking of collisions because they provide a way in which to analyze these collisions. Collisions themselves can be categorized into 3 main different types: elastic collisions, inelastic collisions, maximally inelastic collisions. All 3 collisions will get touched on in more detail further on. &lt;br /&gt;
*[[Elastic Collisions]]&lt;br /&gt;
A collision is deemed &amp;quot;elastic&amp;quot; when the internal energy of the objects in the system does not change (in other words, change in internal energy equals 0). Because in an elastic collision no kinetic energy is converted over to internal energy, in any elastic collision Kfinal always equals Kinitial.&lt;br /&gt;
*[[Inelastic Collisions]]&lt;br /&gt;
A collision is said to be &amp;quot;inelastic&amp;quot; when it is not elastic; therefore, an inelastic collision is an interaction in which some change in internal energy occurs between the colliding objects (in other words, change in internal energy does not equal 0). Examples of such changes that occur between colliding objects include, but are not limited to, things like they get hot, or they vibrate/rotate, or they deform. Because some of the kinetic energy is converted to internal energy during an inelastic collision, Kfinal does not equal Kinitial.&lt;br /&gt;
*[[Maximally Inelastic Collision]]&lt;br /&gt;
Maximally inelastic collisions, also known as &amp;quot;sticking collisions&amp;quot;, are the most extreme kinds of inelastic collisions. Just as its secondary name implies, a maximally inelastic collision is one in which the colliding objects stick together creating maximum dissipation. This does &lt;br /&gt;
*[[Head-on Collision of Equal Masses]]&lt;br /&gt;
*[[Head-on Collision of Unequal Masses]]&lt;br /&gt;
*[[Frame of Reference]]&lt;br /&gt;
*[[Scattering: Collisions in 2D and 3D]]&lt;br /&gt;
*[[Rutherford Experiment and Atomic Collisions]]&lt;br /&gt;
*[[Coefficient of Restitution]]&lt;br /&gt;
*[[testing123]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Fields===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
* [[Electric Field]] of a&lt;br /&gt;
** [[Point Charge]]&lt;br /&gt;
** [[Electric Dipole]]&lt;br /&gt;
** [[Capacitor]]&lt;br /&gt;
** [[Charged Rod]]&lt;br /&gt;
** [[Charged Ring]]&lt;br /&gt;
** [[Charged Disk]]&lt;br /&gt;
** [[Charged Spherical Shell]]&lt;br /&gt;
** [[Charged Cylinder]]&lt;br /&gt;
** [[Charge Density]]&lt;br /&gt;
**[[A Solid Sphere Charged Throughout Its Volume]]&lt;br /&gt;
*[[Electric Potential]] &lt;br /&gt;
**[[Potential Difference Path Independence]]&lt;br /&gt;
**[[Potential Difference in a Uniform Field]]&lt;br /&gt;
**[[Potential Difference of point charge in a non-Uniform Field]]&lt;br /&gt;
**[[Sign of Potential Difference]]&lt;br /&gt;
**[[Potential Difference in an Insulator]]&lt;br /&gt;
**[[Energy Density and Electric Field]]&lt;br /&gt;
** [[Systems of Charged Objects]]&lt;br /&gt;
*[[Electric Force]]&lt;br /&gt;
*[[Polarization]]&lt;br /&gt;
**[[Polarization of an Atom]]&lt;br /&gt;
*[[Charge Motion in Metals]]&lt;br /&gt;
*[[Charge Transfer]]&lt;br /&gt;
*[[Magnetic Field]]&lt;br /&gt;
**[[Right-Hand Rule]]&lt;br /&gt;
**[[Direction of Magnetic Field]]&lt;br /&gt;
**[[Magnetic Field of a Long Straight Wire]]&lt;br /&gt;
**[[Magnetic Field of a Loop]]&lt;br /&gt;
**[[Magnetic Field of a Solenoid]]&lt;br /&gt;
**[[Bar Magnet]]&lt;br /&gt;
**[[Magnetic Dipole Moment]]&lt;br /&gt;
***[[Stern-Gerlach Experiment]]&lt;br /&gt;
**[[Magnetic Torque]]&lt;br /&gt;
**[[Magnetic Force]]&lt;br /&gt;
**[[Earth&#039;s Magnetic Field]]&lt;br /&gt;
**[[Atomic Structure of Magnets]]&lt;br /&gt;
*[[Combining Electric and Magnetic Forces]]&lt;br /&gt;
**[[Hall Effect]]&lt;br /&gt;
**[[Lorentz Force]]&lt;br /&gt;
**[[Biot-Savart Law]]&lt;br /&gt;
**[[Biot-Savart Law for Currents]]&lt;br /&gt;
**[[Integration Techniques for Magnetic Field]]&lt;br /&gt;
**[[Sparks in Air]]&lt;br /&gt;
**[[Motional Emf]]&lt;br /&gt;
**[[Detecting a Magnetic Field]]&lt;br /&gt;
**[[Moving Point Charge]]&lt;br /&gt;
**[[Non-Coulomb Electric Field]]&lt;br /&gt;
**[[Motors and Generators]]&lt;br /&gt;
**[[Solenoid Applications]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Simple Circuits===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[Components]]&lt;br /&gt;
*[[Steady State]]&lt;br /&gt;
*[[Non Steady State]]&lt;br /&gt;
*[[Charging and Discharging a Capacitor]]&lt;br /&gt;
*[[Thin and Thick Wires]]&lt;br /&gt;
*[[Node Rule]]&lt;br /&gt;
*[[Loop Rule]]&lt;br /&gt;
*[[Resistivity]]&lt;br /&gt;
*[[Power in a circuit]]&lt;br /&gt;
*[[Ammeters,Voltmeters,Ohmmeters]]&lt;br /&gt;
*[[Current]]&lt;br /&gt;
**[[AC]]&lt;br /&gt;
*[[Ohm&#039;s Law]]&lt;br /&gt;
*[[Series Circuits]]&lt;br /&gt;
*[[Parallel Circuits]]&lt;br /&gt;
*[[RC]]&lt;br /&gt;
*[[AC vs DC]]&lt;br /&gt;
*[[Charge in a RC Circuit]]&lt;br /&gt;
*[[Current in a RC circuit]]&lt;br /&gt;
*[[Circular Loop of Wire]]&lt;br /&gt;
*[[Current in a RL Circuit]]&lt;br /&gt;
*[[RL Circuit]]&lt;br /&gt;
*[[Surface Charge Distributions]]&lt;br /&gt;
*[[Feedback]]&lt;br /&gt;
*[[Transformers (Circuits)]]&lt;br /&gt;
*[[Resistors and Conductivity]]&lt;br /&gt;
*[[Semiconductor Devices]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Maxwell&#039;s Equations===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[Gauss&#039;s Flux Theorem]]&lt;br /&gt;
**[[Electric Fields]]&lt;br /&gt;
***[[Examples of Flux Through Surfaces and Objects]]&lt;br /&gt;
**[[Magnetic Fields]]&lt;br /&gt;
*[[Ampere&#039;s Law]]&lt;br /&gt;
**[[Magnetic Field of Coaxial Cable Using Ampere&#039;s Law]]&lt;br /&gt;
**[[Magnetic Field of a Long Thick Wire Using Ampere&#039;s Law]]&lt;br /&gt;
**[[Magnetic Field of a Toroid Using Ampere&#039;s Law]]&lt;br /&gt;
*[[Faraday&#039;s Law]]&lt;br /&gt;
**[[Curly Electric Fields]]&lt;br /&gt;
**[[Inductance]]&lt;br /&gt;
***[[Transformers (Physics)]]&lt;br /&gt;
***[[Energy Density]]&lt;br /&gt;
**[[Lenz&#039;s Law]]&lt;br /&gt;
***[[Lenz Effect and the Jumping Ring]]&lt;br /&gt;
**[[Lenz&#039;s Rule]]&lt;br /&gt;
**[[Motional Emf using Faraday&#039;s Law]]&lt;br /&gt;
*[[Ampere-Maxwell Law]]&lt;br /&gt;
*[[Superconductors]]&lt;br /&gt;
**[[Meissner effect]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Radiation===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[Producing a Radiative Electric Field]]&lt;br /&gt;
*[[Sinusoidal Electromagnetic Radiaton]]&lt;br /&gt;
*[[Lenses]]&lt;br /&gt;
*[[Energy and Momentum Analysis in Radiation]]&lt;br /&gt;
**[[Poynting Vector]]&lt;br /&gt;
*[[Electromagnetic Propagation]]&lt;br /&gt;
**[[Wavelength and Frequency]]&lt;br /&gt;
*[[Snell&#039;s Law]]&lt;br /&gt;
*[[Effects of Radiation on Matter]]&lt;br /&gt;
*[[Light Propagation Through a Medium]]&lt;br /&gt;
*[[Light Scaterring: Why is the Sky Blue]]&lt;br /&gt;
*[[Light Refraction: Bending of light]]&lt;br /&gt;
*[[Cherenkov Radiation]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Sound===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[Doppler Effect]]&lt;br /&gt;
*[[Nature, Behavior, and Properties of Sound]]&lt;br /&gt;
*[[Resonance]]&lt;br /&gt;
*[[Sound Barrier]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Waves===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[Bragg&#039;s Law]]&lt;br /&gt;
*[[Multisource Interference: Diffraction]]&lt;br /&gt;
*[[Standing waves]]&lt;br /&gt;
*[[Gravitational waves]]&lt;br /&gt;
*[[Plasma waves]]&lt;br /&gt;
*[[Wave-Particle Duality]]&lt;br /&gt;
*[[Electromagnetic Waves]]&lt;br /&gt;
*[[Electromagnetic Spectrum]]&lt;br /&gt;
*[[Color Light Wave]]&lt;br /&gt;
*[[Mechanical Waves]]&lt;br /&gt;
*[[Pendulum Motion]]&lt;br /&gt;
*[[Transverse and Longitudinal Waves]]&lt;br /&gt;
*[[Planck&#039;s Relation]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Real Life Applications of Electromagnetic Principles===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[Electromagnetic Junkyard Cranes]]&lt;br /&gt;
*[[Maglev Trains]]&lt;br /&gt;
*[[Spark Plugs]]&lt;br /&gt;
*[[Metal Detectors]]&lt;br /&gt;
*[[Speakers]]&lt;br /&gt;
*[[Radios]]&lt;br /&gt;
*[[Ampullae of Lorenzini]]&lt;br /&gt;
*[[Electrocytes]]&lt;br /&gt;
*[[Generator]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div class=&amp;quot;toccolours mw-collapsible mw-collapsed&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Optics===&lt;br /&gt;
&amp;lt;div class=&amp;quot;mw-collapsible-content&amp;quot;&amp;gt;&lt;br /&gt;
*[[Mirrors]]&lt;br /&gt;
*[[Refraction]]&lt;br /&gt;
*[[Quantum Properties of Light]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
== Resources ==&lt;br /&gt;
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]&lt;br /&gt;
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]&lt;br /&gt;
* A page to keep track of all the physics [[Constants]]&lt;br /&gt;
* A page for review of [[Vectors]] and vector operations&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3854</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3854"/>
		<updated>2015-11-29T23:18:26Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* Difficult */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy change? The specific heat of the block and bullet is 6 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt; which is 1.961 m/s.&lt;br /&gt;
Now we can use the conservation of Energy principle to solve for the thermal energy: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0.  &amp;lt;/math&amp;gt; Then we break the change of kinetic energy into it&#039;s initial and final conditions to get :&lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,bullet}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the values we get : &lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(v_{final})^2}{(m_{final})} - (\frac{1}{2}{m_{bullet} (v_{bullet})^2}) &amp;lt;/math&amp;gt;. &lt;br /&gt;
Entering the values from the word problem, our final answer is 490J.&lt;br /&gt;
&lt;br /&gt;
To find the change in temperature, we need to use the heat equation : &amp;lt;math&amp;gt; Q = mCΔT &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the given information of specific heat, thermal energy that we solved for, and the mass of the final object, we get an increase of 16 degrees.&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
[[File: 11-091-playground.jpg |border|right]]&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039; &lt;br /&gt;
Sally (5 years old) is at the playground and decides that she wants to go on the ride that spins really fast in circles. The playground ride consists of a currently stationary disk of mass M = 45 kg and radius R = 2.4 m mounted on a low-friction axle. Sally weighs about 18 kg. She is super excited to play and runs at speed of 2.3 m/s on a line tangential to the disk and jumps onto the outer edge of the disk. She initially decided to just run around and spin the wheel, but later she decides that she wants to jump on and let the wheel keep going. What is the change of energy of the system?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
This problem is difficult because it requires the use of the three big equations of classical physics 1.&lt;br /&gt;
First we need to use the conservation of angular momentum and calculate the initial angular momentum which is &amp;lt;math&amp;gt; L = RPsinθ &amp;lt;/math&amp;gt;.&lt;br /&gt;
In this case, the momentum is 60 &amp;lt;math&amp;gt; m^2 kg/s &amp;lt;/math&amp;gt;.&lt;br /&gt;
Next we need to find the angular velocity of the ride with Sally. Using the equation: &amp;lt;math&amp;gt; L_i = Iω + RPsinθ &amp;lt;/math&amp;gt; where we can use the relationship that &amp;lt;math&amp;gt; v = ωr &amp;lt;/math&amp;gt; to find the more useful equation : &amp;lt;math&amp;gt; L_i = Iω + RmwR &amp;lt;/math&amp;gt;. Since this is a wheel, the moment of inertia will be &amp;lt;math&amp;gt;.5MR^2&amp;lt;/math&amp;gt;. Solving for ω  gives us .639 radians.&lt;br /&gt;
&lt;br /&gt;
Now we can solve for the change in energies using the formula : &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt;. However in this case we need to break the kinetic energies into rotational and translational and then their respective final and initial parts. So we get the rather large equation : &amp;lt;math&amp;gt; K_{rot,f} + K_{trans,f} + ΔU = K_{rot,i} + K_{trans,i} &amp;lt;/math&amp;gt; where we can convert &amp;lt;math&amp;gt; K_{rot} &amp;lt;/math&amp;gt; to &amp;lt;math&amp;gt;.5Iω^2&lt;br /&gt;
&amp;lt;/math&amp;gt;. Using the conservation of linear momentum theorem, we can find Sally&#039;s final velocity with the equation :  &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;. Plugging in values, we find that her final velocity is 1.02m/s. Now we can plug all our numbers into the previous equation and solve for the change in energy which is 373J.&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
&lt;br /&gt;
This topic is very important in my major, Chemical Engineering. Chemical processes deal with with heat flow and transporting chemicals. A hypothetical situation would be creating polyethylene glycol. This is a compound made by combining many ethylene oxides. This process is essentially an maximally inelastic collision, because the ethylene oxides will have their own flow rate from a a previous process that creates the molecule. This ethylene oxide will enter a new chamber and combine with the previous polyethylene glycol chain that is moving around to form a new molecule that now is a combination of the two and has a new velocity. So there will be a change of kinetic energy and in the form of heat since there are new bonds being formed. To keep the process going the heat must either be cooled or heated depending the chemical engineer&#039;s desire to stop or continue formation of polyethylene glycol. The change in thermal energy is key to this process and is created by this maximally inelastic collision that occurs.&lt;br /&gt;
&lt;br /&gt;
[[File:pet.gif]]&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
The idea of maximally inelastic collisions is part of the conservation of linear momentum which is implied by Newton&#039;s Laws. Most objects tend to bounce off each other creating the idea of collision. Most objects that are visibly colliding tend to lose energy through a variety of ways but theoretically objects could collide and not lose kinetic energy. This created the two types of collision inelastic and elastic. Elastic defines collisions that have no change in kinetic energy, these are usually microscopic such as Rutherford Scattering. All other objects tend to be inelastic since some energy in lost between the objects and so their respective kinetic energy changes. However, some objects can stick together and therefore combine their masses. This is a special case of inelastic collisions and tend to be a small portion of collisions that actually occur in real life, but some examples seen are when car&#039;s collide or when a sticky substance stays on the object it is throw at.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
There are several other topics within this wiki that can give you more information on collisions as a whole including&lt;br /&gt;
[[Inelastic Collisions]] and [[Elastic Collisions]]. These topics along with the basic fundamentals such as [[Kinetic Energy]] and [[ Momentum Principle]] that we used to derive the equations will show how exactly maximally inelastic collisions are shown by classical physics.&lt;br /&gt;
===Further reading===&lt;br /&gt;
These extensive resources cover this topic in more depth&lt;br /&gt;
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]&lt;br /&gt;
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]&lt;br /&gt;
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]&lt;br /&gt;
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]&lt;br /&gt;
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]&lt;br /&gt;
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]&lt;br /&gt;
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]&lt;br /&gt;
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
These are some internet articles that can show more animations and pictures to help understand this concept&lt;br /&gt;
*[http://www.ux1.eiu.edu/~cfadd/1150/07Mom/Inelastic.html Inelastic Collisions]&lt;br /&gt;
*[http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:examples:maximally_inelastic_collision_of_two_identical_carts Carts]&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
The biggest reference I used was the textbook : Matter and Interactions 4th edition.&lt;br /&gt;
Full Citation:&lt;br /&gt;
Chabay, Ruth W., and Bruce A. Sherwood. Matter and Interactions. Hoboken, NJ: Wiley, 2011. Print.&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3849</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3849"/>
		<updated>2015-11-29T23:17:24Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* Difficult */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy change? The specific heat of the block and bullet is 6 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt; which is 1.961 m/s.&lt;br /&gt;
Now we can use the conservation of Energy principle to solve for the thermal energy: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0.  &amp;lt;/math&amp;gt; Then we break the change of kinetic energy into it&#039;s initial and final conditions to get :&lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,bullet}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the values we get : &lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(v_{final})^2}{(m_{final})} - (\frac{1}{2}{m_{bullet} (v_{bullet})^2}) &amp;lt;/math&amp;gt;. &lt;br /&gt;
Entering the values from the word problem, our final answer is 490J.&lt;br /&gt;
&lt;br /&gt;
To find the change in temperature, we need to use the heat equation : &amp;lt;math&amp;gt; Q = mCΔT &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the given information of specific heat, thermal energy that we solved for, and the mass of the final object, we get an increase of 16 degrees.&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
[[File: 11-091-playground.jpg |border|right]]&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039; &lt;br /&gt;
Sally (5 years old) is at the playground and decides that she wants to go on the ride that spins really fast in circles. The playground ride consists of a currently stationary disk of mass M = 45 kg and radius R = 2.4 m mounted on a low-friction axle. Sally weighs about 18 kg. She is super excited to play and runs at speed of 2.3 m/s on a line tangential to the disk and jumps onto the outer edge of the disk. She initially decided to just run around and spin the wheel, but later she decides that she wants to jump on and let the wheel keep going. What is the change of energy of the system?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
First we need to use the conservation of angular momentum and calculate the initial angular momentum which is &amp;lt;math&amp;gt; L = RPsinθ &amp;lt;/math&amp;gt;.&lt;br /&gt;
In this case, the momentum is 60 &amp;lt;math&amp;gt; m^2 kg/s &amp;lt;/math&amp;gt;.&lt;br /&gt;
Next we need to find the angular velocity of the ride with Sally. Using the equation: &amp;lt;math&amp;gt; L_i = Iω + RPsinθ &amp;lt;/math&amp;gt; where we can use the relationship that &amp;lt;math&amp;gt; v = ωr &amp;lt;/math&amp;gt; to find the more useful equation : &amp;lt;math&amp;gt; L_i = Iω + RmwR &amp;lt;/math&amp;gt;. Since this is a wheel, the moment of inertia will be &amp;lt;math&amp;gt;.5MR^2&amp;lt;/math&amp;gt;. Solving for ω  gives us .639 radians.&lt;br /&gt;
&lt;br /&gt;
Now we can solve for the change in energies using the formula : &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt;. However in this case we need to break the kinetic energies into rotational and translational and then their respective final and initial parts. So we get the rather large equation : &amp;lt;math&amp;gt; K_{rot,f} + K_{trans,f} + ΔU = K_{rot,i} + K_{trans,i} &amp;lt;/math&amp;gt; where we can convert &amp;lt;math&amp;gt; K_{rot} &amp;lt;/math&amp;gt; to &amp;lt;math&amp;gt;.5Iω^2&lt;br /&gt;
&amp;lt;/math&amp;gt;. Using the conservation of linear momentum theorem, we can find Sally&#039;s final velocity with the equation :  &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;. Plugging in values, we find that her final velocity is 1.02m/s. Now we can plug all our numbers into the previous equation and solve for the change in energy which is 373J.&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
&lt;br /&gt;
This topic is very important in my major, Chemical Engineering. Chemical processes deal with with heat flow and transporting chemicals. A hypothetical situation would be creating polyethylene glycol. This is a compound made by combining many ethylene oxides. This process is essentially an maximally inelastic collision, because the ethylene oxides will have their own flow rate from a a previous process that creates the molecule. This ethylene oxide will enter a new chamber and combine with the previous polyethylene glycol chain that is moving around to form a new molecule that now is a combination of the two and has a new velocity. So there will be a change of kinetic energy and in the form of heat since there are new bonds being formed. To keep the process going the heat must either be cooled or heated depending the chemical engineer&#039;s desire to stop or continue formation of polyethylene glycol. The change in thermal energy is key to this process and is created by this maximally inelastic collision that occurs.&lt;br /&gt;
&lt;br /&gt;
[[File:pet.gif]]&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
The idea of maximally inelastic collisions is part of the conservation of linear momentum which is implied by Newton&#039;s Laws. Most objects tend to bounce off each other creating the idea of collision. Most objects that are visibly colliding tend to lose energy through a variety of ways but theoretically objects could collide and not lose kinetic energy. This created the two types of collision inelastic and elastic. Elastic defines collisions that have no change in kinetic energy, these are usually microscopic such as Rutherford Scattering. All other objects tend to be inelastic since some energy in lost between the objects and so their respective kinetic energy changes. However, some objects can stick together and therefore combine their masses. This is a special case of inelastic collisions and tend to be a small portion of collisions that actually occur in real life, but some examples seen are when car&#039;s collide or when a sticky substance stays on the object it is throw at.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
There are several other topics within this wiki that can give you more information on collisions as a whole including&lt;br /&gt;
[[Inelastic Collisions]] and [[Elastic Collisions]]. These topics along with the basic fundamentals such as [[Kinetic Energy]] and [[ Momentum Principle]] that we used to derive the equations will show how exactly maximally inelastic collisions are shown by classical physics.&lt;br /&gt;
===Further reading===&lt;br /&gt;
These extensive resources cover this topic in more depth&lt;br /&gt;
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]&lt;br /&gt;
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]&lt;br /&gt;
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]&lt;br /&gt;
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]&lt;br /&gt;
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]&lt;br /&gt;
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]&lt;br /&gt;
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]&lt;br /&gt;
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
These are some internet articles that can show more animations and pictures to help understand this concept&lt;br /&gt;
*[http://www.ux1.eiu.edu/~cfadd/1150/07Mom/Inelastic.html Inelastic Collisions]&lt;br /&gt;
*[http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:examples:maximally_inelastic_collision_of_two_identical_carts Carts]&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
The biggest reference I used was the textbook : Matter and Interactions 4th edition.&lt;br /&gt;
Full Citation:&lt;br /&gt;
Chabay, Ruth W., and Bruce A. Sherwood. Matter and Interactions. Hoboken, NJ: Wiley, 2011. Print.&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3847</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3847"/>
		<updated>2015-11-29T23:16:04Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* Difficult */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy change? The specific heat of the block and bullet is 6 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt; which is 1.961 m/s.&lt;br /&gt;
Now we can use the conservation of Energy principle to solve for the thermal energy: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0.  &amp;lt;/math&amp;gt; Then we break the change of kinetic energy into it&#039;s initial and final conditions to get :&lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,bullet}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the values we get : &lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(v_{final})^2}{(m_{final})} - (\frac{1}{2}{m_{bullet} (v_{bullet})^2}) &amp;lt;/math&amp;gt;. &lt;br /&gt;
Entering the values from the word problem, our final answer is 490J.&lt;br /&gt;
&lt;br /&gt;
To find the change in temperature, we need to use the heat equation : &amp;lt;math&amp;gt; Q = mCΔT &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the given information of specific heat, thermal energy that we solved for, and the mass of the final object, we get an increase of 16 degrees.&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
[[File: 11-091-playground.jpg |border|right]]&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039; &lt;br /&gt;
Sally (5 years old) is at the playground and decides that she wants to go on the ride that spins really fast in circles. The playground ride consists of a currently stationary disk of mass M = 45 kg and radius R = 2.4 m mounted on a low-friction axle. Sally weighs about 18 kg. She is super excited to play and runs at speed of 2.3 m/s on a line tangential to the disk and jumps onto the outer edge of the disk. She initially decided to just run around and spin the wheel, but later she decides that she wants to jump on and let the wheel keep going. What is the change of energy of the system?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
First we need to use the conservation of angular momentum and calculate the initial angular momentum which is &amp;lt;math&amp;gt; L = RPsinθ &amp;lt;/math&amp;gt;.&lt;br /&gt;
In this case, the momentum is 60 &amp;lt;math&amp;gt; m^2 kg/s &amp;lt;/math&amp;gt;.&lt;br /&gt;
Next we need to find the angular velocity of the ride with Sally. Using the equation: &amp;lt;math&amp;gt; L_i = Iω + RPsinθ &amp;lt;/math&amp;gt; where we can use the relationship that &amp;lt;math&amp;gt; v = ωr &amp;lt;/math&amp;gt; to find the more useful equation : &amp;lt;math&amp;gt; L_i = Iω + RmwR &amp;lt;/math&amp;gt;. Since this is a wheel, the moment of inertia will be &amp;lt;math&amp;gt;.5MR^2&amp;lt;/math&amp;gt;. Solving for ω  gives us .639 radians.&lt;br /&gt;
&lt;br /&gt;
