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http://www.physicsbook.gatech.edu/index.php?title=Electric_field&diff=23794
Electric field
2016-11-23T06:08:22Z
<p>Daveed: </p>
<hr />
<div>====Electric field====<br />
<br />
Claimed by David Gamero (Fall 2016)<br />
<div class="mw-collapsible-content"><br />
<br />
The electric field created by a charge is present throughout space at all times, whether or not there is another charge around to feel its effects. The electric field created by a charge penetrates through matter. The field permeates the neighboring space, biding its time until it can affect anything brought into its space of interaction. <br />
<br />
==The Main Idea==<br />
To be exact, the definition of the Electric Field is as follows: <br />
The electric field is a region around a charged particle or object within which a force would be exerted on other objects.<br />
If we put a charged particle at a location and it experiences a force, it would be logical to assume that there is something present that<br />
is interacting with the particle. This "virtual force" is, in essence, the electric field.<br />
===A Mathematical Model===<br />
<br />
The electric field can be expressed mathematically as follows:<br />
<br />
<math>{\vec{F_{net}} = 0 \Leftrightarrow \frac{d\vec{v}}{dt}} = 0</math><br />
<br />
<math>{\vec{F_{2}} = {q_{1}}{\vec{E_{1}}} \Leftrightarrow \frac{d\vec{v}}{dt}} </math><br />
<br />
which can be translated to postulate that the force on particle 2 is determined by the charge of particle 2 and the electric<br />
field.<br />
<br />
You can also visualize the electric field lines using a simulator[http://www.flashphysics.org/electricField.html].<br />
<br />
The net electric field at a location in space is the vector sum of the individual contributions from all the sources of electric field in that space. This uses the principle of superposition.<br />
Electric field is a expressed as a vector that tends towards negative charges and away from positive.<br />
<br />
==Coulomb and NonCoulomb Electric Fields==<br />
<br />
Commonly this topic refers to Coulomb Electric fields, which are produced from superposing individual radial fields from charges and explicitly defined regions of electric field. There exists a second kind called NonCoulomb electric fields that are produced from a varying magnetic field. These electric fields are similar to the pattern of magnetic field produced from a wire because they are both circular. NonCoulomb electric fields (<math>E_{NC}</math>) follow the curled right-hand-rule with the thumb pointing in the direction of <math> \frac{-dB}{dt} </math> and the fingers curl along the direction of <math>E_{NC}</math>.<br />
<br />
==Examples==<br />
<br />
The following examples are to test your basic understanding of the Electric Field. For more examples that test your knowledge of all three of the laws, peruse the class textbook.<br />
<br />
===Simple===<br />
Which way is the electric field going for a negatively charged particle?<br />
<br />
[[File:Simple111.png]]<br />
<br />
It's easy to see that the electric field is pointing toward the negatively charged particle. The electric field is tending<br />
toward the negatively charged particle.<br />
<br />
===Middling===<br />
Two charged objects are separated by a distance d. The first charge is larger in magnitude than the second charge:<br />
<br />
A) The first charge exerts a larger force on the second charge. <br />
<br />
B) The second charge exerts a larger force on the first charge. <br />
<br />
C) The charges exert forces on each other that are equal in magnitude and opposite in direction. <br />
<br />
D) The charges exert forces on each other equal in magnitude and pointing in the same direction. <br />
<br />
The answer is C, which can be reasoned even by an extension of Newton's Third Law. Using the simple equation in this page, it is also possible to derive and reason this result. Notice that the forces are opposite in direction! The equations above relate vectors, an important concept in physics.<br />
Note: Just because the forces are equal does not mean that the accelerations, velocities, or motions of the charges are equal; these depend on both the initial velocities and the masses of both charges.<br />
<br />
<br />
===Difficult===<br />
The number of electric field lines passing through a unit cross-sectional area is indicative of:<br />
<br />
A)field direction<br />
<br />
B)charge density<br />
<br />
C)field strength<br />
<br />
D)charge motion<br />
<br />
E)rate of energy transfer<br />
<br />
The answer is C since the number of electric field lines through an area is how field strength can be qualitatively and quantitatively determined. Field lines come out of positive charges and go into negative charges.<br />
Field strength can be inferred by placing a charge with known electric and mass properties and measuring the force exerted. In the absence of other external forces, this exerted force is a product of the charge and the electric field at that location.<br />
<br />
==Connectedness==<br />
<br />
The electric field is made up. It's a lie. It's a concept that an English intellectual by the name of Michael Faraday made up centuries ago to think about the universe in a different way. But it this concept that is Faraday's greatest gift to the world. The electric field allows us to think about point charges, charge distributions, and current. It allows us to better understand electricity, a concept that would go on to spur some of the greatest inventions of the entire history of humankind. And now, with advances in areas like quantum computing and bioengineering where circuits are regularly employed to push the boundaries of science and engineering, we have Michael Faraday to thank. Devices that save lives or improve their quality, such as neuroprosthetics or pacemakers, rely on the principles theorized by Faraday long ago. Electric field is a useful visualization of a complex reality composed of interacting waves and interactions. The method of describing electric fields with vectors allowed for the Maxwell Equations to be derived, which drastically improved our understanding of electricity, magnetism, and how they are related.<br />