Now we can solve for the change in energies using the formula : &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt;. However in this case we need to break the kinetic energies into rotational and translational and then their respective final and initial parts. So we get the rather large equation : &amp;lt;math&amp;gt; K_{rot,f} + K_{trans,f} + ΔU = K_{rot,i} + K_{trans,i} &amp;lt;/math&amp;gt; where we can convert &amp;lt;math&amp;gt; K_{rot} &amp;lt;/math&amp;gt; to &amp;lt;math&amp;gt;.5Iω^2&lt;br /&gt;
&amp;lt;/math&amp;gt;. Using the conservation of linear momentum theorem, we can find Sally&#039;s final velocity with the equation :&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
&lt;br /&gt;
This topic is very important in my major, Chemical Engineering. Chemical processes deal with with heat flow and transporting chemicals. A hypothetical situation would be creating polyethylene glycol. This is a compound made by combining many ethylene oxides. This process is essentially an maximally inelastic collision, because the ethylene oxides will have their own flow rate from a a previous process that creates the molecule. This ethylene oxide will enter a new chamber and combine with the previous polyethylene glycol chain that is moving around to form a new molecule that now is a combination of the two and has a new velocity. So there will be a change of kinetic energy and in the form of heat since there are new bonds being formed. To keep the process going the heat must either be cooled or heated depending the chemical engineer&#039;s desire to stop or continue formation of polyethylene glycol. The change in thermal energy is key to this process and is created by this maximally inelastic collision that occurs.&lt;br /&gt;
&lt;br /&gt;
[[File:pet.gif]]&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
The idea of maximally inelastic collisions is part of the conservation of linear momentum which is implied by Newton&#039;s Laws. Most objects tend to bounce off each other creating the idea of collision. Most objects that are visibly colliding tend to lose energy through a variety of ways but theoretically objects could collide and not lose kinetic energy. This created the two types of collision inelastic and elastic. Elastic defines collisions that have no change in kinetic energy, these are usually microscopic such as Rutherford Scattering. All other objects tend to be inelastic since some energy in lost between the objects and so their respective kinetic energy changes. However, some objects can stick together and therefore combine their masses. This is a special case of inelastic collisions and tend to be a small portion of collisions that actually occur in real life, but some examples seen are when car&#039;s collide or when a sticky substance stays on the object it is throw at.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
There are several other topics within this wiki that can give you more information on collisions as a whole including&lt;br /&gt;
[[Inelastic Collisions]] and [[Elastic Collisions]]. These topics along with the basic fundamentals such as [[Kinetic Energy]] and [[ Momentum Principle]] that we used to derive the equations will show how exactly maximally inelastic collisions are shown by classical physics.&lt;br /&gt;
===Further reading===&lt;br /&gt;
These extensive resources cover this topic in more depth&lt;br /&gt;
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]&lt;br /&gt;
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]&lt;br /&gt;
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]&lt;br /&gt;
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]&lt;br /&gt;
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]&lt;br /&gt;
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]&lt;br /&gt;
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]&lt;br /&gt;
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
These are some internet articles that can show more animations and pictures to help understand this concept&lt;br /&gt;
*[http://www.ux1.eiu.edu/~cfadd/1150/07Mom/Inelastic.html Inelastic Collisions]&lt;br /&gt;
*[http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:examples:maximally_inelastic_collision_of_two_identical_carts Carts]&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
The biggest reference I used was the textbook : Matter and Interactions 4th edition.&lt;br /&gt;
Full Citation:&lt;br /&gt;
Chabay, Ruth W., and Bruce A. Sherwood. Matter and Interactions. Hoboken, NJ: Wiley, 2011. Print.&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3840</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3840"/>
		<updated>2015-11-29T23:14:49Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* Difficult */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy change? The specific heat of the block and bullet is 6 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt; which is 1.961 m/s.&lt;br /&gt;
Now we can use the conservation of Energy principle to solve for the thermal energy: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0.  &amp;lt;/math&amp;gt; Then we break the change of kinetic energy into it&#039;s initial and final conditions to get :&lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,bullet}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the values we get : &lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(v_{final})^2}{(m_{final})} - (\frac{1}{2}{m_{bullet} (v_{bullet})^2}) &amp;lt;/math&amp;gt;. &lt;br /&gt;
Entering the values from the word problem, our final answer is 490J.&lt;br /&gt;
&lt;br /&gt;
To find the change in temperature, we need to use the heat equation : &amp;lt;math&amp;gt; Q = mCΔT &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the given information of specific heat, thermal energy that we solved for, and the mass of the final object, we get an increase of 16 degrees.&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
[[File: 11-091-playground.jpg |border|right]]&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039; &lt;br /&gt;
Sally (5 years old) is at the playground and decides that she wants to go on the ride that spins really fast in circles. The playground ride consists of a currently stationary disk of mass M = 45 kg and radius R = 2.4 m mounted on a low-friction axle. Sally weighs about 18 kg. She is super excited to play and runs at speed of 2.3 m/s on a line tangential to the disk and jumps onto the outer edge of the disk. She initially decided to just run around and spin the wheel, but later she decides that she wants to jump on and let the wheel keep going. What is the change of energy of the system?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
First we need to use the conservation of angular momentum and calculate the initial angular momentum which is &amp;lt;math&amp;gt; L = RPsinθ &amp;lt;/math&amp;gt;.&lt;br /&gt;
In this case, the momentum is 60 &amp;lt;math&amp;gt; m^2 kg/s &amp;lt;/math&amp;gt;.&lt;br /&gt;
Next we need to find the angular velocity of the ride with Sally. Using the equation: &amp;lt;math&amp;gt; L_i = Iω + RPsinθ &amp;lt;/math&amp;gt; where we can use the relationship that &amp;lt;math&amp;gt; v = ωr &amp;lt;/math&amp;gt; to find the more useful equation : &amp;lt;math&amp;gt; L_i = Iω + RmwR &amp;lt;/math&amp;gt;. Since this is a wheel, the moment of inertia will be &amp;lt;math&amp;gt;.5MR^2&amp;lt;/math&amp;gt;. Solving for ω  gives us .639 radians.&lt;br /&gt;
&lt;br /&gt;
Now we can solve for the change in energies using the formula : &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt;. However in this case we need to break the kinetic energies into rotational and translational and then their respective final and initial parts. So we get the rather large equation : &amp;lt;math&amp;gt; K_{rot,f} + K_{trans,f} + ΔU = K_{rot,i} + K_{trans,i} &amp;lt;/math&amp;gt; where we can convert &amp;lt;math&amp;gt; K_{rot} &amp;lt;/math&amp;gt; to &amp;lt;math&amp;gt;.5Iω^2&lt;br /&gt;
&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
&lt;br /&gt;
This topic is very important in my major, Chemical Engineering. Chemical processes deal with with heat flow and transporting chemicals. A hypothetical situation would be creating polyethylene glycol. This is a compound made by combining many ethylene oxides. This process is essentially an maximally inelastic collision, because the ethylene oxides will have their own flow rate from a a previous process that creates the molecule. This ethylene oxide will enter a new chamber and combine with the previous polyethylene glycol chain that is moving around to form a new molecule that now is a combination of the two and has a new velocity. So there will be a change of kinetic energy and in the form of heat since there are new bonds being formed. To keep the process going the heat must either be cooled or heated depending the chemical engineer&#039;s desire to stop or continue formation of polyethylene glycol. The change in thermal energy is key to this process and is created by this maximally inelastic collision that occurs.&lt;br /&gt;
&lt;br /&gt;
[[File:pet.gif]]&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
The idea of maximally inelastic collisions is part of the conservation of linear momentum which is implied by Newton&#039;s Laws. Most objects tend to bounce off each other creating the idea of collision. Most objects that are visibly colliding tend to lose energy through a variety of ways but theoretically objects could collide and not lose kinetic energy. This created the two types of collision inelastic and elastic. Elastic defines collisions that have no change in kinetic energy, these are usually microscopic such as Rutherford Scattering. All other objects tend to be inelastic since some energy in lost between the objects and so their respective kinetic energy changes. However, some objects can stick together and therefore combine their masses. This is a special case of inelastic collisions and tend to be a small portion of collisions that actually occur in real life, but some examples seen are when car&#039;s collide or when a sticky substance stays on the object it is throw at.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
There are several other topics within this wiki that can give you more information on collisions as a whole including&lt;br /&gt;
[[Inelastic Collisions]] and [[Elastic Collisions]]. These topics along with the basic fundamentals such as [[Kinetic Energy]] and [[ Momentum Principle]] that we used to derive the equations will show how exactly maximally inelastic collisions are shown by classical physics.&lt;br /&gt;
===Further reading===&lt;br /&gt;
These extensive resources cover this topic in more depth&lt;br /&gt;
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]&lt;br /&gt;
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]&lt;br /&gt;
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]&lt;br /&gt;
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]&lt;br /&gt;
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]&lt;br /&gt;
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]&lt;br /&gt;
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]&lt;br /&gt;
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
These are some internet articles that can show more animations and pictures to help understand this concept&lt;br /&gt;
*[http://www.ux1.eiu.edu/~cfadd/1150/07Mom/Inelastic.html Inelastic Collisions]&lt;br /&gt;
*[http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:examples:maximally_inelastic_collision_of_two_identical_carts Carts]&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
The biggest reference I used was the textbook : Matter and Interactions 4th edition.&lt;br /&gt;
Full Citation:&lt;br /&gt;
Chabay, Ruth W., and Bruce A. Sherwood. Matter and Interactions. Hoboken, NJ: Wiley, 2011. Print.&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3837</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3837"/>
		<updated>2015-11-29T23:13:38Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* Difficult */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy change? The specific heat of the block and bullet is 6 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt; which is 1.961 m/s.&lt;br /&gt;
Now we can use the conservation of Energy principle to solve for the thermal energy: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0.  &amp;lt;/math&amp;gt; Then we break the change of kinetic energy into it&#039;s initial and final conditions to get :&lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,bullet}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the values we get : &lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(v_{final})^2}{(m_{final})} - (\frac{1}{2}{m_{bullet} (v_{bullet})^2}) &amp;lt;/math&amp;gt;. &lt;br /&gt;
Entering the values from the word problem, our final answer is 490J.&lt;br /&gt;
&lt;br /&gt;
To find the change in temperature, we need to use the heat equation : &amp;lt;math&amp;gt; Q = mCΔT &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the given information of specific heat, thermal energy that we solved for, and the mass of the final object, we get an increase of 16 degrees.&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
[[File: 11-091-playground.jpg |border|right]]&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039; &lt;br /&gt;
Sally (5 years old) is at the playground and decides that she wants to go on the ride that spins really fast in circles. The playground ride consists of a currently stationary disk of mass M = 45 kg and radius R = 2.4 m mounted on a low-friction axle. Sally weighs about 18 kg. She is super excited to play and runs at speed of 2.3 m/s on a line tangential to the disk and jumps onto the outer edge of the disk. She initially decided to just run around and spin the wheel, but later she decides that she wants to jump on and let the wheel keep going. What is the change of energy of the system?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
First we need to use the conservation of angular momentum and calculate the initial angular momentum which is &amp;lt;math&amp;gt; L = RPsinθ &amp;lt;/math&amp;gt;.&lt;br /&gt;
In this case, the momentum is 60 &amp;lt;math&amp;gt; m^2 kg/s &amp;lt;/math&amp;gt;.&lt;br /&gt;
Next we need to find the angular velocity of the ride with Sally. Using the equation: &amp;lt;math&amp;gt; L_i = Iω + RPsinθ &amp;lt;/math&amp;gt; where we can use the relationship that &amp;lt;math&amp;gt; v = ωr &amp;lt;/math&amp;gt; to find the more useful equation : &amp;lt;math&amp;gt; L_i = Iω + RmwR &amp;lt;/math&amp;gt;. Solving for w gives us .639 radians.&lt;br /&gt;
&lt;br /&gt;
Now we can solve for the change in energies using the formula : &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt;. However in this case we need to break the kinetic energies into rotational and translational and then their respective final and initial parts. So we get the rather large equation : &amp;lt;math&amp;gt; K_{rot,f} + K_{trans,f} + ΔU = K_{rot,i} + K_{trans,i} &amp;lt;/math&amp;gt; where we can convert &amp;lt;math&amp;gt; K_{rot} &amp;lt;/math&amp;gt; to &amp;lt;math&amp;gt;.5Iω^2&lt;br /&gt;
&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
&lt;br /&gt;
This topic is very important in my major, Chemical Engineering. Chemical processes deal with with heat flow and transporting chemicals. A hypothetical situation would be creating polyethylene glycol. This is a compound made by combining many ethylene oxides. This process is essentially an maximally inelastic collision, because the ethylene oxides will have their own flow rate from a a previous process that creates the molecule. This ethylene oxide will enter a new chamber and combine with the previous polyethylene glycol chain that is moving around to form a new molecule that now is a combination of the two and has a new velocity. So there will be a change of kinetic energy and in the form of heat since there are new bonds being formed. To keep the process going the heat must either be cooled or heated depending the chemical engineer&#039;s desire to stop or continue formation of polyethylene glycol. The change in thermal energy is key to this process and is created by this maximally inelastic collision that occurs.&lt;br /&gt;
&lt;br /&gt;
[[File:pet.gif]]&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
The idea of maximally inelastic collisions is part of the conservation of linear momentum which is implied by Newton&#039;s Laws. Most objects tend to bounce off each other creating the idea of collision. Most objects that are visibly colliding tend to lose energy through a variety of ways but theoretically objects could collide and not lose kinetic energy. This created the two types of collision inelastic and elastic. Elastic defines collisions that have no change in kinetic energy, these are usually microscopic such as Rutherford Scattering. All other objects tend to be inelastic since some energy in lost between the objects and so their respective kinetic energy changes. However, some objects can stick together and therefore combine their masses. This is a special case of inelastic collisions and tend to be a small portion of collisions that actually occur in real life, but some examples seen are when car&#039;s collide or when a sticky substance stays on the object it is throw at.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
There are several other topics within this wiki that can give you more information on collisions as a whole including&lt;br /&gt;
[[Inelastic Collisions]] and [[Elastic Collisions]]. These topics along with the basic fundamentals such as [[Kinetic Energy]] and [[ Momentum Principle]] that we used to derive the equations will show how exactly maximally inelastic collisions are shown by classical physics.&lt;br /&gt;
===Further reading===&lt;br /&gt;
These extensive resources cover this topic in more depth&lt;br /&gt;
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]&lt;br /&gt;
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]&lt;br /&gt;
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]&lt;br /&gt;
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]&lt;br /&gt;
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]&lt;br /&gt;
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]&lt;br /&gt;
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]&lt;br /&gt;
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
These are some internet articles that can show more animations and pictures to help understand this concept&lt;br /&gt;
*[http://www.ux1.eiu.edu/~cfadd/1150/07Mom/Inelastic.html Inelastic Collisions]&lt;br /&gt;
*[http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:examples:maximally_inelastic_collision_of_two_identical_carts Carts]&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
The biggest reference I used was the textbook : Matter and Interactions 4th edition.&lt;br /&gt;
Full Citation:&lt;br /&gt;
Chabay, Ruth W., and Bruce A. Sherwood. Matter and Interactions. Hoboken, NJ: Wiley, 2011. Print.&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3836</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3836"/>
		<updated>2015-11-29T23:13:12Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* Difficult */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy change? The specific heat of the block and bullet is 6 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt; which is 1.961 m/s.&lt;br /&gt;
Now we can use the conservation of Energy principle to solve for the thermal energy: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0.  &amp;lt;/math&amp;gt; Then we break the change of kinetic energy into it&#039;s initial and final conditions to get :&lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,bullet}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the values we get : &lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(v_{final})^2}{(m_{final})} - (\frac{1}{2}{m_{bullet} (v_{bullet})^2}) &amp;lt;/math&amp;gt;. &lt;br /&gt;
Entering the values from the word problem, our final answer is 490J.&lt;br /&gt;
&lt;br /&gt;
To find the change in temperature, we need to use the heat equation : &amp;lt;math&amp;gt; Q = mCΔT &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the given information of specific heat, thermal energy that we solved for, and the mass of the final object, we get an increase of 16 degrees.&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
[[File: 11-091-playground.jpg |border|right]]&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039; &lt;br /&gt;
Sally (5 years old) is at the playground and decides that she wants to go on the ride that spins really fast in circles. The playground ride consists of a currently stationary disk of mass M = 45 kg and radius R = 2.4 m mounted on a low-friction axle. Sally weighs about 18 kg. She is super excited to play and runs at speed of 2.3 m/s on a line tangential to the disk and jumps onto the outer edge of the disk. She initially decided to just run around and spin the wheel, but later she decides that she wants to jump on and let the wheel keep going. What is the change of energy of the system?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
First we need to use the conservation of angular momentum and calculate the initial angular momentum which is &amp;lt;math&amp;gt; L = RPsinθ &amp;lt;/math&amp;gt;.&lt;br /&gt;
In this case, the momentum is 60 &amp;lt;math&amp;gt; m^2*kg/s &amp;lt;/math&amp;gt;.&lt;br /&gt;
Next we need to find the angular velocity of the ride with Sally. Using the equation: &amp;lt;math&amp;gt; L_i = Iω + RPsinθ &amp;lt;/math&amp;gt; where we can use the relationship that &amp;lt;math&amp;gt; v = ωr &amp;lt;/math&amp;gt; to find the more useful equation : &amp;lt;math&amp;gt; L_i = Iω + RmwR &amp;lt;/math&amp;gt;. Solving for w gives us .639 radians.&lt;br /&gt;
&lt;br /&gt;
Now we can solve for the change in energies using the formula : &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt;. However in this case we need to break the kinetic energies into rotational and translational and then their respective final and initial parts. So we get the rather large equation : &amp;lt;math&amp;gt; K_{rot,f} + K_{trans,f} + ΔU = K_{rot,i} + K_{trans,i} &amp;lt;/math&amp;gt; where we can convert &amp;lt;math&amp;gt; K_{rot} &amp;lt;/math&amp;gt; to &amp;lt;math&amp;gt;.5Iω^2&lt;br /&gt;
&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
&lt;br /&gt;
This topic is very important in my major, Chemical Engineering. Chemical processes deal with with heat flow and transporting chemicals. A hypothetical situation would be creating polyethylene glycol. This is a compound made by combining many ethylene oxides. This process is essentially an maximally inelastic collision, because the ethylene oxides will have their own flow rate from a a previous process that creates the molecule. This ethylene oxide will enter a new chamber and combine with the previous polyethylene glycol chain that is moving around to form a new molecule that now is a combination of the two and has a new velocity. So there will be a change of kinetic energy and in the form of heat since there are new bonds being formed. To keep the process going the heat must either be cooled or heated depending the chemical engineer&#039;s desire to stop or continue formation of polyethylene glycol. The change in thermal energy is key to this process and is created by this maximally inelastic collision that occurs.&lt;br /&gt;
&lt;br /&gt;
[[File:pet.gif]]&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
The idea of maximally inelastic collisions is part of the conservation of linear momentum which is implied by Newton&#039;s Laws. Most objects tend to bounce off each other creating the idea of collision. Most objects that are visibly colliding tend to lose energy through a variety of ways but theoretically objects could collide and not lose kinetic energy. This created the two types of collision inelastic and elastic. Elastic defines collisions that have no change in kinetic energy, these are usually microscopic such as Rutherford Scattering. All other objects tend to be inelastic since some energy in lost between the objects and so their respective kinetic energy changes. However, some objects can stick together and therefore combine their masses. This is a special case of inelastic collisions and tend to be a small portion of collisions that actually occur in real life, but some examples seen are when car&#039;s collide or when a sticky substance stays on the object it is throw at.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
There are several other topics within this wiki that can give you more information on collisions as a whole including&lt;br /&gt;
[[Inelastic Collisions]] and [[Elastic Collisions]]. These topics along with the basic fundamentals such as [[Kinetic Energy]] and [[ Momentum Principle]] that we used to derive the equations will show how exactly maximally inelastic collisions are shown by classical physics.&lt;br /&gt;
===Further reading===&lt;br /&gt;
These extensive resources cover this topic in more depth&lt;br /&gt;
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]&lt;br /&gt;
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]&lt;br /&gt;
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]&lt;br /&gt;
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]&lt;br /&gt;
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]&lt;br /&gt;
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]&lt;br /&gt;
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]&lt;br /&gt;
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
These are some internet articles that can show more animations and pictures to help understand this concept&lt;br /&gt;
*[http://www.ux1.eiu.edu/~cfadd/1150/07Mom/Inelastic.html Inelastic Collisions]&lt;br /&gt;
*[http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:examples:maximally_inelastic_collision_of_two_identical_carts Carts]&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
The biggest reference I used was the textbook : Matter and Interactions 4th edition.&lt;br /&gt;
Full Citation:&lt;br /&gt;
Chabay, Ruth W., and Bruce A. Sherwood. Matter and Interactions. Hoboken, NJ: Wiley, 2011. Print.&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3835</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3835"/>
		<updated>2015-11-29T23:12:53Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* Difficult */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy change? The specific heat of the block and bullet is 6 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt; which is 1.961 m/s.&lt;br /&gt;
Now we can use the conservation of Energy principle to solve for the thermal energy: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0.  &amp;lt;/math&amp;gt; Then we break the change of kinetic energy into it&#039;s initial and final conditions to get :&lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,bullet}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the values we get : &lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(v_{final})^2}{(m_{final})} - (\frac{1}{2}{m_{bullet} (v_{bullet})^2}) &amp;lt;/math&amp;gt;. &lt;br /&gt;
Entering the values from the word problem, our final answer is 490J.&lt;br /&gt;
&lt;br /&gt;
To find the change in temperature, we need to use the heat equation : &amp;lt;math&amp;gt; Q = mCΔT &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the given information of specific heat, thermal energy that we solved for, and the mass of the final object, we get an increase of 16 degrees.&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
[[File: 11-091-playground.jpg |border|right]]&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039; &lt;br /&gt;
Sally (5 years old) is at the playground and decides that she wants to go on the ride that spins really fast in circles. The playground ride consists of a currently stationary disk of mass M = 45 kg and radius R = 2.4 m mounted on a low-friction axle. Sally weighs about 18 kg. She is super excited to play and runs at speed of 2.3 m/s on a line tangential to the disk and jumps onto the outer edge of the disk. She initially decided to just run around and spin the wheel, but later she decides that she wants to jump on and let the wheel keep going. What is the change of energy of the system?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
First we need to use the conservation of angular momentum and calculate the initial angular momentum which is &amp;lt;math&amp;gt; L = R*Psinθ &amp;lt;/math&amp;gt;.&lt;br /&gt;
In this case, the momentum is 60 &amp;lt;math&amp;gt; m^2*kg/s &amp;lt;/math&amp;gt;.&lt;br /&gt;
Next we need to find the angular velocity of the ride with Sally. Using the equation: &amp;lt;math&amp;gt; L_i = Iω + R*Psinθ &amp;lt;/math&amp;gt; where we can use the relationship that &amp;lt;math&amp;gt; v = ωr &amp;lt;/math&amp;gt; to find the more useful equation : &amp;lt;math&amp;gt; L_i = Iω + RmwR &amp;lt;/math&amp;gt;. Solving for w gives us .639 radians.&lt;br /&gt;
&lt;br /&gt;
Now we can solve for the change in energies using the formula : &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt;. However in this case we need to break the kinetic energies into rotational and translational and then their respective final and initial parts. So we get the rather large equation : &amp;lt;math&amp;gt; K_{rot,f} + K_{trans,f} + ΔU = K_{rot,i} + K_{trans,i} &amp;lt;/math&amp;gt; where we can convert &amp;lt;math&amp;gt; K_{rot} &amp;lt;/math&amp;gt; to &amp;lt;math&amp;gt;.5Iω^2&lt;br /&gt;
&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
&lt;br /&gt;
This topic is very important in my major, Chemical Engineering. Chemical processes deal with with heat flow and transporting chemicals. A hypothetical situation would be creating polyethylene glycol. This is a compound made by combining many ethylene oxides. This process is essentially an maximally inelastic collision, because the ethylene oxides will have their own flow rate from a a previous process that creates the molecule. This ethylene oxide will enter a new chamber and combine with the previous polyethylene glycol chain that is moving around to form a new molecule that now is a combination of the two and has a new velocity. So there will be a change of kinetic energy and in the form of heat since there are new bonds being formed. To keep the process going the heat must either be cooled or heated depending the chemical engineer&#039;s desire to stop or continue formation of polyethylene glycol. The change in thermal energy is key to this process and is created by this maximally inelastic collision that occurs.&lt;br /&gt;
&lt;br /&gt;
[[File:pet.gif]]&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
The idea of maximally inelastic collisions is part of the conservation of linear momentum which is implied by Newton&#039;s Laws. Most objects tend to bounce off each other creating the idea of collision. Most objects that are visibly colliding tend to lose energy through a variety of ways but theoretically objects could collide and not lose kinetic energy. This created the two types of collision inelastic and elastic. Elastic defines collisions that have no change in kinetic energy, these are usually microscopic such as Rutherford Scattering. All other objects tend to be inelastic since some energy in lost between the objects and so their respective kinetic energy changes. However, some objects can stick together and therefore combine their masses. This is a special case of inelastic collisions and tend to be a small portion of collisions that actually occur in real life, but some examples seen are when car&#039;s collide or when a sticky substance stays on the object it is throw at.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
There are several other topics within this wiki that can give you more information on collisions as a whole including&lt;br /&gt;
[[Inelastic Collisions]] and [[Elastic Collisions]]. These topics along with the basic fundamentals such as [[Kinetic Energy]] and [[ Momentum Principle]] that we used to derive the equations will show how exactly maximally inelastic collisions are shown by classical physics.&lt;br /&gt;
===Further reading===&lt;br /&gt;
These extensive resources cover this topic in more depth&lt;br /&gt;
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]&lt;br /&gt;
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]&lt;br /&gt;
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]&lt;br /&gt;
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]&lt;br /&gt;
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]&lt;br /&gt;
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]&lt;br /&gt;
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]&lt;br /&gt;
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
These are some internet articles that can show more animations and pictures to help understand this concept&lt;br /&gt;
*[http://www.ux1.eiu.edu/~cfadd/1150/07Mom/Inelastic.html Inelastic Collisions]&lt;br /&gt;
*[http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:examples:maximally_inelastic_collision_of_two_identical_carts Carts]&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
The biggest reference I used was the textbook : Matter and Interactions 4th edition.&lt;br /&gt;
Full Citation:&lt;br /&gt;
Chabay, Ruth W., and Bruce A. Sherwood. Matter and Interactions. Hoboken, NJ: Wiley, 2011. Print.&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3833</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3833"/>
		<updated>2015-11-29T23:12:03Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* Difficult */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy change? The specific heat of the block and bullet is 6 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt; which is 1.961 m/s.&lt;br /&gt;
Now we can use the conservation of Energy principle to solve for the thermal energy: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0.  &amp;lt;/math&amp;gt; Then we break the change of kinetic energy into it&#039;s initial and final conditions to get :&lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,bullet}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the values we get : &lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(v_{final})^2}{(m_{final})} - (\frac{1}{2}{m_{bullet} (v_{bullet})^2}) &amp;lt;/math&amp;gt;. &lt;br /&gt;
Entering the values from the word problem, our final answer is 490J.&lt;br /&gt;
&lt;br /&gt;
To find the change in temperature, we need to use the heat equation : &amp;lt;math&amp;gt; Q = mCΔT &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the given information of specific heat, thermal energy that we solved for, and the mass of the final object, we get an increase of 16 degrees.&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
[[File: 11-091-playground.jpg |border|right]]&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039; &lt;br /&gt;
Sally (5 years old) is at the playground and decides that she wants to go on the ride that spins really fast in circles. The playground ride consists of a disk of mass M = 45 kg and radius R = 2.4 m mounted on a low-friction axle. Sally weighs about 18 kg. She is super excited to play and runs at speed of 2.3 m/s on a line tangential to the disk and jumps onto the outer edge of the disk. She initially decided to just run around and spin the wheel, but later she decides that she wants to jump on and let the wheel keep going. What is the change of energy of the system?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
First we need to use the conservation of angular momentum and calculate the initial angular momentum which is &amp;lt;math&amp;gt; L = R*Psinθ &amp;lt;/math&amp;gt;.&lt;br /&gt;
In this case, the momentum is 60 &amp;lt;math&amp;gt; m^2*kg/s &amp;lt;/math&amp;gt;.&lt;br /&gt;
Next we need to find the angular velocity of the ride with Sally. Using the equation: &amp;lt;math&amp;gt; L_i = Iω + R*Psinθ &amp;lt;/math&amp;gt; where we can use the relationship that &amp;lt;math&amp;gt; v = ωr &amp;lt;/math&amp;gt; to find the more useful equation : &amp;lt;math&amp;gt; L_i = Iω + RmwR &amp;lt;/math&amp;gt;. Solving for w gives us .639 radians.&lt;br /&gt;
&lt;br /&gt;
Now we can solve for the change in energies using the formula : &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt;. However in this case we need to break the kinetic energies into rotational and translational and then their respective final and initial parts. So we get the rather large equation : &amp;lt;math&amp;gt; K_{rot,f} + K_{trans,f} + ΔU = K_{rot,i} + K_{trans,i} &amp;lt;/math&amp;gt; where we can convert &amp;lt;math&amp;gt; K_{rot} &amp;lt;/math&amp;gt; to &amp;lt;math&amp;gt;.5Iω^2&lt;br /&gt;
&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
&lt;br /&gt;
This topic is very important in my major, Chemical Engineering. Chemical processes deal with with heat flow and transporting chemicals. A hypothetical situation would be creating polyethylene glycol. This is a compound made by combining many ethylene oxides. This process is essentially an maximally inelastic collision, because the ethylene oxides will have their own flow rate from a a previous process that creates the molecule. This ethylene oxide will enter a new chamber and combine with the previous polyethylene glycol chain that is moving around to form a new molecule that now is a combination of the two and has a new velocity. So there will be a change of kinetic energy and in the form of heat since there are new bonds being formed. To keep the process going the heat must either be cooled or heated depending the chemical engineer&#039;s desire to stop or continue formation of polyethylene glycol. The change in thermal energy is key to this process and is created by this maximally inelastic collision that occurs.&lt;br /&gt;
&lt;br /&gt;
[[File:pet.gif]]&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
The idea of maximally inelastic collisions is part of the conservation of linear momentum which is implied by Newton&#039;s Laws. Most objects tend to bounce off each other creating the idea of collision. Most objects that are visibly colliding tend to lose energy through a variety of ways but theoretically objects could collide and not lose kinetic energy. This created the two types of collision inelastic and elastic. Elastic defines collisions that have no change in kinetic energy, these are usually microscopic such as Rutherford Scattering. All other objects tend to be inelastic since some energy in lost between the objects and so their respective kinetic energy changes. However, some objects can stick together and therefore combine their masses. This is a special case of inelastic collisions and tend to be a small portion of collisions that actually occur in real life, but some examples seen are when car&#039;s collide or when a sticky substance stays on the object it is throw at.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
There are several other topics within this wiki that can give you more information on collisions as a whole including&lt;br /&gt;
[[Inelastic Collisions]] and [[Elastic Collisions]]. These topics along with the basic fundamentals such as [[Kinetic Energy]] and [[ Momentum Principle]] that we used to derive the equations will show how exactly maximally inelastic collisions are shown by classical physics.&lt;br /&gt;
===Further reading===&lt;br /&gt;
These extensive resources cover this topic in more depth&lt;br /&gt;
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]&lt;br /&gt;
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]&lt;br /&gt;
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]&lt;br /&gt;
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]&lt;br /&gt;
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]&lt;br /&gt;
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]&lt;br /&gt;
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]&lt;br /&gt;
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
These are some internet articles that can show more animations and pictures to help understand this concept&lt;br /&gt;
*[http://www.ux1.eiu.edu/~cfadd/1150/07Mom/Inelastic.html Inelastic Collisions]&lt;br /&gt;
*[http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:examples:maximally_inelastic_collision_of_two_identical_carts Carts]&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
The biggest reference I used was the textbook : Matter and Interactions 4th edition.&lt;br /&gt;
Full Citation:&lt;br /&gt;
Chabay, Ruth W., and Bruce A. Sherwood. Matter and Interactions. Hoboken, NJ: Wiley, 2011. Print.&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3831</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3831"/>
		<updated>2015-11-29T23:10:59Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* Difficult */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy change? The specific heat of the block and bullet is 6 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt; which is 1.961 m/s.&lt;br /&gt;
Now we can use the conservation of Energy principle to solve for the thermal energy: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0.  &amp;lt;/math&amp;gt; Then we break the change of kinetic energy into it&#039;s initial and final conditions to get :&lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,bullet}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the values we get : &lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(v_{final})^2}{(m_{final})} - (\frac{1}{2}{m_{bullet} (v_{bullet})^2}) &amp;lt;/math&amp;gt;. &lt;br /&gt;
Entering the values from the word problem, our final answer is 490J.&lt;br /&gt;
&lt;br /&gt;
To find the change in temperature, we need to use the heat equation : &amp;lt;math&amp;gt; Q = mCΔT &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the given information of specific heat, thermal energy that we solved for, and the mass of the final object, we get an increase of 16 degrees.&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
[[File: 11-091-playground.jpg |border|right]]&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039; &lt;br /&gt;
Sally (5 years old) is at the playground and decides that she wants to go on the ride that spins really fast in circles. The playground ride consists of a disk of mass M = 45 kg and radius R = 2.4 m mounted on a low-friction axle. Sally weighs about 18 kg. She is super excited to play and runs at speed of 2.3 m/s on a line tangential to the disk and jumps onto the outer edge of the disk. She initially decided to just run around and spin the wheel, but later she decides that she wants to jump on and let the wheel keep going. What is the change of energy of the system?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
First we need to use the conservation of angular momentum and calculate the initial angular momentum which is &amp;lt;math&amp;gt; L = R*Psinθ &amp;lt;/math&amp;gt;.&lt;br /&gt;
In this case, the momentum is 60 &amp;lt;math&amp;gt; m^2*kg/s &amp;lt;/math&amp;gt;.&lt;br /&gt;
Next we need to find the angular velocity of the ride with Sally. Using the equation: &amp;lt;math&amp;gt; L_i = Iw + R*Psinθ &amp;lt;/math&amp;gt; where we can use the relationship that v = wr to find the more useful equation : &amp;lt;math&amp;gt; L_i = Iw + RmwR &amp;lt;/math&amp;gt;. Solving for w gives us .639 radians.&lt;br /&gt;
&lt;br /&gt;
Now we can solve for the change in energies using the formula : &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt;. However in this case we need to break the kinetic energies into rotational and translational and then their respective final and initial parts. So we get the rather large equation : &amp;lt;math&amp;gt; K_{rot,f} + K_{trans,f} + ΔU = K_{rot,i} + K_{trans,i} &amp;lt;/math&amp;gt; where we can convert &amp;lt;math&amp;gt; K_{rot} &amp;lt;/math&amp;gt; to &amp;lt;math&amp;gt;.5Iw^2&lt;br /&gt;
&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
&lt;br /&gt;
This topic is very important in my major, Chemical Engineering. Chemical processes deal with with heat flow and transporting chemicals. A hypothetical situation would be creating polyethylene glycol. This is a compound made by combining many ethylene oxides. This process is essentially an maximally inelastic collision, because the ethylene oxides will have their own flow rate from a a previous process that creates the molecule. This ethylene oxide will enter a new chamber and combine with the previous polyethylene glycol chain that is moving around to form a new molecule that now is a combination of the two and has a new velocity. So there will be a change of kinetic energy and in the form of heat since there are new bonds being formed. To keep the process going the heat must either be cooled or heated depending the chemical engineer&#039;s desire to stop or continue formation of polyethylene glycol. The change in thermal energy is key to this process and is created by this maximally inelastic collision that occurs.&lt;br /&gt;
&lt;br /&gt;
[[File:pet.gif]]&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
The idea of maximally inelastic collisions is part of the conservation of linear momentum which is implied by Newton&#039;s Laws. Most objects tend to bounce off each other creating the idea of collision. Most objects that are visibly colliding tend to lose energy through a variety of ways but theoretically objects could collide and not lose kinetic energy. This created the two types of collision inelastic and elastic. Elastic defines collisions that have no change in kinetic energy, these are usually microscopic such as Rutherford Scattering. All other objects tend to be inelastic since some energy in lost between the objects and so their respective kinetic energy changes. However, some objects can stick together and therefore combine their masses. This is a special case of inelastic collisions and tend to be a small portion of collisions that actually occur in real life, but some examples seen are when car&#039;s collide or when a sticky substance stays on the object it is throw at.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
There are several other topics within this wiki that can give you more information on collisions as a whole including&lt;br /&gt;
[[Inelastic Collisions]] and [[Elastic Collisions]]. These topics along with the basic fundamentals such as [[Kinetic Energy]] and [[ Momentum Principle]] that we used to derive the equations will show how exactly maximally inelastic collisions are shown by classical physics.&lt;br /&gt;
===Further reading===&lt;br /&gt;
These extensive resources cover this topic in more depth&lt;br /&gt;
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]&lt;br /&gt;
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]&lt;br /&gt;
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]&lt;br /&gt;
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]&lt;br /&gt;
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]&lt;br /&gt;
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]&lt;br /&gt;
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]&lt;br /&gt;
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
These are some internet articles that can show more animations and pictures to help understand this concept&lt;br /&gt;
*[http://www.ux1.eiu.edu/~cfadd/1150/07Mom/Inelastic.html Inelastic Collisions]&lt;br /&gt;
*[http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:examples:maximally_inelastic_collision_of_two_identical_carts Carts]&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
The biggest reference I used was the textbook : Matter and Interactions 4th edition.&lt;br /&gt;
Full Citation:&lt;br /&gt;
Chabay, Ruth W., and Bruce A. Sherwood. Matter and Interactions. Hoboken, NJ: Wiley, 2011. Print.&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3828</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3828"/>
		<updated>2015-11-29T23:10:04Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* Difficult */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy change? The specific heat of the block and bullet is 6 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt; which is 1.961 m/s.&lt;br /&gt;
Now we can use the conservation of Energy principle to solve for the thermal energy: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0.  &amp;lt;/math&amp;gt; Then we break the change of kinetic energy into it&#039;s initial and final conditions to get :&lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,bullet}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the values we get : &lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(v_{final})^2}{(m_{final})} - (\frac{1}{2}{m_{bullet} (v_{bullet})^2}) &amp;lt;/math&amp;gt;. &lt;br /&gt;
Entering the values from the word problem, our final answer is 490J.&lt;br /&gt;
&lt;br /&gt;
To find the change in temperature, we need to use the heat equation : &amp;lt;math&amp;gt; Q = mCΔT &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the given information of specific heat, thermal energy that we solved for, and the mass of the final object, we get an increase of 16 degrees.&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
[[File: 11-091-playground.jpg |border|right]]&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039; &lt;br /&gt;
Sally (5 years old) is at the playground and decides that she wants to go on the ride that spins really fast in circles. The playground ride consists of a disk of mass M = 45 kg and radius R = 2.4 m mounted on a low-friction axle. Sally weighs about 18 kg. She is super excited to play and runs at speed of 2.3 m/s on a line tangential to the disk and jumps onto the outer edge of the disk. She initially decided to just run around and spin the wheel, but later she decides that she wants to jump on and let the wheel keep going. What is the change of energy of the system?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
First we need to use the conservation of angular momentum and calculate the initial angular momentum which is &amp;lt;math&amp;gt; L = R x P &amp;lt;/math&amp;gt;.&lt;br /&gt;
In this case, the momentum is 60 &amp;lt;math&amp;gt; m^2*kg/s &amp;lt;/math&amp;gt;.&lt;br /&gt;
Next we need to find the angular velocity of the ride with Sally. Using the equation: &amp;lt;math&amp;gt; L_i = Iw + R x P &amp;lt;/math&amp;gt; where we can use the relationship that v = wr to find the more useful equation : &amp;lt;math&amp;gt; L_i = Iw + RmwR &amp;lt;/math&amp;gt;. Solving for w gives us .639 radians.&lt;br /&gt;
&lt;br /&gt;
Now we can solve for the change in energies using the formula : &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt;. However in this case we need to break the kinetic energies into rotational and translational and then their respective final and initial parts. So we get the rather large equation : &amp;lt;math&amp;gt; K_{rot,f} + K_{trans,f} + ΔU = K_{rot,i} + K_{trans,i} &amp;lt;/math&amp;gt; where we can convert &amp;lt;math&amp;gt; K_{rot} &amp;lt;/math&amp;gt; to &amp;lt;math&amp;gt;.5Iw^2&lt;br /&gt;
&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
&lt;br /&gt;
This topic is very important in my major, Chemical Engineering. Chemical processes deal with with heat flow and transporting chemicals. A hypothetical situation would be creating polyethylene glycol. This is a compound made by combining many ethylene oxides. This process is essentially an maximally inelastic collision, because the ethylene oxides will have their own flow rate from a a previous process that creates the molecule. This ethylene oxide will enter a new chamber and combine with the previous polyethylene glycol chain that is moving around to form a new molecule that now is a combination of the two and has a new velocity. So there will be a change of kinetic energy and in the form of heat since there are new bonds being formed. To keep the process going the heat must either be cooled or heated depending the chemical engineer&#039;s desire to stop or continue formation of polyethylene glycol. The change in thermal energy is key to this process and is created by this maximally inelastic collision that occurs.&lt;br /&gt;
&lt;br /&gt;
[[File:pet.gif]]&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
The idea of maximally inelastic collisions is part of the conservation of linear momentum which is implied by Newton&#039;s Laws. Most objects tend to bounce off each other creating the idea of collision. Most objects that are visibly colliding tend to lose energy through a variety of ways but theoretically objects could collide and not lose kinetic energy. This created the two types of collision inelastic and elastic. Elastic defines collisions that have no change in kinetic energy, these are usually microscopic such as Rutherford Scattering. All other objects tend to be inelastic since some energy in lost between the objects and so their respective kinetic energy changes. However, some objects can stick together and therefore combine their masses. This is a special case of inelastic collisions and tend to be a small portion of collisions that actually occur in real life, but some examples seen are when car&#039;s collide or when a sticky substance stays on the object it is throw at.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
There are several other topics within this wiki that can give you more information on collisions as a whole including&lt;br /&gt;
[[Inelastic Collisions]] and [[Elastic Collisions]]. These topics along with the basic fundamentals such as [[Kinetic Energy]] and [[ Momentum Principle]] that we used to derive the equations will show how exactly maximally inelastic collisions are shown by classical physics.&lt;br /&gt;
===Further reading===&lt;br /&gt;
These extensive resources cover this topic in more depth&lt;br /&gt;
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]&lt;br /&gt;
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]&lt;br /&gt;
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]&lt;br /&gt;
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]&lt;br /&gt;
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]&lt;br /&gt;
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]&lt;br /&gt;
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]&lt;br /&gt;
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
These are some internet articles that can show more animations and pictures to help understand this concept&lt;br /&gt;
*[http://www.ux1.eiu.edu/~cfadd/1150/07Mom/Inelastic.html Inelastic Collisions]&lt;br /&gt;
*[http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:examples:maximally_inelastic_collision_of_two_identical_carts Carts]&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
The biggest reference I used was the textbook : Matter and Interactions 4th edition.&lt;br /&gt;
Full Citation:&lt;br /&gt;
Chabay, Ruth W., and Bruce A. Sherwood. Matter and Interactions. Hoboken, NJ: Wiley, 2011. Print.&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3826</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3826"/>
		<updated>2015-11-29T23:09:49Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* Difficult */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy change? The specific heat of the block and bullet is 6 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt; which is 1.961 m/s.&lt;br /&gt;
Now we can use the conservation of Energy principle to solve for the thermal energy: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0.  &amp;lt;/math&amp;gt; Then we break the change of kinetic energy into it&#039;s initial and final conditions to get :&lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,bullet}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the values we get : &lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(v_{final})^2}{(m_{final})} - (\frac{1}{2}{m_{bullet} (v_{bullet})^2}) &amp;lt;/math&amp;gt;. &lt;br /&gt;
Entering the values from the word problem, our final answer is 490J.&lt;br /&gt;
&lt;br /&gt;
To find the change in temperature, we need to use the heat equation : &amp;lt;math&amp;gt; Q = mCΔT &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the given information of specific heat, thermal energy that we solved for, and the mass of the final object, we get an increase of 16 degrees.&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
[[File: 11-091-playground.jpg |border|right]]&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039; &lt;br /&gt;
Sally (5 years old) is at the playground and decides that she wants to go on the ride that spins really fast in circles. The playground ride consists of a disk of mass M = 45 kg and radius R = 2.4 m mounted on a low-friction axle. Sally weighs about 18 kg. She is super excited to play and runs at speed of 2.3 m/s on a line tangential to the disk and jumps onto the outer edge of the disk. She initially decided to just run around and spin the wheel, but later she decides that she wants to jump on and let the wheel keep going. What is the change of energy of the system?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
First we need to use the conservation of angular momentum and calculate the initial angular momentum which is &amp;lt;math&amp;gt; L = R X P &amp;lt;/math&amp;gt;.&lt;br /&gt;
In this case, the momentum is 60 &amp;lt;math&amp;gt; m^2*kg/s &amp;lt;/math&amp;gt;.&lt;br /&gt;
Next we need to find the angular velocity of the ride with Sally. Using the equation: &amp;lt;math&amp;gt; L_i = Iw + R X P &amp;lt;/math&amp;gt; where we can use the relationship that v = wr to find the more useful equation : &amp;lt;math&amp;gt; L_i = Iw + RmwR &amp;lt;/math&amp;gt;. Solving for w gives us .639 radians.&lt;br /&gt;
&lt;br /&gt;
Now we can solve for the change in energies using the formula : &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt;. However in this case we need to break the kinetic energies into rotational and translational and then their respective final and initial parts. So we get the rather large equation : &amp;lt;math&amp;gt; K_{rot,f} + K_{trans,f} + ΔU = K_{rot,i} + K_{trans,i} &amp;lt;/math&amp;gt; where we can convert &amp;lt;math&amp;gt; K_{rot} &amp;lt;/math&amp;gt; to &amp;lt;math&amp;gt;.5Iw^2&lt;br /&gt;
&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
&lt;br /&gt;
This topic is very important in my major, Chemical Engineering. Chemical processes deal with with heat flow and transporting chemicals. A hypothetical situation would be creating polyethylene glycol. This is a compound made by combining many ethylene oxides. This process is essentially an maximally inelastic collision, because the ethylene oxides will have their own flow rate from a a previous process that creates the molecule. This ethylene oxide will enter a new chamber and combine with the previous polyethylene glycol chain that is moving around to form a new molecule that now is a combination of the two and has a new velocity. So there will be a change of kinetic energy and in the form of heat since there are new bonds being formed. To keep the process going the heat must either be cooled or heated depending the chemical engineer&#039;s desire to stop or continue formation of polyethylene glycol. The change in thermal energy is key to this process and is created by this maximally inelastic collision that occurs.&lt;br /&gt;
&lt;br /&gt;
[[File:pet.gif]]&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
The idea of maximally inelastic collisions is part of the conservation of linear momentum which is implied by Newton&#039;s Laws. Most objects tend to bounce off each other creating the idea of collision. Most objects that are visibly colliding tend to lose energy through a variety of ways but theoretically objects could collide and not lose kinetic energy. This created the two types of collision inelastic and elastic. Elastic defines collisions that have no change in kinetic energy, these are usually microscopic such as Rutherford Scattering. All other objects tend to be inelastic since some energy in lost between the objects and so their respective kinetic energy changes. However, some objects can stick together and therefore combine their masses. This is a special case of inelastic collisions and tend to be a small portion of collisions that actually occur in real life, but some examples seen are when car&#039;s collide or when a sticky substance stays on the object it is throw at.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
There are several other topics within this wiki that can give you more information on collisions as a whole including&lt;br /&gt;
[[Inelastic Collisions]] and [[Elastic Collisions]]. These topics along with the basic fundamentals such as [[Kinetic Energy]] and [[ Momentum Principle]] that we used to derive the equations will show how exactly maximally inelastic collisions are shown by classical physics.&lt;br /&gt;
===Further reading===&lt;br /&gt;
These extensive resources cover this topic in more depth&lt;br /&gt;
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]&lt;br /&gt;
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]&lt;br /&gt;
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]&lt;br /&gt;
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]&lt;br /&gt;
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]&lt;br /&gt;
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]&lt;br /&gt;
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]&lt;br /&gt;
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
These are some internet articles that can show more animations and pictures to help understand this concept&lt;br /&gt;
*[http://www.ux1.eiu.edu/~cfadd/1150/07Mom/Inelastic.html Inelastic Collisions]&lt;br /&gt;
*[http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:examples:maximally_inelastic_collision_of_two_identical_carts Carts]&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
The biggest reference I used was the textbook : Matter and Interactions 4th edition.&lt;br /&gt;
Full Citation:&lt;br /&gt;
Chabay, Ruth W., and Bruce A. Sherwood. Matter and Interactions. Hoboken, NJ: Wiley, 2011. Print.&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3822</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3822"/>
		<updated>2015-11-29T23:08:49Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* Difficult */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy change? The specific heat of the block and bullet is 6 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt; which is 1.961 m/s.&lt;br /&gt;
Now we can use the conservation of Energy principle to solve for the thermal energy: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0.  &amp;lt;/math&amp;gt; Then we break the change of kinetic energy into it&#039;s initial and final conditions to get :&lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,bullet}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the values we get : &lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(v_{final})^2}{(m_{final})} - (\frac{1}{2}{m_{bullet} (v_{bullet})^2}) &amp;lt;/math&amp;gt;. &lt;br /&gt;
Entering the values from the word problem, our final answer is 490J.&lt;br /&gt;
&lt;br /&gt;
To find the change in temperature, we need to use the heat equation : &amp;lt;math&amp;gt; Q = mCΔT &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the given information of specific heat, thermal energy that we solved for, and the mass of the final object, we get an increase of 16 degrees.&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
[[File: 11-091-playground.jpg |border|right]]&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039; &lt;br /&gt;
Sally (5 years old) is at the playground and decides that she wants to go on the ride that spins really fast in circles. The playground ride consists of a disk of mass M = 45 kg and radius R = 2.4 m mounted on a low-friction axle. Sally weighs about 18 kg. She is super excited to play and runs at speed of 2.3 m/s on a line tangential to the disk and jumps onto the outer edge of the disk. She initially decided to just run around and spin the wheel, but later she decides that she wants to jump on and let the wheel keep going. What is the change of energy of the system?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
First we need to use the conservation of angular momentum and calculate the initial angular momentum which is &amp;lt;math&amp;gt; L = R X P &amp;lt;/math&amp;gt;.&lt;br /&gt;
In this case, the momentum is 60 &amp;lt;math&amp;gt; m^2*kg/s &amp;lt;/math&amp;gt;.&lt;br /&gt;
Next we need to find the angular velocity of the ride with Sally. Using the equation: &amp;lt;math&amp;gt; L_i = Iw + R X P &amp;lt;/math&amp;gt; where we can use the relationship that v = wr to find the more useful equation : &amp;lt;math&amp;gt; L_i = Iw + RmwR. Solving for w gives us .639 radians.&lt;br /&gt;
&lt;br /&gt;
Now we can solve for the change in energies using the formula : &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt;. However in this case we need to break the kinetic energies into rotational and translational and then their respective final and initial parts. So we get the rather large equation : &amp;lt;math&amp;gt; K_{rot,f} + K_{trans,f} + ΔU = K_{rot,i} + K_{trans,i} &amp;lt;/math&amp;gt; where we can convert &amp;lt;math&amp;gt; K_rot &amp;lt;/math&amp;gt; to &amp;lt;math&amp;gt;.5Iw^2&lt;br /&gt;
&amp;lt;/math&amp;gt;.&lt;br /&gt;
==Connectedness==&lt;br /&gt;
&lt;br /&gt;
This topic is very important in my major, Chemical Engineering. Chemical processes deal with with heat flow and transporting chemicals. A hypothetical situation would be creating polyethylene glycol. This is a compound made by combining many ethylene oxides. This process is essentially an maximally inelastic collision, because the ethylene oxides will have their own flow rate from a a previous process that creates the molecule. This ethylene oxide will enter a new chamber and combine with the previous polyethylene glycol chain that is moving around to form a new molecule that now is a combination of the two and has a new velocity. So there will be a change of kinetic energy and in the form of heat since there are new bonds being formed. To keep the process going the heat must either be cooled or heated depending the chemical engineer&#039;s desire to stop or continue formation of polyethylene glycol. The change in thermal energy is key to this process and is created by this maximally inelastic collision that occurs.&lt;br /&gt;
&lt;br /&gt;
[[File:pet.gif]]&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
The idea of maximally inelastic collisions is part of the conservation of linear momentum which is implied by Newton&#039;s Laws. Most objects tend to bounce off each other creating the idea of collision. Most objects that are visibly colliding tend to lose energy through a variety of ways but theoretically objects could collide and not lose kinetic energy. This created the two types of collision inelastic and elastic. Elastic defines collisions that have no change in kinetic energy, these are usually microscopic such as Rutherford Scattering. All other objects tend to be inelastic since some energy in lost between the objects and so their respective kinetic energy changes. However, some objects can stick together and therefore combine their masses. This is a special case of inelastic collisions and tend to be a small portion of collisions that actually occur in real life, but some examples seen are when car&#039;s collide or when a sticky substance stays on the object it is throw at.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
There are several other topics within this wiki that can give you more information on collisions as a whole including&lt;br /&gt;
[[Inelastic Collisions]] and [[Elastic Collisions]]. These topics along with the basic fundamentals such as [[Kinetic Energy]] and [[ Momentum Principle]] that we used to derive the equations will show how exactly maximally inelastic collisions are shown by classical physics.&lt;br /&gt;
===Further reading===&lt;br /&gt;
These extensive resources cover this topic in more depth&lt;br /&gt;
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]&lt;br /&gt;
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]&lt;br /&gt;
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]&lt;br /&gt;
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]&lt;br /&gt;
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]&lt;br /&gt;
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]&lt;br /&gt;
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]&lt;br /&gt;
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
These are some internet articles that can show more animations and pictures to help understand this concept&lt;br /&gt;
*[http://www.ux1.eiu.edu/~cfadd/1150/07Mom/Inelastic.html Inelastic Collisions]&lt;br /&gt;
*[http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:examples:maximally_inelastic_collision_of_two_identical_carts Carts]&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
The biggest reference I used was the textbook : Matter and Interactions 4th edition.&lt;br /&gt;
Full Citation:&lt;br /&gt;
Chabay, Ruth W., and Bruce A. Sherwood. Matter and Interactions. Hoboken, NJ: Wiley, 2011. Print.&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3820</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3820"/>
		<updated>2015-11-29T23:05:51Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* Difficult */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy change? The specific heat of the block and bullet is 6 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt; which is 1.961 m/s.&lt;br /&gt;
Now we can use the conservation of Energy principle to solve for the thermal energy: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0.  &amp;lt;/math&amp;gt; Then we break the change of kinetic energy into it&#039;s initial and final conditions to get :&lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,bullet}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the values we get : &lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(v_{final})^2}{(m_{final})} - (\frac{1}{2}{m_{bullet} (v_{bullet})^2}) &amp;lt;/math&amp;gt;. &lt;br /&gt;
Entering the values from the word problem, our final answer is 490J.&lt;br /&gt;
&lt;br /&gt;
To find the change in temperature, we need to use the heat equation : &amp;lt;math&amp;gt; Q = mCΔT &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the given information of specific heat, thermal energy that we solved for, and the mass of the final object, we get an increase of 16 degrees.&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
[[File: 11-091-playground.jpg |border|right]]&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039; &lt;br /&gt;
Sally (5 years old) is at the playground and decides that she wants to go on the ride that spins really fast in circles. The playground ride consists of a disk of mass M = 45 kg and radius R = 2.4 m mounted on a low-friction axle. Sally weighs about 18 kg. She is super excited to play and runs at speed of 2.3 m/s on a line tangential to the disk and jumps onto the outer edge of the disk. She initially decided to just run around and spin the wheel, but later she decides that she wants to jump on and let the wheel keep going. What is the change of energy of the system?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
First we need to use the conservation of angular momentum and calculate the initial angular momentum which is &amp;lt;math&amp;gt; L = R X P &amp;lt;/math&amp;gt;.&lt;br /&gt;
In this case, the momentum is 60 &amp;lt;math&amp;gt; m^2*kg/s &amp;lt;/math&amp;gt;.&lt;br /&gt;
Next we need to find the angular velocity of the ride with Sally. Using the equation: &amp;lt;math&amp;gt; L_i = Iw + R X P &amp;lt;/math&amp;gt; where we can use the relationship that v = wr to find the more useful equation : &amp;lt;math&amp;gt; L_i = Iw + RmwR. Solving for w gives us .639 radians.&lt;br /&gt;
&lt;br /&gt;
Now we can solve for the change in energies using the formula : &amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
&lt;br /&gt;
This topic is very important in my major, Chemical Engineering. Chemical processes deal with with heat flow and transporting chemicals. A hypothetical situation would be creating polyethylene glycol. This is a compound made by combining many ethylene oxides. This process is essentially an maximally inelastic collision, because the ethylene oxides will have their own flow rate from a a previous process that creates the molecule. This ethylene oxide will enter a new chamber and combine with the previous polyethylene glycol chain that is moving around to form a new molecule that now is a combination of the two and has a new velocity. So there will be a change of kinetic energy and in the form of heat since there are new bonds being formed. To keep the process going the heat must either be cooled or heated depending the chemical engineer&#039;s desire to stop or continue formation of polyethylene glycol. The change in thermal energy is key to this process and is created by this maximally inelastic collision that occurs.&lt;br /&gt;
&lt;br /&gt;
[[File:pet.gif]]&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
The idea of maximally inelastic collisions is part of the conservation of linear momentum which is implied by Newton&#039;s Laws. Most objects tend to bounce off each other creating the idea of collision. Most objects that are visibly colliding tend to lose energy through a variety of ways but theoretically objects could collide and not lose kinetic energy. This created the two types of collision inelastic and elastic. Elastic defines collisions that have no change in kinetic energy, these are usually microscopic such as Rutherford Scattering. All other objects tend to be inelastic since some energy in lost between the objects and so their respective kinetic energy changes. However, some objects can stick together and therefore combine their masses. This is a special case of inelastic collisions and tend to be a small portion of collisions that actually occur in real life, but some examples seen are when car&#039;s collide or when a sticky substance stays on the object it is throw at.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
There are several other topics within this wiki that can give you more information on collisions as a whole including&lt;br /&gt;
[[Inelastic Collisions]] and [[Elastic Collisions]]. These topics along with the basic fundamentals such as [[Kinetic Energy]] and [[ Momentum Principle]] that we used to derive the equations will show how exactly maximally inelastic collisions are shown by classical physics.&lt;br /&gt;
===Further reading===&lt;br /&gt;
These extensive resources cover this topic in more depth&lt;br /&gt;
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]&lt;br /&gt;
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]&lt;br /&gt;
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]&lt;br /&gt;
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]&lt;br /&gt;
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]&lt;br /&gt;
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]&lt;br /&gt;
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]&lt;br /&gt;
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
These are some internet articles that can show more animations and pictures to help understand this concept&lt;br /&gt;
*[http://www.ux1.eiu.edu/~cfadd/1150/07Mom/Inelastic.html Inelastic Collisions]&lt;br /&gt;
*[http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:examples:maximally_inelastic_collision_of_two_identical_carts Carts]&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
The biggest reference I used was the textbook : Matter and Interactions 4th edition.&lt;br /&gt;
Full Citation:&lt;br /&gt;
Chabay, Ruth W., and Bruce A. Sherwood. Matter and Interactions. Hoboken, NJ: Wiley, 2011. Print.&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3736</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3736"/>
		<updated>2015-11-29T22:23:59Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* References */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy change? The specific heat of the block and bullet is 6 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt; which is 1.961 m/s.&lt;br /&gt;
Now we can use the conservation of Energy principle to solve for the thermal energy: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0.  &amp;lt;/math&amp;gt; Then we break the change of kinetic energy into it&#039;s initial and final conditions to get :&lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,bullet}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the values we get : &lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(v_{final})^2}{(m_{final})} - (\frac{1}{2}{m_{bullet} (v_{bullet})^2}) &amp;lt;/math&amp;gt;. &lt;br /&gt;
Entering the values from the word problem, our final answer is 490J.&lt;br /&gt;
&lt;br /&gt;
To find the change in temperature, we need to use the heat equation : &amp;lt;math&amp;gt; Q = mCΔT &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the given information of specific heat, thermal energy that we solved for, and the mass of the final object, we get an increase of 16 degrees.&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
[[File: 11-091-playground.jpg |border|right]]&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039; &lt;br /&gt;
Sally (5 years old) is at the playground and decides that she wants to go on the ride that spins really fast in circles. The playground ride consists of a disk of mass M = 57 kg and radius R = 2.0 m mounted on a low-friction axle. Sally weighs about 20 kg. She is super excited to play and runs at speed of 3 m/s on a line tangential to the disk and jumps onto the outer edge of the disk. She initially decided to just run around and spin the wheel, but later she decides that she wants to jump on and let the wheel keep going. What is the change of energy of the system?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
&lt;br /&gt;
This topic is very important in my major, Chemical Engineering. Chemical processes deal with with heat flow and transporting chemicals. A hypothetical situation would be creating polyethylene glycol. This is a compound made by combining many ethylene oxides. This process is essentially an maximally inelastic collision, because the ethylene oxides will have their own flow rate from a a previous process that creates the molecule. This ethylene oxide will enter a new chamber and combine with the previous polyethylene glycol chain that is moving around to form a new molecule that now is a combination of the two and has a new velocity. So there will be a change of kinetic energy and in the form of heat since there are new bonds being formed. To keep the process going the heat must either be cooled or heated depending the chemical engineer&#039;s desire to stop or continue formation of polyethylene glycol. The change in thermal energy is key to this process and is created by this maximally inelastic collision that occurs.&lt;br /&gt;
&lt;br /&gt;
[[File:pet.gif]]&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
The idea of maximally inelastic collisions is part of the conservation of linear momentum which is implied by Newton&#039;s Laws. Most objects tend to bounce off each other creating the idea of collision. Most objects that are visibly colliding tend to lose energy through a variety of ways but theoretically objects could collide and not lose kinetic energy. This created the two types of collision inelastic and elastic. Elastic defines collisions that have no change in kinetic energy, these are usually microscopic such as Rutherford Scattering. All other objects tend to be inelastic since some energy in lost between the objects and so their respective kinetic energy changes. However, some objects can stick together and therefore combine their masses. This is a special case of inelastic collisions and tend to be a small portion of collisions that actually occur in real life, but some examples seen are when car&#039;s collide or when a sticky substance stays on the object it is throw at.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
There are several other topics within this wiki that can give you more information on collisions as a whole including&lt;br /&gt;
[[Inelastic Collisions]] and [[Elastic Collisions]]. These topics along with the basic fundamentals such as [[Kinetic Energy]] and [[ Momentum Principle]] that we used to derive the equations will show how exactly maximally inelastic collisions are shown by classical physics.&lt;br /&gt;
===Further reading===&lt;br /&gt;
These extensive resources cover this topic in more depth&lt;br /&gt;
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]&lt;br /&gt;
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]&lt;br /&gt;
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]&lt;br /&gt;
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]&lt;br /&gt;
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]&lt;br /&gt;
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]&lt;br /&gt;
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]&lt;br /&gt;
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
These are some internet articles that can show more animations and pictures to help understand this concept&lt;br /&gt;
*[http://www.ux1.eiu.edu/~cfadd/1150/07Mom/Inelastic.html Inelastic Collisions]&lt;br /&gt;
*[http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:examples:maximally_inelastic_collision_of_two_identical_carts Carts]&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
The biggest reference I used was the textbook : Matter and Interactions 4th edition.&lt;br /&gt;
Full Citation:&lt;br /&gt;
Chabay, Ruth W., and Bruce A. Sherwood. Matter and Interactions. Hoboken, NJ: Wiley, 2011. Print.&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3733</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3733"/>
		<updated>2015-11-29T22:23:36Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* References */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy change? The specific heat of the block and bullet is 6 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt; which is 1.961 m/s.&lt;br /&gt;
Now we can use the conservation of Energy principle to solve for the thermal energy: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0.  &amp;lt;/math&amp;gt; Then we break the change of kinetic energy into it&#039;s initial and final conditions to get :&lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,bullet}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the values we get : &lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(v_{final})^2}{(m_{final})} - (\frac{1}{2}{m_{bullet} (v_{bullet})^2}) &amp;lt;/math&amp;gt;. &lt;br /&gt;
Entering the values from the word problem, our final answer is 490J.&lt;br /&gt;
&lt;br /&gt;
To find the change in temperature, we need to use the heat equation : &amp;lt;math&amp;gt; Q = mCΔT &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the given information of specific heat, thermal energy that we solved for, and the mass of the final object, we get an increase of 16 degrees.&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
[[File: 11-091-playground.jpg |border|right]]&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039; &lt;br /&gt;
Sally (5 years old) is at the playground and decides that she wants to go on the ride that spins really fast in circles. The playground ride consists of a disk of mass M = 57 kg and radius R = 2.0 m mounted on a low-friction axle. Sally weighs about 20 kg. She is super excited to play and runs at speed of 3 m/s on a line tangential to the disk and jumps onto the outer edge of the disk. She initially decided to just run around and spin the wheel, but later she decides that she wants to jump on and let the wheel keep going. What is the change of energy of the system?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
&lt;br /&gt;
This topic is very important in my major, Chemical Engineering. Chemical processes deal with with heat flow and transporting chemicals. A hypothetical situation would be creating polyethylene glycol. This is a compound made by combining many ethylene oxides. This process is essentially an maximally inelastic collision, because the ethylene oxides will have their own flow rate from a a previous process that creates the molecule. This ethylene oxide will enter a new chamber and combine with the previous polyethylene glycol chain that is moving around to form a new molecule that now is a combination of the two and has a new velocity. So there will be a change of kinetic energy and in the form of heat since there are new bonds being formed. To keep the process going the heat must either be cooled or heated depending the chemical engineer&#039;s desire to stop or continue formation of polyethylene glycol. The change in thermal energy is key to this process and is created by this maximally inelastic collision that occurs.&lt;br /&gt;
&lt;br /&gt;
[[File:pet.gif]]&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
The idea of maximally inelastic collisions is part of the conservation of linear momentum which is implied by Newton&#039;s Laws. Most objects tend to bounce off each other creating the idea of collision. Most objects that are visibly colliding tend to lose energy through a variety of ways but theoretically objects could collide and not lose kinetic energy. This created the two types of collision inelastic and elastic. Elastic defines collisions that have no change in kinetic energy, these are usually microscopic such as Rutherford Scattering. All other objects tend to be inelastic since some energy in lost between the objects and so their respective kinetic energy changes. However, some objects can stick together and therefore combine their masses. This is a special case of inelastic collisions and tend to be a small portion of collisions that actually occur in real life, but some examples seen are when car&#039;s collide or when a sticky substance stays on the object it is throw at.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
There are several other topics within this wiki that can give you more information on collisions as a whole including&lt;br /&gt;
[[Inelastic Collisions]] and [[Elastic Collisions]]. These topics along with the basic fundamentals such as [[Kinetic Energy]] and [[ Momentum Principle]] that we used to derive the equations will show how exactly maximally inelastic collisions are shown by classical physics.&lt;br /&gt;
===Further reading===&lt;br /&gt;
These extensive resources cover this topic in more depth&lt;br /&gt;
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]&lt;br /&gt;
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]&lt;br /&gt;
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]&lt;br /&gt;
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]&lt;br /&gt;
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]&lt;br /&gt;
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]&lt;br /&gt;
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]&lt;br /&gt;
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
These are some internet articles that can show more animations and pictures to help understand this concept&lt;br /&gt;
*[http://www.ux1.eiu.edu/~cfadd/1150/07Mom/Inelastic.html Inelastic Collisions]&lt;br /&gt;
*[http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:examples:maximally_inelastic_collision_of_two_identical_carts Carts]&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
The biggest reference I used was the textbook:&lt;br /&gt;
Matter and Interactions 4e by Chabay and Sherwood&lt;br /&gt;
Full Citation:&lt;br /&gt;
Chabay, Ruth W., and Bruce A. Sherwood. Matter and Interactions. Hoboken, NJ: Wiley, 2011. Print.&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3726</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3726"/>
		<updated>2015-11-29T22:21:30Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* References */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy change? The specific heat of the block and bullet is 6 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt; which is 1.961 m/s.&lt;br /&gt;
Now we can use the conservation of Energy principle to solve for the thermal energy: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0.  &amp;lt;/math&amp;gt; Then we break the change of kinetic energy into it&#039;s initial and final conditions to get :&lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,bullet}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the values we get : &lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(v_{final})^2}{(m_{final})} - (\frac{1}{2}{m_{bullet} (v_{bullet})^2}) &amp;lt;/math&amp;gt;. &lt;br /&gt;
Entering the values from the word problem, our final answer is 490J.&lt;br /&gt;
&lt;br /&gt;
To find the change in temperature, we need to use the heat equation : &amp;lt;math&amp;gt; Q = mCΔT &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the given information of specific heat, thermal energy that we solved for, and the mass of the final object, we get an increase of 16 degrees.&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
[[File: 11-091-playground.jpg |border|right]]&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039; &lt;br /&gt;
Sally (5 years old) is at the playground and decides that she wants to go on the ride that spins really fast in circles. The playground ride consists of a disk of mass M = 57 kg and radius R = 2.0 m mounted on a low-friction axle. Sally weighs about 20 kg. She is super excited to play and runs at speed of 3 m/s on a line tangential to the disk and jumps onto the outer edge of the disk. She initially decided to just run around and spin the wheel, but later she decides that she wants to jump on and let the wheel keep going. What is the change of energy of the system?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
&lt;br /&gt;
This topic is very important in my major, Chemical Engineering. Chemical processes deal with with heat flow and transporting chemicals. A hypothetical situation would be creating polyethylene glycol. This is a compound made by combining many ethylene oxides. This process is essentially an maximally inelastic collision, because the ethylene oxides will have their own flow rate from a a previous process that creates the molecule. This ethylene oxide will enter a new chamber and combine with the previous polyethylene glycol chain that is moving around to form a new molecule that now is a combination of the two and has a new velocity. So there will be a change of kinetic energy and in the form of heat since there are new bonds being formed. To keep the process going the heat must either be cooled or heated depending the chemical engineer&#039;s desire to stop or continue formation of polyethylene glycol. The change in thermal energy is key to this process and is created by this maximally inelastic collision that occurs.&lt;br /&gt;
&lt;br /&gt;
[[File:pet.gif]]&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
The idea of maximally inelastic collisions is part of the conservation of linear momentum which is implied by Newton&#039;s Laws. Most objects tend to bounce off each other creating the idea of collision. Most objects that are visibly colliding tend to lose energy through a variety of ways but theoretically objects could collide and not lose kinetic energy. This created the two types of collision inelastic and elastic. Elastic defines collisions that have no change in kinetic energy, these are usually microscopic such as Rutherford Scattering. All other objects tend to be inelastic since some energy in lost between the objects and so their respective kinetic energy changes. However, some objects can stick together and therefore combine their masses. This is a special case of inelastic collisions and tend to be a small portion of collisions that actually occur in real life, but some examples seen are when car&#039;s collide or when a sticky substance stays on the object it is throw at.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
There are several other topics within this wiki that can give you more information on collisions as a whole including&lt;br /&gt;
[[Inelastic Collisions]] and [[Elastic Collisions]]. These topics along with the basic fundamentals such as [[Kinetic Energy]] and [[ Momentum Principle]] that we used to derive the equations will show how exactly maximally inelastic collisions are shown by classical physics.&lt;br /&gt;
===Further reading===&lt;br /&gt;
These extensive resources cover this topic in more depth&lt;br /&gt;
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]&lt;br /&gt;
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]&lt;br /&gt;
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]&lt;br /&gt;
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]&lt;br /&gt;
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]&lt;br /&gt;
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]&lt;br /&gt;
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]&lt;br /&gt;
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
These are some internet articles that can show more animations and pictures to help understand this concept&lt;br /&gt;
*[http://www.ux1.eiu.edu/~cfadd/1150/07Mom/Inelastic.html Inelastic Collisions]&lt;br /&gt;
*[http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:examples:maximally_inelastic_collision_of_two_identical_carts Carts]&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
This section contains the the references you used while writing this page&lt;br /&gt;
&lt;br /&gt;
[[Category:Inelastic Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3722</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3722"/>
		<updated>2015-11-29T22:20:59Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* References */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy change? The specific heat of the block and bullet is 6 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt; which is 1.961 m/s.&lt;br /&gt;
Now we can use the conservation of Energy principle to solve for the thermal energy: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0.  &amp;lt;/math&amp;gt; Then we break the change of kinetic energy into it&#039;s initial and final conditions to get :&lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,bullet}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the values we get : &lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(v_{final})^2}{(m_{final})} - (\frac{1}{2}{m_{bullet} (v_{bullet})^2}) &amp;lt;/math&amp;gt;. &lt;br /&gt;
Entering the values from the word problem, our final answer is 490J.&lt;br /&gt;
&lt;br /&gt;
To find the change in temperature, we need to use the heat equation : &amp;lt;math&amp;gt; Q = mCΔT &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the given information of specific heat, thermal energy that we solved for, and the mass of the final object, we get an increase of 16 degrees.&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
[[File: 11-091-playground.jpg |border|right]]&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039; &lt;br /&gt;
Sally (5 years old) is at the playground and decides that she wants to go on the ride that spins really fast in circles. The playground ride consists of a disk of mass M = 57 kg and radius R = 2.0 m mounted on a low-friction axle. Sally weighs about 20 kg. She is super excited to play and runs at speed of 3 m/s on a line tangential to the disk and jumps onto the outer edge of the disk. She initially decided to just run around and spin the wheel, but later she decides that she wants to jump on and let the wheel keep going. What is the change of energy of the system?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
&lt;br /&gt;
This topic is very important in my major, Chemical Engineering. Chemical processes deal with with heat flow and transporting chemicals. A hypothetical situation would be creating polyethylene glycol. This is a compound made by combining many ethylene oxides. This process is essentially an maximally inelastic collision, because the ethylene oxides will have their own flow rate from a a previous process that creates the molecule. This ethylene oxide will enter a new chamber and combine with the previous polyethylene glycol chain that is moving around to form a new molecule that now is a combination of the two and has a new velocity. So there will be a change of kinetic energy and in the form of heat since there are new bonds being formed. To keep the process going the heat must either be cooled or heated depending the chemical engineer&#039;s desire to stop or continue formation of polyethylene glycol. The change in thermal energy is key to this process and is created by this maximally inelastic collision that occurs.&lt;br /&gt;
&lt;br /&gt;
[[File:pet.gif]]&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
The idea of maximally inelastic collisions is part of the conservation of linear momentum which is implied by Newton&#039;s Laws. Most objects tend to bounce off each other creating the idea of collision. Most objects that are visibly colliding tend to lose energy through a variety of ways but theoretically objects could collide and not lose kinetic energy. This created the two types of collision inelastic and elastic. Elastic defines collisions that have no change in kinetic energy, these are usually microscopic such as Rutherford Scattering. All other objects tend to be inelastic since some energy in lost between the objects and so their respective kinetic energy changes. However, some objects can stick together and therefore combine their masses. This is a special case of inelastic collisions and tend to be a small portion of collisions that actually occur in real life, but some examples seen are when car&#039;s collide or when a sticky substance stays on the object it is throw at.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
There are several other topics within this wiki that can give you more information on collisions as a whole including&lt;br /&gt;
[[Inelastic Collisions]] and [[Elastic Collisions]]. These topics along with the basic fundamentals such as [[Kinetic Energy]] and [[ Momentum Principle]] that we used to derive the equations will show how exactly maximally inelastic collisions are shown by classical physics.&lt;br /&gt;
===Further reading===&lt;br /&gt;
These extensive resources cover this topic in more depth&lt;br /&gt;
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]&lt;br /&gt;
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]&lt;br /&gt;
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]&lt;br /&gt;
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]&lt;br /&gt;
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]&lt;br /&gt;
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]&lt;br /&gt;
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]&lt;br /&gt;
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
These are some internet articles that can show more animations and pictures to help understand this concept&lt;br /&gt;
*[http://www.ux1.eiu.edu/~cfadd/1150/07Mom/Inelastic.html Inelastic Collisions]&lt;br /&gt;
*[http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:examples:maximally_inelastic_collision_of_two_identical_carts Carts]&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
This section contains the the references you used while writing this page&lt;br /&gt;
&lt;br /&gt;
[[Category:Collision]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3716</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3716"/>
		<updated>2015-11-29T22:19:59Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* External links */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy change? The specific heat of the block and bullet is 6 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt; which is 1.961 m/s.&lt;br /&gt;
Now we can use the conservation of Energy principle to solve for the thermal energy: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0.  &amp;lt;/math&amp;gt; Then we break the change of kinetic energy into it&#039;s initial and final conditions to get :&lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,bullet}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the values we get : &lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(v_{final})^2}{(m_{final})} - (\frac{1}{2}{m_{bullet} (v_{bullet})^2}) &amp;lt;/math&amp;gt;. &lt;br /&gt;
Entering the values from the word problem, our final answer is 490J.&lt;br /&gt;
&lt;br /&gt;
To find the change in temperature, we need to use the heat equation : &amp;lt;math&amp;gt; Q = mCΔT &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the given information of specific heat, thermal energy that we solved for, and the mass of the final object, we get an increase of 16 degrees.&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
[[File: 11-091-playground.jpg |border|right]]&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039; &lt;br /&gt;
Sally (5 years old) is at the playground and decides that she wants to go on the ride that spins really fast in circles. The playground ride consists of a disk of mass M = 57 kg and radius R = 2.0 m mounted on a low-friction axle. Sally weighs about 20 kg. She is super excited to play and runs at speed of 3 m/s on a line tangential to the disk and jumps onto the outer edge of the disk. She initially decided to just run around and spin the wheel, but later she decides that she wants to jump on and let the wheel keep going. What is the change of energy of the system?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
&lt;br /&gt;
This topic is very important in my major, Chemical Engineering. Chemical processes deal with with heat flow and transporting chemicals. A hypothetical situation would be creating polyethylene glycol. This is a compound made by combining many ethylene oxides. This process is essentially an maximally inelastic collision, because the ethylene oxides will have their own flow rate from a a previous process that creates the molecule. This ethylene oxide will enter a new chamber and combine with the previous polyethylene glycol chain that is moving around to form a new molecule that now is a combination of the two and has a new velocity. So there will be a change of kinetic energy and in the form of heat since there are new bonds being formed. To keep the process going the heat must either be cooled or heated depending the chemical engineer&#039;s desire to stop or continue formation of polyethylene glycol. The change in thermal energy is key to this process and is created by this maximally inelastic collision that occurs.&lt;br /&gt;
&lt;br /&gt;
[[File:pet.gif]]&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
The idea of maximally inelastic collisions is part of the conservation of linear momentum which is implied by Newton&#039;s Laws. Most objects tend to bounce off each other creating the idea of collision. Most objects that are visibly colliding tend to lose energy through a variety of ways but theoretically objects could collide and not lose kinetic energy. This created the two types of collision inelastic and elastic. Elastic defines collisions that have no change in kinetic energy, these are usually microscopic such as Rutherford Scattering. All other objects tend to be inelastic since some energy in lost between the objects and so their respective kinetic energy changes. However, some objects can stick together and therefore combine their masses. This is a special case of inelastic collisions and tend to be a small portion of collisions that actually occur in real life, but some examples seen are when car&#039;s collide or when a sticky substance stays on the object it is throw at.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
There are several other topics within this wiki that can give you more information on collisions as a whole including&lt;br /&gt;
[[Inelastic Collisions]] and [[Elastic Collisions]]. These topics along with the basic fundamentals such as [[Kinetic Energy]] and [[ Momentum Principle]] that we used to derive the equations will show how exactly maximally inelastic collisions are shown by classical physics.&lt;br /&gt;
===Further reading===&lt;br /&gt;
These extensive resources cover this topic in more depth&lt;br /&gt;
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]&lt;br /&gt;
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]&lt;br /&gt;
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]&lt;br /&gt;
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]&lt;br /&gt;
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]&lt;br /&gt;
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]&lt;br /&gt;
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]&lt;br /&gt;
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
These are some internet articles that can show more animations and pictures to help understand this concept&lt;br /&gt;
*[http://www.ux1.eiu.edu/~cfadd/1150/07Mom/Inelastic.html Inelastic Collisions]&lt;br /&gt;
*[http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:examples:maximally_inelastic_collision_of_two_identical_carts Carts]&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
This section contains the the references you used while writing this page&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3710</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3710"/>
		<updated>2015-11-29T22:18:25Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* Further reading */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy change? The specific heat of the block and bullet is 6 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt; which is 1.961 m/s.&lt;br /&gt;
Now we can use the conservation of Energy principle to solve for the thermal energy: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0.  &amp;lt;/math&amp;gt; Then we break the change of kinetic energy into it&#039;s initial and final conditions to get :&lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,bullet}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the values we get : &lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(v_{final})^2}{(m_{final})} - (\frac{1}{2}{m_{bullet} (v_{bullet})^2}) &amp;lt;/math&amp;gt;. &lt;br /&gt;
Entering the values from the word problem, our final answer is 490J.&lt;br /&gt;
&lt;br /&gt;
To find the change in temperature, we need to use the heat equation : &amp;lt;math&amp;gt; Q = mCΔT &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the given information of specific heat, thermal energy that we solved for, and the mass of the final object, we get an increase of 16 degrees.&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
[[File: 11-091-playground.jpg |border|right]]&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039; &lt;br /&gt;
Sally (5 years old) is at the playground and decides that she wants to go on the ride that spins really fast in circles. The playground ride consists of a disk of mass M = 57 kg and radius R = 2.0 m mounted on a low-friction axle. Sally weighs about 20 kg. She is super excited to play and runs at speed of 3 m/s on a line tangential to the disk and jumps onto the outer edge of the disk. She initially decided to just run around and spin the wheel, but later she decides that she wants to jump on and let the wheel keep going. What is the change of energy of the system?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
&lt;br /&gt;
This topic is very important in my major, Chemical Engineering. Chemical processes deal with with heat flow and transporting chemicals. A hypothetical situation would be creating polyethylene glycol. This is a compound made by combining many ethylene oxides. This process is essentially an maximally inelastic collision, because the ethylene oxides will have their own flow rate from a a previous process that creates the molecule. This ethylene oxide will enter a new chamber and combine with the previous polyethylene glycol chain that is moving around to form a new molecule that now is a combination of the two and has a new velocity. So there will be a change of kinetic energy and in the form of heat since there are new bonds being formed. To keep the process going the heat must either be cooled or heated depending the chemical engineer&#039;s desire to stop or continue formation of polyethylene glycol. The change in thermal energy is key to this process and is created by this maximally inelastic collision that occurs.&lt;br /&gt;
&lt;br /&gt;
[[File:pet.gif]]&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
The idea of maximally inelastic collisions is part of the conservation of linear momentum which is implied by Newton&#039;s Laws. Most objects tend to bounce off each other creating the idea of collision. Most objects that are visibly colliding tend to lose energy through a variety of ways but theoretically objects could collide and not lose kinetic energy. This created the two types of collision inelastic and elastic. Elastic defines collisions that have no change in kinetic energy, these are usually microscopic such as Rutherford Scattering. All other objects tend to be inelastic since some energy in lost between the objects and so their respective kinetic energy changes. However, some objects can stick together and therefore combine their masses. This is a special case of inelastic collisions and tend to be a small portion of collisions that actually occur in real life, but some examples seen are when car&#039;s collide or when a sticky substance stays on the object it is throw at.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
There are several other topics within this wiki that can give you more information on collisions as a whole including&lt;br /&gt;
[[Inelastic Collisions]] and [[Elastic Collisions]]. These topics along with the basic fundamentals such as [[Kinetic Energy]] and [[ Momentum Principle]] that we used to derive the equations will show how exactly maximally inelastic collisions are shown by classical physics.&lt;br /&gt;
===Further reading===&lt;br /&gt;
These extensive resources cover this topic in more depth&lt;br /&gt;
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]&lt;br /&gt;
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]&lt;br /&gt;
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]&lt;br /&gt;
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]&lt;br /&gt;
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]&lt;br /&gt;
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]&lt;br /&gt;
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]&lt;br /&gt;
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
Internet resources on this topic&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
This section contains the the references you used while writing this page&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3707</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3707"/>
		<updated>2015-11-29T22:16:50Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* See also */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy change? The specific heat of the block and bullet is 6 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt; which is 1.961 m/s.&lt;br /&gt;
Now we can use the conservation of Energy principle to solve for the thermal energy: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0.  &amp;lt;/math&amp;gt; Then we break the change of kinetic energy into it&#039;s initial and final conditions to get :&lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,bullet}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the values we get : &lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(v_{final})^2}{(m_{final})} - (\frac{1}{2}{m_{bullet} (v_{bullet})^2}) &amp;lt;/math&amp;gt;. &lt;br /&gt;
Entering the values from the word problem, our final answer is 490J.&lt;br /&gt;
&lt;br /&gt;
To find the change in temperature, we need to use the heat equation : &amp;lt;math&amp;gt; Q = mCΔT &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the given information of specific heat, thermal energy that we solved for, and the mass of the final object, we get an increase of 16 degrees.&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
[[File: 11-091-playground.jpg |border|right]]&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039; &lt;br /&gt;
Sally (5 years old) is at the playground and decides that she wants to go on the ride that spins really fast in circles. The playground ride consists of a disk of mass M = 57 kg and radius R = 2.0 m mounted on a low-friction axle. Sally weighs about 20 kg. She is super excited to play and runs at speed of 3 m/s on a line tangential to the disk and jumps onto the outer edge of the disk. She initially decided to just run around and spin the wheel, but later she decides that she wants to jump on and let the wheel keep going. What is the change of energy of the system?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
&lt;br /&gt;
This topic is very important in my major, Chemical Engineering. Chemical processes deal with with heat flow and transporting chemicals. A hypothetical situation would be creating polyethylene glycol. This is a compound made by combining many ethylene oxides. This process is essentially an maximally inelastic collision, because the ethylene oxides will have their own flow rate from a a previous process that creates the molecule. This ethylene oxide will enter a new chamber and combine with the previous polyethylene glycol chain that is moving around to form a new molecule that now is a combination of the two and has a new velocity. So there will be a change of kinetic energy and in the form of heat since there are new bonds being formed. To keep the process going the heat must either be cooled or heated depending the chemical engineer&#039;s desire to stop or continue formation of polyethylene glycol. The change in thermal energy is key to this process and is created by this maximally inelastic collision that occurs.&lt;br /&gt;
&lt;br /&gt;
[[File:pet.gif]]&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
The idea of maximally inelastic collisions is part of the conservation of linear momentum which is implied by Newton&#039;s Laws. Most objects tend to bounce off each other creating the idea of collision. Most objects that are visibly colliding tend to lose energy through a variety of ways but theoretically objects could collide and not lose kinetic energy. This created the two types of collision inelastic and elastic. Elastic defines collisions that have no change in kinetic energy, these are usually microscopic such as Rutherford Scattering. All other objects tend to be inelastic since some energy in lost between the objects and so their respective kinetic energy changes. However, some objects can stick together and therefore combine their masses. This is a special case of inelastic collisions and tend to be a small portion of collisions that actually occur in real life, but some examples seen are when car&#039;s collide or when a sticky substance stays on the object it is throw at.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
There are several other topics within this wiki that can give you more information on collisions as a whole including&lt;br /&gt;
[[Inelastic Collisions]] and [[Elastic Collisions]]. These topics along with the basic fundamentals such as [[Kinetic Energy]] and [[ Momentum Principle]] that we used to derive the equations will show how exactly maximally inelastic collisions are shown by classical physics.&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
Books, Articles or other print media on this topic&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
Internet resources on this topic&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
This section contains the the references you used while writing this page&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3706</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3706"/>
		<updated>2015-11-29T22:16:16Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* See also */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy change? The specific heat of the block and bullet is 6 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt; which is 1.961 m/s.&lt;br /&gt;
Now we can use the conservation of Energy principle to solve for the thermal energy: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0.  &amp;lt;/math&amp;gt; Then we break the change of kinetic energy into it&#039;s initial and final conditions to get :&lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,bullet}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the values we get : &lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(v_{final})^2}{(m_{final})} - (\frac{1}{2}{m_{bullet} (v_{bullet})^2}) &amp;lt;/math&amp;gt;. &lt;br /&gt;
Entering the values from the word problem, our final answer is 490J.&lt;br /&gt;
&lt;br /&gt;
To find the change in temperature, we need to use the heat equation : &amp;lt;math&amp;gt; Q = mCΔT &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the given information of specific heat, thermal energy that we solved for, and the mass of the final object, we get an increase of 16 degrees.&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
[[File: 11-091-playground.jpg |border|right]]&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039; &lt;br /&gt;
Sally (5 years old) is at the playground and decides that she wants to go on the ride that spins really fast in circles. The playground ride consists of a disk of mass M = 57 kg and radius R = 2.0 m mounted on a low-friction axle. Sally weighs about 20 kg. She is super excited to play and runs at speed of 3 m/s on a line tangential to the disk and jumps onto the outer edge of the disk. She initially decided to just run around and spin the wheel, but later she decides that she wants to jump on and let the wheel keep going. What is the change of energy of the system?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
&lt;br /&gt;
This topic is very important in my major, Chemical Engineering. Chemical processes deal with with heat flow and transporting chemicals. A hypothetical situation would be creating polyethylene glycol. This is a compound made by combining many ethylene oxides. This process is essentially an maximally inelastic collision, because the ethylene oxides will have their own flow rate from a a previous process that creates the molecule. This ethylene oxide will enter a new chamber and combine with the previous polyethylene glycol chain that is moving around to form a new molecule that now is a combination of the two and has a new velocity. So there will be a change of kinetic energy and in the form of heat since there are new bonds being formed. To keep the process going the heat must either be cooled or heated depending the chemical engineer&#039;s desire to stop or continue formation of polyethylene glycol. The change in thermal energy is key to this process and is created by this maximally inelastic collision that occurs.&lt;br /&gt;
&lt;br /&gt;
[[File:pet.gif]]&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
The idea of maximally inelastic collisions is part of the conservation of linear momentum which is implied by Newton&#039;s Laws. Most objects tend to bounce off each other creating the idea of collision. Most objects that are visibly colliding tend to lose energy through a variety of ways but theoretically objects could collide and not lose kinetic energy. This created the two types of collision inelastic and elastic. Elastic defines collisions that have no change in kinetic energy, these are usually microscopic such as Rutherford Scattering. All other objects tend to be inelastic since some energy in lost between the objects and so their respective kinetic energy changes. However, some objects can stick together and therefore combine their masses. This is a special case of inelastic collisions and tend to be a small portion of collisions that actually occur in real life, but some examples seen are when car&#039;s collide or when a sticky substance stays on the object it is throw at.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
There are several other topics within this wiki that can give you more information on collisions as a whole including&lt;br /&gt;
[[Inelastic Collisions]] and [[Elastic Collisions]]. These topics along with the basic fundamentals such as [[Kinetic Energy]] and [[Linear Momentum]] that we used to derive the equations will show how exactly maximally inelastic collisions are shown by classical physics.&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
Books, Articles or other print media on this topic&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
Internet resources on this topic&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
This section contains the the references you used while writing this page&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3705</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3705"/>
		<updated>2015-11-29T22:16:01Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* See also */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy change? The specific heat of the block and bullet is 6 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt; which is 1.961 m/s.&lt;br /&gt;
Now we can use the conservation of Energy principle to solve for the thermal energy: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0.  &amp;lt;/math&amp;gt; Then we break the change of kinetic energy into it&#039;s initial and final conditions to get :&lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,bullet}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the values we get : &lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(v_{final})^2}{(m_{final})} - (\frac{1}{2}{m_{bullet} (v_{bullet})^2}) &amp;lt;/math&amp;gt;. &lt;br /&gt;
Entering the values from the word problem, our final answer is 490J.&lt;br /&gt;
&lt;br /&gt;
To find the change in temperature, we need to use the heat equation : &amp;lt;math&amp;gt; Q = mCΔT &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the given information of specific heat, thermal energy that we solved for, and the mass of the final object, we get an increase of 16 degrees.&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
[[File: 11-091-playground.jpg |border|right]]&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039; &lt;br /&gt;
Sally (5 years old) is at the playground and decides that she wants to go on the ride that spins really fast in circles. The playground ride consists of a disk of mass M = 57 kg and radius R = 2.0 m mounted on a low-friction axle. Sally weighs about 20 kg. She is super excited to play and runs at speed of 3 m/s on a line tangential to the disk and jumps onto the outer edge of the disk. She initially decided to just run around and spin the wheel, but later she decides that she wants to jump on and let the wheel keep going. What is the change of energy of the system?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
&lt;br /&gt;
This topic is very important in my major, Chemical Engineering. Chemical processes deal with with heat flow and transporting chemicals. A hypothetical situation would be creating polyethylene glycol. This is a compound made by combining many ethylene oxides. This process is essentially an maximally inelastic collision, because the ethylene oxides will have their own flow rate from a a previous process that creates the molecule. This ethylene oxide will enter a new chamber and combine with the previous polyethylene glycol chain that is moving around to form a new molecule that now is a combination of the two and has a new velocity. So there will be a change of kinetic energy and in the form of heat since there are new bonds being formed. To keep the process going the heat must either be cooled or heated depending the chemical engineer&#039;s desire to stop or continue formation of polyethylene glycol. The change in thermal energy is key to this process and is created by this maximally inelastic collision that occurs.&lt;br /&gt;
&lt;br /&gt;
[[File:pet.gif]]&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
The idea of maximally inelastic collisions is part of the conservation of linear momentum which is implied by Newton&#039;s Laws. Most objects tend to bounce off each other creating the idea of collision. Most objects that are visibly colliding tend to lose energy through a variety of ways but theoretically objects could collide and not lose kinetic energy. This created the two types of collision inelastic and elastic. Elastic defines collisions that have no change in kinetic energy, these are usually microscopic such as Rutherford Scattering. All other objects tend to be inelastic since some energy in lost between the objects and so their respective kinetic energy changes. However, some objects can stick together and therefore combine their masses. This is a special case of inelastic collisions and tend to be a small portion of collisions that actually occur in real life, but some examples seen are when car&#039;s collide or when a sticky substance stays on the object it is throw at.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
There are several other topics within this wiki that can give you more information on collisions as a whole including&lt;br /&gt;
[[Inelastic Collisions]] and [[Elastic Collisions]]. These topics along with the basic fundamentals such as [[Kinetic Energy]] and [[Momentum]] that we used to derive the equations will show how exactly maximally inelastic collisions are shown by classical physics.&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
Books, Articles or other print media on this topic&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
Internet resources on this topic&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
This section contains the the references you used while writing this page&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3702</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3702"/>
		<updated>2015-11-29T22:14:53Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* See also */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy change? The specific heat of the block and bullet is 6 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt; which is 1.961 m/s.&lt;br /&gt;
Now we can use the conservation of Energy principle to solve for the thermal energy: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0.  &amp;lt;/math&amp;gt; Then we break the change of kinetic energy into it&#039;s initial and final conditions to get :&lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,bullet}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the values we get : &lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(v_{final})^2}{(m_{final})} - (\frac{1}{2}{m_{bullet} (v_{bullet})^2}) &amp;lt;/math&amp;gt;. &lt;br /&gt;
Entering the values from the word problem, our final answer is 490J.&lt;br /&gt;
&lt;br /&gt;
To find the change in temperature, we need to use the heat equation : &amp;lt;math&amp;gt; Q = mCΔT &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the given information of specific heat, thermal energy that we solved for, and the mass of the final object, we get an increase of 16 degrees.&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
[[File: 11-091-playground.jpg |border|right]]&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039; &lt;br /&gt;
Sally (5 years old) is at the playground and decides that she wants to go on the ride that spins really fast in circles. The playground ride consists of a disk of mass M = 57 kg and radius R = 2.0 m mounted on a low-friction axle. Sally weighs about 20 kg. She is super excited to play and runs at speed of 3 m/s on a line tangential to the disk and jumps onto the outer edge of the disk. She initially decided to just run around and spin the wheel, but later she decides that she wants to jump on and let the wheel keep going. What is the change of energy of the system?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
&lt;br /&gt;
This topic is very important in my major, Chemical Engineering. Chemical processes deal with with heat flow and transporting chemicals. A hypothetical situation would be creating polyethylene glycol. This is a compound made by combining many ethylene oxides. This process is essentially an maximally inelastic collision, because the ethylene oxides will have their own flow rate from a a previous process that creates the molecule. This ethylene oxide will enter a new chamber and combine with the previous polyethylene glycol chain that is moving around to form a new molecule that now is a combination of the two and has a new velocity. So there will be a change of kinetic energy and in the form of heat since there are new bonds being formed. To keep the process going the heat must either be cooled or heated depending the chemical engineer&#039;s desire to stop or continue formation of polyethylene glycol. The change in thermal energy is key to this process and is created by this maximally inelastic collision that occurs.&lt;br /&gt;
&lt;br /&gt;
[[File:pet.gif]]&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
The idea of maximally inelastic collisions is part of the conservation of linear momentum which is implied by Newton&#039;s Laws. Most objects tend to bounce off each other creating the idea of collision. Most objects that are visibly colliding tend to lose energy through a variety of ways but theoretically objects could collide and not lose kinetic energy. This created the two types of collision inelastic and elastic. Elastic defines collisions that have no change in kinetic energy, these are usually microscopic such as Rutherford Scattering. All other objects tend to be inelastic since some energy in lost between the objects and so their respective kinetic energy changes. However, some objects can stick together and therefore combine their masses. This is a special case of inelastic collisions and tend to be a small portion of collisions that actually occur in real life, but some examples seen are when car&#039;s collide or when a sticky substance stays on the object it is throw at.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
There are several other topics within this wiki that can give you more information on collisions as a whole including&lt;br /&gt;
[[Inelastic Collisions]] and [[Elastic Collisions]]&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
Books, Articles or other print media on this topic&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
Internet resources on this topic&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
This section contains the the references you used while writing this page&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3699</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3699"/>
		<updated>2015-11-29T22:12:52Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* Connectedness */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy change? The specific heat of the block and bullet is 6 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt; which is 1.961 m/s.&lt;br /&gt;
Now we can use the conservation of Energy principle to solve for the thermal energy: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0.  &amp;lt;/math&amp;gt; Then we break the change of kinetic energy into it&#039;s initial and final conditions to get :&lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,bullet}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the values we get : &lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(v_{final})^2}{(m_{final})} - (\frac{1}{2}{m_{bullet} (v_{bullet})^2}) &amp;lt;/math&amp;gt;. &lt;br /&gt;
Entering the values from the word problem, our final answer is 490J.&lt;br /&gt;
&lt;br /&gt;
To find the change in temperature, we need to use the heat equation : &amp;lt;math&amp;gt; Q = mCΔT &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the given information of specific heat, thermal energy that we solved for, and the mass of the final object, we get an increase of 16 degrees.&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
[[File: 11-091-playground.jpg |border|right]]&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039; &lt;br /&gt;
Sally (5 years old) is at the playground and decides that she wants to go on the ride that spins really fast in circles. The playground ride consists of a disk of mass M = 57 kg and radius R = 2.0 m mounted on a low-friction axle. Sally weighs about 20 kg. She is super excited to play and runs at speed of 3 m/s on a line tangential to the disk and jumps onto the outer edge of the disk. She initially decided to just run around and spin the wheel, but later she decides that she wants to jump on and let the wheel keep going. What is the change of energy of the system?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
&lt;br /&gt;
This topic is very important in my major, Chemical Engineering. Chemical processes deal with with heat flow and transporting chemicals. A hypothetical situation would be creating polyethylene glycol. This is a compound made by combining many ethylene oxides. This process is essentially an maximally inelastic collision, because the ethylene oxides will have their own flow rate from a a previous process that creates the molecule. This ethylene oxide will enter a new chamber and combine with the previous polyethylene glycol chain that is moving around to form a new molecule that now is a combination of the two and has a new velocity. So there will be a change of kinetic energy and in the form of heat since there are new bonds being formed. To keep the process going the heat must either be cooled or heated depending the chemical engineer&#039;s desire to stop or continue formation of polyethylene glycol. The change in thermal energy is key to this process and is created by this maximally inelastic collision that occurs.&lt;br /&gt;
&lt;br /&gt;
[[File:pet.gif]]&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
The idea of maximally inelastic collisions is part of the conservation of linear momentum which is implied by Newton&#039;s Laws. Most objects tend to bounce off each other creating the idea of collision. Most objects that are visibly colliding tend to lose energy through a variety of ways but theoretically objects could collide and not lose kinetic energy. This created the two types of collision inelastic and elastic. Elastic defines collisions that have no change in kinetic energy, these are usually microscopic such as Rutherford Scattering. All other objects tend to be inelastic since some energy in lost between the objects and so their respective kinetic energy changes. However, some objects can stick together and therefore combine their masses. This is a special case of inelastic collisions and tend to be a small portion of collisions that actually occur in real life, but some examples seen are when car&#039;s collide or when a sticky substance stays on the object it is throw at.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Are there related topics or categories in this wiki resource for the curious reader to explore?  How does this topic fit into that context?&lt;br /&gt;
&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
Books, Articles or other print media on this topic&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
Internet resources on this topic&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
This section contains the the references you used while writing this page&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=File:Pet.gif&amp;diff=3697</id>
		<title>File:Pet.gif</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=File:Pet.gif&amp;diff=3697"/>
		<updated>2015-11-29T22:12:26Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3695</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3695"/>
		<updated>2015-11-29T22:12:10Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* Connectedness */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy change? The specific heat of the block and bullet is 6 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt; which is 1.961 m/s.&lt;br /&gt;
Now we can use the conservation of Energy principle to solve for the thermal energy: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0.  &amp;lt;/math&amp;gt; Then we break the change of kinetic energy into it&#039;s initial and final conditions to get :&lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,bullet}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the values we get : &lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(v_{final})^2}{(m_{final})} - (\frac{1}{2}{m_{bullet} (v_{bullet})^2}) &amp;lt;/math&amp;gt;. &lt;br /&gt;
Entering the values from the word problem, our final answer is 490J.&lt;br /&gt;
&lt;br /&gt;
To find the change in temperature, we need to use the heat equation : &amp;lt;math&amp;gt; Q = mCΔT &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the given information of specific heat, thermal energy that we solved for, and the mass of the final object, we get an increase of 16 degrees.&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
[[File: 11-091-playground.jpg |border|right]]&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039; &lt;br /&gt;
Sally (5 years old) is at the playground and decides that she wants to go on the ride that spins really fast in circles. The playground ride consists of a disk of mass M = 57 kg and radius R = 2.0 m mounted on a low-friction axle. Sally weighs about 20 kg. She is super excited to play and runs at speed of 3 m/s on a line tangential to the disk and jumps onto the outer edge of the disk. She initially decided to just run around and spin the wheel, but later she decides that she wants to jump on and let the wheel keep going. What is the change of energy of the system?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
&lt;br /&gt;
This topic is very important in my major, Chemical Engineering. Chemical processes deal with with heat flow and transporting chemicals. A hypothetical situation would be creating polyethylene glycol. This is a compound made by combining many ethylene oxides. This process is essentially an maximally inelastic collision, because the ethylene oxides will have their own flow rate from a a previous process that creates the molecule. This ethylene oxide will enter a new chamber and combine with the previous polyethylene glycol chain that is moving around to form a new molecule that now is a combination of the two and has a new velocity. So there will be a change of kinetic energy and in the form of heat since there are new bonds being formed. To keep the process going the heat must either be cooled or heated depending the chemical engineer&#039;s desire to stop or continue formation of polyethylene glycol. The change in thermal energy is key to this process and is created by this maximally inelastic collision that occurs.&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
The idea of maximally inelastic collisions is part of the conservation of linear momentum which is implied by Newton&#039;s Laws. Most objects tend to bounce off each other creating the idea of collision. Most objects that are visibly colliding tend to lose energy through a variety of ways but theoretically objects could collide and not lose kinetic energy. This created the two types of collision inelastic and elastic. Elastic defines collisions that have no change in kinetic energy, these are usually microscopic such as Rutherford Scattering. All other objects tend to be inelastic since some energy in lost between the objects and so their respective kinetic energy changes. However, some objects can stick together and therefore combine their masses. This is a special case of inelastic collisions and tend to be a small portion of collisions that actually occur in real life, but some examples seen are when car&#039;s collide or when a sticky substance stays on the object it is throw at.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Are there related topics or categories in this wiki resource for the curious reader to explore?  How does this topic fit into that context?&lt;br /&gt;
&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
Books, Articles or other print media on this topic&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
Internet resources on this topic&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
This section contains the the references you used while writing this page&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3684</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3684"/>
		<updated>2015-11-29T22:03:17Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* Difficult */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy change? The specific heat of the block and bullet is 6 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt; which is 1.961 m/s.&lt;br /&gt;
Now we can use the conservation of Energy principle to solve for the thermal energy: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0.  &amp;lt;/math&amp;gt; Then we break the change of kinetic energy into it&#039;s initial and final conditions to get :&lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,bullet}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the values we get : &lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(v_{final})^2}{(m_{final})} - (\frac{1}{2}{m_{bullet} (v_{bullet})^2}) &amp;lt;/math&amp;gt;. &lt;br /&gt;
Entering the values from the word problem, our final answer is 490J.&lt;br /&gt;
&lt;br /&gt;
To find the change in temperature, we need to use the heat equation : &amp;lt;math&amp;gt; Q = mCΔT &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the given information of specific heat, thermal energy that we solved for, and the mass of the final object, we get an increase of 16 degrees.&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
[[File: 11-091-playground.jpg |border|right]]&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039; &lt;br /&gt;
Sally (5 years old) is at the playground and decides that she wants to go on the ride that spins really fast in circles. The playground ride consists of a disk of mass M = 57 kg and radius R = 2.0 m mounted on a low-friction axle. Sally weighs about 20 kg. She is super excited to play and runs at speed of 3 m/s on a line tangential to the disk and jumps onto the outer edge of the disk. She initially decided to just run around and spin the wheel, but later she decides that she wants to jump on and let the wheel keep going. What is the change of energy of the system?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
#How is this topic connected to something that you are interested in?&lt;br /&gt;
#How is it connected to your major?&lt;br /&gt;
#Is there an interesting industrial application?&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
The idea of maximally inelastic collisions is part of the conservation of linear momentum which is implied by Newton&#039;s Laws. Most objects tend to bounce off each other creating the idea of collision. Most objects that are visibly colliding tend to lose energy through a variety of ways but theoretically objects could collide and not lose kinetic energy. This created the two types of collision inelastic and elastic. Elastic defines collisions that have no change in kinetic energy, these are usually microscopic such as Rutherford Scattering. All other objects tend to be inelastic since some energy in lost between the objects and so their respective kinetic energy changes. However, some objects can stick together and therefore combine their masses. This is a special case of inelastic collisions and tend to be a small portion of collisions that actually occur in real life, but some examples seen are when car&#039;s collide or when a sticky substance stays on the object it is throw at.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Are there related topics or categories in this wiki resource for the curious reader to explore?  How does this topic fit into that context?&lt;br /&gt;
&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
Books, Articles or other print media on this topic&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
Internet resources on this topic&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
This section contains the the references you used while writing this page&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3681</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3681"/>
		<updated>2015-11-29T22:01:39Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* Difficult */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy change? The specific heat of the block and bullet is 6 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt; which is 1.961 m/s.&lt;br /&gt;
Now we can use the conservation of Energy principle to solve for the thermal energy: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0.  &amp;lt;/math&amp;gt; Then we break the change of kinetic energy into it&#039;s initial and final conditions to get :&lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,bullet}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the values we get : &lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(v_{final})^2}{(m_{final})} - (\frac{1}{2}{m_{bullet} (v_{bullet})^2}) &amp;lt;/math&amp;gt;. &lt;br /&gt;
Entering the values from the word problem, our final answer is 490J.&lt;br /&gt;
&lt;br /&gt;
To find the change in temperature, we need to use the heat equation : &amp;lt;math&amp;gt; Q = mCΔT &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the given information of specific heat, thermal energy that we solved for, and the mass of the final object, we get an increase of 16 degrees.&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
[[File: 11-091-playground.jpg |border|right]]&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039; Sally (5 years old) is at the playground and decides that she wants to go on the ride that spins really fast in circles. The playground ride consists of a disk of mass M = 57 kg and radius R = 2.0 m mounted on a low-friction axle. Sally weighs about 20 kg. She is super excited to play and runs at speed of 3 m/s on a line tangential to the disk and jumps onto the outer edge of the disk. She initially decided to just run around and spin the wheel, but later she decides that she wants to jump on and let the wheel keep going. What is the change of energy of the system?&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
#How is this topic connected to something that you are interested in?&lt;br /&gt;
#How is it connected to your major?&lt;br /&gt;
#Is there an interesting industrial application?&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
The idea of maximally inelastic collisions is part of the conservation of linear momentum which is implied by Newton&#039;s Laws. Most objects tend to bounce off each other creating the idea of collision. Most objects that are visibly colliding tend to lose energy through a variety of ways but theoretically objects could collide and not lose kinetic energy. This created the two types of collision inelastic and elastic. Elastic defines collisions that have no change in kinetic energy, these are usually microscopic such as Rutherford Scattering. All other objects tend to be inelastic since some energy in lost between the objects and so their respective kinetic energy changes. However, some objects can stick together and therefore combine their masses. This is a special case of inelastic collisions and tend to be a small portion of collisions that actually occur in real life, but some examples seen are when car&#039;s collide or when a sticky substance stays on the object it is throw at.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Are there related topics or categories in this wiki resource for the curious reader to explore?  How does this topic fit into that context?&lt;br /&gt;
&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
Books, Articles or other print media on this topic&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
Internet resources on this topic&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
This section contains the the references you used while writing this page&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3679</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3679"/>
		<updated>2015-11-29T22:01:05Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* Difficult */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy change? The specific heat of the block and bullet is 6 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt; which is 1.961 m/s.&lt;br /&gt;
Now we can use the conservation of Energy principle to solve for the thermal energy: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0.  &amp;lt;/math&amp;gt; Then we break the change of kinetic energy into it&#039;s initial and final conditions to get :&lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,bullet}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the values we get : &lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(v_{final})^2}{(m_{final})} - (\frac{1}{2}{m_{bullet} (v_{bullet})^2}) &amp;lt;/math&amp;gt;. &lt;br /&gt;
Entering the values from the word problem, our final answer is 490J.&lt;br /&gt;
&lt;br /&gt;
To find the change in temperature, we need to use the heat equation : &amp;lt;math&amp;gt; Q = mCΔT &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the given information of specific heat, thermal energy that we solved for, and the mass of the final object, we get an increase of 16 degrees.&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
[[File: 11-091-playground.jpg |&amp;quot;border&amp;quot; |&amp;quot;right&amp;quot;]]&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039; Sally (5 years old) is at the playground and decides that she wants to go on the ride that spins really fast in circles. The playground ride consists of a disk of mass M = 57 kg and radius R = 2.0 m mounted on a low-friction axle. Sally weighs about 20 kg. She is super excited to play and runs at speed of 3 m/s on a line tangential to the disk and jumps onto the outer edge of the disk. She initially decided to just run around and spin the wheel, but later she decides that she wants to jump on and let the wheel keep going. What is the change of energy of the system?&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
#How is this topic connected to something that you are interested in?&lt;br /&gt;
#How is it connected to your major?&lt;br /&gt;
#Is there an interesting industrial application?&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
The idea of maximally inelastic collisions is part of the conservation of linear momentum which is implied by Newton&#039;s Laws. Most objects tend to bounce off each other creating the idea of collision. Most objects that are visibly colliding tend to lose energy through a variety of ways but theoretically objects could collide and not lose kinetic energy. This created the two types of collision inelastic and elastic. Elastic defines collisions that have no change in kinetic energy, these are usually microscopic such as Rutherford Scattering. All other objects tend to be inelastic since some energy in lost between the objects and so their respective kinetic energy changes. However, some objects can stick together and therefore combine their masses. This is a special case of inelastic collisions and tend to be a small portion of collisions that actually occur in real life, but some examples seen are when car&#039;s collide or when a sticky substance stays on the object it is throw at.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Are there related topics or categories in this wiki resource for the curious reader to explore?  How does this topic fit into that context?&lt;br /&gt;
&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
Books, Articles or other print media on this topic&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
Internet resources on this topic&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
This section contains the the references you used while writing this page&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3677</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3677"/>
		<updated>2015-11-29T22:00:33Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* Difficult */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy change? The specific heat of the block and bullet is 6 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt; which is 1.961 m/s.&lt;br /&gt;
Now we can use the conservation of Energy principle to solve for the thermal energy: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0.  &amp;lt;/math&amp;gt; Then we break the change of kinetic energy into it&#039;s initial and final conditions to get :&lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,bullet}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the values we get : &lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(v_{final})^2}{(m_{final})} - (\frac{1}{2}{m_{bullet} (v_{bullet})^2}) &amp;lt;/math&amp;gt;. &lt;br /&gt;
Entering the values from the word problem, our final answer is 490J.&lt;br /&gt;
&lt;br /&gt;
To find the change in temperature, we need to use the heat equation : &amp;lt;math&amp;gt; Q = mCΔT &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the given information of specific heat, thermal energy that we solved for, and the mass of the final object, we get an increase of 16 degrees.&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
[[File: 11-091-playground.jpg &amp;quot;border&amp;quot; &amp;quot;right&amp;quot;]]&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039; Sally (5 years old) is at the playground and decides that she wants to go on the ride that spins really fast in circles. The playground ride consists of a disk of mass M = 57 kg and radius R = 2.0 m mounted on a low-friction axle. Sally weighs about 20 kg. She is super excited to play and runs at speed of 3 m/s on a line tangential to the disk and jumps onto the outer edge of the disk. She initially decided to just run around and spin the wheel, but later she decides that she wants to jump on and let the wheel keep going. What is the change of energy of the system?&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
#How is this topic connected to something that you are interested in?&lt;br /&gt;
#How is it connected to your major?&lt;br /&gt;
#Is there an interesting industrial application?&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
The idea of maximally inelastic collisions is part of the conservation of linear momentum which is implied by Newton&#039;s Laws. Most objects tend to bounce off each other creating the idea of collision. Most objects that are visibly colliding tend to lose energy through a variety of ways but theoretically objects could collide and not lose kinetic energy. This created the two types of collision inelastic and elastic. Elastic defines collisions that have no change in kinetic energy, these are usually microscopic such as Rutherford Scattering. All other objects tend to be inelastic since some energy in lost between the objects and so their respective kinetic energy changes. However, some objects can stick together and therefore combine their masses. This is a special case of inelastic collisions and tend to be a small portion of collisions that actually occur in real life, but some examples seen are when car&#039;s collide or when a sticky substance stays on the object it is throw at.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Are there related topics or categories in this wiki resource for the curious reader to explore?  How does this topic fit into that context?&lt;br /&gt;
&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
Books, Articles or other print media on this topic&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
Internet resources on this topic&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
This section contains the the references you used while writing this page&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3676</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3676"/>
		<updated>2015-11-29T21:59:47Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* Difficult */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy change? The specific heat of the block and bullet is 6 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt; which is 1.961 m/s.&lt;br /&gt;
Now we can use the conservation of Energy principle to solve for the thermal energy: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0.  &amp;lt;/math&amp;gt; Then we break the change of kinetic energy into it&#039;s initial and final conditions to get :&lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,bullet}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the values we get : &lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(v_{final})^2}{(m_{final})} - (\frac{1}{2}{m_{bullet} (v_{bullet})^2}) &amp;lt;/math&amp;gt;. &lt;br /&gt;
Entering the values from the word problem, our final answer is 490J.&lt;br /&gt;
&lt;br /&gt;
To find the change in temperature, we need to use the heat equation : &amp;lt;math&amp;gt; Q = mCΔT &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the given information of specific heat, thermal energy that we solved for, and the mass of the final object, we get an increase of 16 degrees.&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
[[File: 11-091-playground.jpg ]]&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039; Sally (5 years old) is at the playground and decides that she wants to go on the ride that spins really fast in circles. The playground ride consists of a disk of mass M = 57 kg and radius R = 2.0 m mounted on a low-friction axle. Sally weighs about 20 kg. She is super excited to play and runs at speed of 3 m/s on a line tangential to the disk and jumps onto the outer edge of the disk. She initially decided to just run around and spin the wheel, but later she decides that she wants to jump on and let the wheel keep going. What is the change of energy of the system?&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
#How is this topic connected to something that you are interested in?&lt;br /&gt;
#How is it connected to your major?&lt;br /&gt;
#Is there an interesting industrial application?&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
The idea of maximally inelastic collisions is part of the conservation of linear momentum which is implied by Newton&#039;s Laws. Most objects tend to bounce off each other creating the idea of collision. Most objects that are visibly colliding tend to lose energy through a variety of ways but theoretically objects could collide and not lose kinetic energy. This created the two types of collision inelastic and elastic. Elastic defines collisions that have no change in kinetic energy, these are usually microscopic such as Rutherford Scattering. All other objects tend to be inelastic since some energy in lost between the objects and so their respective kinetic energy changes. However, some objects can stick together and therefore combine their masses. This is a special case of inelastic collisions and tend to be a small portion of collisions that actually occur in real life, but some examples seen are when car&#039;s collide or when a sticky substance stays on the object it is throw at.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Are there related topics or categories in this wiki resource for the curious reader to explore?  How does this topic fit into that context?&lt;br /&gt;
&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
Books, Articles or other print media on this topic&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
Internet resources on this topic&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
This section contains the the references you used while writing this page&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=File:11-091-playground.jpg&amp;diff=3671</id>
		<title>File:11-091-playground.jpg</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=File:11-091-playground.jpg&amp;diff=3671"/>
		<updated>2015-11-29T21:58:34Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3670</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3670"/>
		<updated>2015-11-29T21:58:16Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* Difficult */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy change? The specific heat of the block and bullet is 6 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt; which is 1.961 m/s.&lt;br /&gt;
Now we can use the conservation of Energy principle to solve for the thermal energy: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0.  &amp;lt;/math&amp;gt; Then we break the change of kinetic energy into it&#039;s initial and final conditions to get :&lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,bullet}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the values we get : &lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(v_{final})^2}{(m_{final})} - (\frac{1}{2}{m_{bullet} (v_{bullet})^2}) &amp;lt;/math&amp;gt;. &lt;br /&gt;
Entering the values from the word problem, our final answer is 490J.&lt;br /&gt;
&lt;br /&gt;
To find the change in temperature, we need to use the heat equation : &amp;lt;math&amp;gt; Q = mCΔT &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the given information of specific heat, thermal energy that we solved for, and the mass of the final object, we get an increase of 16 degrees.&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
[[File:11-091-playground.jpg]]&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039; Sally (5 years old) is at the playground and decides that she wants to go on the ride that spins really fast in circles. The playground ride consists of a disk of mass M = 57 kg and radius R = 2.0 m mounted on a low-friction axle. Sally weighs about 20 kg. She is super excited to play and runs at speed of 3 m/s on a line tangential to the disk and jumps onto the outer edge of the disk. She initially decided to just run around and spin the wheel, but later she decides that she wants to jump on and let the wheel keep going. What is the change of energy of the system?&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
#How is this topic connected to something that you are interested in?&lt;br /&gt;
#How is it connected to your major?&lt;br /&gt;
#Is there an interesting industrial application?&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
The idea of maximally inelastic collisions is part of the conservation of linear momentum which is implied by Newton&#039;s Laws. Most objects tend to bounce off each other creating the idea of collision. Most objects that are visibly colliding tend to lose energy through a variety of ways but theoretically objects could collide and not lose kinetic energy. This created the two types of collision inelastic and elastic. Elastic defines collisions that have no change in kinetic energy, these are usually microscopic such as Rutherford Scattering. All other objects tend to be inelastic since some energy in lost between the objects and so their respective kinetic energy changes. However, some objects can stick together and therefore combine their masses. This is a special case of inelastic collisions and tend to be a small portion of collisions that actually occur in real life, but some examples seen are when car&#039;s collide or when a sticky substance stays on the object it is throw at.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Are there related topics or categories in this wiki resource for the curious reader to explore?  How does this topic fit into that context?&lt;br /&gt;
&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
Books, Articles or other print media on this topic&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
Internet resources on this topic&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
This section contains the the references you used while writing this page&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3660</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3660"/>
		<updated>2015-11-29T21:52:53Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* History */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy change? The specific heat of the block and bullet is 6 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt; which is 1.961 m/s.&lt;br /&gt;
Now we can use the conservation of Energy principle to solve for the thermal energy: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0.  &amp;lt;/math&amp;gt; Then we break the change of kinetic energy into it&#039;s initial and final conditions to get :&lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,bullet}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the values we get : &lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(v_{final})^2}{(m_{final})} - (\frac{1}{2}{m_{bullet} (v_{bullet})^2}) &amp;lt;/math&amp;gt;. &lt;br /&gt;
Entering the values from the word problem, our final answer is 490J.&lt;br /&gt;
&lt;br /&gt;
To find the change in temperature, we need to use the heat equation : &amp;lt;math&amp;gt; Q = mCΔT &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the given information of specific heat, thermal energy that we solved for, and the mass of the final object, we get an increase of 16 degrees.&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
#How is this topic connected to something that you are interested in?&lt;br /&gt;
#How is it connected to your major?&lt;br /&gt;
#Is there an interesting industrial application?&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
The idea of maximally inelastic collisions is part of the conservation of linear momentum which is implied by Newton&#039;s Laws. Most objects tend to bounce off each other creating the idea of collision. Most objects that are visibly colliding tend to lose energy through a variety of ways but theoretically objects could collide and not lose kinetic energy. This created the two types of collision inelastic and elastic. Elastic defines collisions that have no change in kinetic energy, these are usually microscopic such as Rutherford Scattering. All other objects tend to be inelastic since some energy in lost between the objects and so their respective kinetic energy changes. However, some objects can stick together and therefore combine their masses. This is a special case of inelastic collisions and tend to be a small portion of collisions that actually occur in real life, but some examples seen are when car&#039;s collide or when a sticky substance stays on the object it is throw at.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Are there related topics or categories in this wiki resource for the curious reader to explore?  How does this topic fit into that context?&lt;br /&gt;
&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
Books, Articles or other print media on this topic&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
Internet resources on this topic&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
This section contains the the references you used while writing this page&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3637</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3637"/>
		<updated>2015-11-29T21:39:48Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* Middling */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy change? The specific heat of the block and bullet is 6 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt; which is 1.961 m/s.&lt;br /&gt;
Now we can use the conservation of Energy principle to solve for the thermal energy: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0.  &amp;lt;/math&amp;gt; Then we break the change of kinetic energy into it&#039;s initial and final conditions to get :&lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,bullet}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the values we get : &lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(v_{final})^2}{(m_{final})} - (\frac{1}{2}{m_{bullet} (v_{bullet})^2}) &amp;lt;/math&amp;gt;. &lt;br /&gt;
Entering the values from the word problem, our final answer is 490J.&lt;br /&gt;
&lt;br /&gt;
To find the change in temperature, we need to use the heat equation : &amp;lt;math&amp;gt; Q = mCΔT &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the given information of specific heat, thermal energy that we solved for, and the mass of the final object, we get an increase of 16 degrees.&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
#How is this topic connected to something that you are interested in?&lt;br /&gt;
#How is it connected to your major?&lt;br /&gt;
#Is there an interesting industrial application?&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Are there related topics or categories in this wiki resource for the curious reader to explore?  How does this topic fit into that context?&lt;br /&gt;
&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
Books, Articles or other print media on this topic&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
Internet resources on this topic&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
This section contains the the references you used while writing this page&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3636</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3636"/>
		<updated>2015-11-29T21:39:11Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* Middling */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy increase? The specific heat of the block and bullet is 6 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt; which is 1.961 m/s.&lt;br /&gt;
Now we can use the conservation of Energy principle to solve for the thermal energy: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0.  &amp;lt;/math&amp;gt; Then we break the change of kinetic energy into it&#039;s initial and final conditions to get :&lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,bullet}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the values we get : &lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(v_{final})^2}{(m_{final})} - (\frac{1}{2}{m_{bullet} (v_{bullet})^2}) &amp;lt;/math&amp;gt;. &lt;br /&gt;
Entering the values from the word problem, our final answer is 490J.&lt;br /&gt;
&lt;br /&gt;
To find the change in temperature, we need to use the heat equation : &amp;lt;math&amp;gt; Q = mCΔT &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the given information of specific heat, thermal energy that we solved for, and the mass of the final object, we get an increase of 16 degrees.&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
#How is this topic connected to something that you are interested in?&lt;br /&gt;
#How is it connected to your major?&lt;br /&gt;
#Is there an interesting industrial application?&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Are there related topics or categories in this wiki resource for the curious reader to explore?  How does this topic fit into that context?&lt;br /&gt;
&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
Books, Articles or other print media on this topic&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
Internet resources on this topic&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
This section contains the the references you used while writing this page&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3633</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3633"/>
		<updated>2015-11-29T21:36:17Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* Middling */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy increase? The specific heat of the block and bullet is .9 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt; which is 1.961 m/s.&lt;br /&gt;
Now we can use the conservation of Energy principle to solve for the thermal energy: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0.  &amp;lt;/math&amp;gt; Then we break the change of kinetic energy into it&#039;s initial and final conditions to get :&lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,bullet}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the values we get : &lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(v_{final})^2}{(m_{final})} - (\frac{1}{2}{m_{bullet} (v_{bullet})^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
#How is this topic connected to something that you are interested in?&lt;br /&gt;
#How is it connected to your major?&lt;br /&gt;
#Is there an interesting industrial application?&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Are there related topics or categories in this wiki resource for the curious reader to explore?  How does this topic fit into that context?&lt;br /&gt;
&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
Books, Articles or other print media on this topic&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
Internet resources on this topic&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
This section contains the the references you used while writing this page&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3630</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3630"/>
		<updated>2015-11-29T21:35:49Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* Middling */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy increase? The specific heat of the block and bullet is .9 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt; which is 1.961 m/s.&lt;br /&gt;
Now we can use the conservation of Energy principle to solve for the thermal energy: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0.  &amp;lt;/math&amp;gt; Then we break the change of kinetic energy into it&#039;s initial and final conditions to get :&lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,bullet}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the values we get : &lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(v_final)^2}{(m_final)} - (\frac{1}{2}{m_bullet (v_bullet)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
#How is this topic connected to something that you are interested in?&lt;br /&gt;
#How is it connected to your major?&lt;br /&gt;
#Is there an interesting industrial application?&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Are there related topics or categories in this wiki resource for the curious reader to explore?  How does this topic fit into that context?&lt;br /&gt;
&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
Books, Articles or other print media on this topic&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
Internet resources on this topic&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
This section contains the the references you used while writing this page&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3629</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3629"/>
		<updated>2015-11-29T21:35:30Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* Middling */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy increase? The specific heat of the block and bullet is .9 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt; which is 1.961 m/s.&lt;br /&gt;
Now we can use the conservation of Energy principle to solve for the thermal energy: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0.  &amp;lt;/math&amp;gt; Then we break the change of kinetic energy into it&#039;s initial and final conditions to get :&lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,bullet}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the values we get : &lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(v_final)^2}{(m_final)} - (\frac{1}{2}{m_bullet (v_bullet)^2})&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
#How is this topic connected to something that you are interested in?&lt;br /&gt;
#How is it connected to your major?&lt;br /&gt;
#Is there an interesting industrial application?&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Are there related topics or categories in this wiki resource for the curious reader to explore?  How does this topic fit into that context?&lt;br /&gt;
&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
Books, Articles or other print media on this topic&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
Internet resources on this topic&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
This section contains the the references you used while writing this page&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3627</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3627"/>
		<updated>2015-11-29T21:34:02Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* Middling */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy increase? The specific heat of the block and bullet is .9 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt; which is 1.961 m/s.&lt;br /&gt;
Now we can use the conservation of Energy principle to solve for the thermal energy: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0.  &amp;lt;/math&amp;gt; Then we break the change of kinetic energy into it&#039;s initial and final conditions to get :&lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,bullet}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
#How is this topic connected to something that you are interested in?&lt;br /&gt;
#How is it connected to your major?&lt;br /&gt;
#Is there an interesting industrial application?&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Are there related topics or categories in this wiki resource for the curious reader to explore?  How does this topic fit into that context?&lt;br /&gt;
&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
Books, Articles or other print media on this topic&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
Internet resources on this topic&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
This section contains the the references you used while writing this page&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3624</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3624"/>
		<updated>2015-11-29T21:33:14Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* Middling */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy increase? The specific heat of the block and bullet is .9 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt; which is 1.961 m/s.&lt;br /&gt;
Now we can use the conservation of Energy principle to solve for the thermal energy: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt;&lt;br /&gt;
&amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,bullet}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
#How is this topic connected to something that you are interested in?&lt;br /&gt;
#How is it connected to your major?&lt;br /&gt;
#Is there an interesting industrial application?&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Are there related topics or categories in this wiki resource for the curious reader to explore?  How does this topic fit into that context?&lt;br /&gt;
&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
Books, Articles or other print media on this topic&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
Internet resources on this topic&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
This section contains the the references you used while writing this page&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3623</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3623"/>
		<updated>2015-11-29T21:30:53Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* Middling */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
A .1 kg bullet is launched at 100 m/s a stationary block that weighs 5kg. The bullet embeds itself into the block. When someone goes to retrieve the bullet and remove it from the block, they notice the block is slightly warmer than it was before. By how much did the block&#039;s thermal energy increase? The specific heat of the block is .9 J/(g*C) so by how many degrees did the block warm up by?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Using the conservation of momentum principle, we can find the final velocity of the object: &amp;lt;math&amp;gt;m_1 v_1 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
#How is this topic connected to something that you are interested in?&lt;br /&gt;
#How is it connected to your major?&lt;br /&gt;
#Is there an interesting industrial application?&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Are there related topics or categories in this wiki resource for the curious reader to explore?  How does this topic fit into that context?&lt;br /&gt;
&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
Books, Articles or other print media on this topic&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
Internet resources on this topic&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
This section contains the the references you used while writing this page&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3620</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3620"/>
		<updated>2015-11-29T21:27:04Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* A Computational Model */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
#How is this topic connected to something that you are interested in?&lt;br /&gt;
#How is it connected to your major?&lt;br /&gt;
#Is there an interesting industrial application?&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Are there related topics or categories in this wiki resource for the curious reader to explore?  How does this topic fit into that context?&lt;br /&gt;
&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
Books, Articles or other print media on this topic&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
Internet resources on this topic&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
This section contains the the references you used while writing this page&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3618</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3618"/>
		<updated>2015-11-29T21:26:41Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* A Computational Model */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
[[File:[https://trinket.io/glowscript/02316a1ea9 link title]]]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
#How is this topic connected to something that you are interested in?&lt;br /&gt;
#How is it connected to your major?&lt;br /&gt;
#Is there an interesting industrial application?&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Are there related topics or categories in this wiki resource for the curious reader to explore?  How does this topic fit into that context?&lt;br /&gt;
&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
Books, Articles or other print media on this topic&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
Internet resources on this topic&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
This section contains the the references you used while writing this page&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3615</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3615"/>
		<updated>2015-11-29T21:25:49Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* Middling */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
#How is this topic connected to something that you are interested in?&lt;br /&gt;
#How is it connected to your major?&lt;br /&gt;
#Is there an interesting industrial application?&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Are there related topics or categories in this wiki resource for the curious reader to explore?  How does this topic fit into that context?&lt;br /&gt;
&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
Books, Articles or other print media on this topic&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
Internet resources on this topic&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
This section contains the the references you used while writing this page&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3614</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3614"/>
		<updated>2015-11-29T21:25:24Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* Simple */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity : &amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;.&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;.&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
#How is this topic connected to something that you are interested in?&lt;br /&gt;
#How is it connected to your major?&lt;br /&gt;
#Is there an interesting industrial application?&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Are there related topics or categories in this wiki resource for the curious reader to explore?  How does this topic fit into that context?&lt;br /&gt;
&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
Books, Articles or other print media on this topic&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
Internet resources on this topic&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
This section contains the the references you used while writing this page&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3612</id>
		<title>Maximally Inelastic Collision</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Maximally_Inelastic_Collision&amp;diff=3612"/>
		<updated>2015-11-29T21:25:00Z</updated>

		<summary type="html">&lt;p&gt;Apatel404: /* Simple */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This topic covers Maximally Inelastic Collisions.&lt;br /&gt;
claimed by apatel404&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object&#039;s kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one. &lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
Maximally Inelastic Collisions can be based off the fundamental principle of momentum: &lt;br /&gt;
::&amp;lt;math&amp;gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt}&amp;lt;/math&amp;gt; &lt;br /&gt;
where &#039;&#039;&#039;p&#039;&#039;&#039; is the momentum of the system, &#039;&#039;&#039;F&#039;&#039;&#039; is the net force from the surroundings, &#039;&#039;&#039;Δt&#039;&#039;&#039; is the change in time for the process.&lt;br /&gt;
&lt;br /&gt;
Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief so, &amp;lt;math&amp;gt;{Δt} ≈ {0}&amp;lt;/math&amp;gt;. So rewriting the equation with the concept that the change in time is 0 yields:&lt;br /&gt;
::&amp;lt;math&amp;gt;{ΔP_{system}} = {0}&amp;lt;/math&amp;gt; where we can break the change in momentum of the system to it&#039;s initial and final components to get: &amp;lt;math&amp;gt;{P_{final}} = {P_{initial}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that:&lt;br /&gt;
&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
where &#039;&#039;&#039;v&#039;&#039;&#039; is the final velocity, which becomes&lt;br /&gt;
::&amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now if we apply the concept of conservation of energy:&lt;br /&gt;
::&amp;lt;math&amp;gt;{E} = {Q} + {W}&amp;lt;/math&amp;gt; where &#039;&#039;&#039;E&#039;&#039;&#039; is the total energy, &#039;&#039;&#039;Q&#039;&#039;&#039; is the heat given off, and &#039;&#039;&#039;W&#039;&#039;&#039; is the work done.&lt;br /&gt;
If we input the various types of energy in for the total energy such as kinetic, potential, and internal we get&lt;br /&gt;
:: &amp;lt;math&amp;gt;{ΔE_k}+{ΔE_p}+{ΔU}= {Q} + {W} &amp;lt;/math&amp;gt; where &#039;&#039;&#039;ΔE_k&#039;&#039;&#039; is the change in kinetic energy,&#039;&#039;&#039;ΔE_p&#039;&#039;&#039; is the change in potential energy, and &#039;&#039;&#039;ΔU&#039;&#039;&#039; is the change in internal energy.&lt;br /&gt;
&lt;br /&gt;
Based on the concept that the two objects have initial velocities and are going to combine into one, we can assume that the work done is negligible, the process is adiabatic,and the change in potential energy is negligible. The equation is simplified to:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔE_k} + {ΔU} = 0 &amp;lt;/math&amp;gt; which we can break into the initial and final components to get: &amp;lt;math&amp;gt; {ΔU} = -({K_{final}} - ({K_{initial,1}} + {K_{initial,2}})) &amp;lt;/math&amp;gt;&lt;br /&gt;
Kinetic Energy for objects that have a velocity smaller than the speed of light is defined as &amp;lt;math&amp;gt; \frac{1}{2}{mv^2} &amp;lt;/math&amp;gt;, so putting in the values for mass and velocity we get that:&lt;br /&gt;
:: &amp;lt;math&amp;gt; {ΔU} = \frac{1}{2}{(m_1 v_1 +m_2 v_2)^2}{(m_1+m_2)} - (\frac{1}{2}{m_1 (v_1)^2} + \frac{1}{2}{m_2 (v_2)^2}) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
[https://trinket.io/glowscript/02316a1ea9 Maximally Inelastic Collisions using Glowscript]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
===Simple===&lt;br /&gt;
&#039;&#039;&#039;Problem:&#039;&#039;&#039;&lt;br /&gt;
Greco wants to eat a very large flan, but Fenton and Gumbart both have small flans, so they decide to combine the flans. Fenton throws a 9 kg mass flan at a velocity of 14 m/s  which strikes Gumbart&#039;s flan that weighs 5 kg mass with a velocity of -5 m/s head-on, and the two flans stick together to make an ultra mega flan for Greco to eat. At what speed will the giant flan have? Greco can only catch objects that are flying at 5 m/s, will he catch it or will it go past him? Assume negligible air resistance.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Solution:&#039;&#039;&#039;&lt;br /&gt;
Use conservation of momentum to solve for the final velocity :&amp;lt;math&amp;gt;m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right)  v \,&amp;lt;/math&amp;gt;&lt;br /&gt;
Solving for the final velocity we get the equation: &amp;lt;math&amp;gt; v=\frac{m_1 v_1 + m_2  v_2}{m_1 + m_2}&amp;lt;/math&amp;gt;&lt;br /&gt;
Plugging in the numbers yields us a final velocity of 7.214 m/s, therefore Greco will be unable to catch the flan.&lt;br /&gt;
&lt;br /&gt;
===Middling===&lt;br /&gt;
===Difficult===&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
#How is this topic connected to something that you are interested in?&lt;br /&gt;
#How is it connected to your major?&lt;br /&gt;
#Is there an interesting industrial application?&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Are there related topics or categories in this wiki resource for the curious reader to explore?  How does this topic fit into that context?&lt;br /&gt;
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===Further reading===&lt;br /&gt;
&lt;br /&gt;
Books, Articles or other print media on this topic&lt;br /&gt;
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===External links===&lt;br /&gt;
&lt;br /&gt;
Internet resources on this topic&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
This section contains the the references you used while writing this page&lt;br /&gt;
&lt;br /&gt;
[[Category:Collisions]]&lt;/div&gt;</summary>
		<author><name>Apatel404</name></author>
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