<br />
<br />
==History==<br />
<br />
It was in 1831 that Hans Christian Oersted demonstrated that by applying an electric current through a wire, a magnetic field could be produced. How was this verified? The needle from a nearby compass was deflected accordingly. Michael Faraday would go on to demonstrate electromagnetic induction, in which Faraday resolved the issue of whether magnetism could produce electricity (which it could if the magnetic effect was set in motion, creating a resulting current). But it was not until 1864 that a Scottish physicist by the name of James Clerk Maxwell came along to provide a unifying statement for electromagnetism by way of his groundbreaking publication 'Dynamical Theory of the Electric Field'. Maxwell's equations were a set of four equations that expressed, mathematically, the behaviors in which electric and magnetic fields participated.<br />
<br />
== See also ==<br />
<br />
===External links===<br />
Interactive Electric Field [https://phet.colorado.edu/sims/charges-and-fields/charges-and-fields_en.html]<br />
<br />
Electric Field Simulator [http://www.flashphysics.org/electricField.html]<br />
<br />
==References==<br />
<br />
The following references were used while writing this page:<br />
<br />
http://www.rare-earth-magnets.com/history-of-magnetism-and-electricity<br />
<br />
https://en.wikipedia.org/wiki/Electric_field</div>
Daveed
http://www.physicsbook.gatech.edu/index.php?title=File:BarMagnetEfield.png&diff=23793
File:BarMagnetEfield.png
2016-11-23T04:21:44Z
<p>Daveed: Daveed uploaded a new version of &quot;File:BarMagnetEfield.png&quot;</p>
<hr />
<div></div>
Daveed
http://www.physicsbook.gatech.edu/index.php?title=Electric_field&diff=23792
Electric field
2016-11-23T04:21:14Z
<p>Daveed: </p>
<hr />
<div>====Electric field====<br />
<br />
Claimed by David Gamero (Fall 2016)<br />
<div class="mw-collapsible-content"><br />
<br />
The electric field created by a charge is present throughout space at all times, whether or not there is another charge around to feel its effects. The electric field created by a charge penetrates through matter. The field permeates the neighboring space, biding its time until it can affect anything brought into its space of interaction. <br />
<br />
==The Main Idea==<br />
To be exact, the definition of the Electric Field is as follows: <br />
The electric field is a region around a charged particle or object within which a force would be exerted on other objects.<br />
If we put a charged particle at a location and it experiences a force, it would be logical to assume that there is something present that<br />
is interacting with the particle. This "virtual force" is in essence the electric field.<br />
===A Mathematical Model===<br />
<br />
The electric field can be expressed mathematically as follows:<br />
<br />
<math>{\vec{F_{net}} = 0 \Leftrightarrow \frac{d\vec{v}}{dt}} = 0</math><br />
<br />
<math>{\vec{F_{2}} = {q_{1}}{\vec{E_{1}}} \Leftrightarrow \frac{d\vec{v}}{dt}} </math><br />
<br />
which can be translated to postulate that the force on particle 2 is determined by the charge of particle 2 and the electric<br />
field.<br />
<br />
You can also visualize the electric field lines using a simulator[http://www.flashphysics.org/electricField.html].<br />
<br />
==Examples==<br />
<br />
The following examples are to test your basic understanding of the Electric Field. For more examples that test your knowledge of all three of the laws, peruse the class textbook.<br />
<br />
===Simple===<br />
Which way is the electric field going for a negatively charged particle?<br />
<br />
[[File:Simple111.png]]<br />
<br />
[[File:BarMagnetEfield.png]]<br />
<br />
It's easy to see that the electric field is pointing toward the negatively charged particle. The electric field is tending<br />
toward the negatively charged particle.<br />
<br />
===Middling===<br />
Two charged objects are separated by a distance d. The first charge is larger in magnitude than the second charge:<br />
<br />
A) The first charge exerts a larger force on the second charge. <br />
<br />
B) The second charge exerts a larger force on the first charge. <br />
<br />
C) The charges exert forces on each other that are equal in magnitude and opposite in direction. <br />
<br />
D) The charges exert forces on each other equal in magnitude and pointing in the same direction. <br />
<br />
The answer is of course C, which can be reasoned even by an extension of Newton's Third Law. Using the simple equation in this page, it is also possible to derive and reason this result. Notice that the forces are opposite in direction! The equations above relate vectors, an important concept on physics.<br />
<br />
===Difficult===<br />
The number of electric field lines passing through a unit cross sectional area is indicative of:<br />
<br />
A)field direction<br />
<br />
B)charge density<br />
<br />
C)field strength<br />
<br />
D)charge motion<br />
<br />
E)rate of energy transfer<br />
<br />
The answer is C, since the number of electric field lines through area is how field strength can be qualitatively and quantitatively determined.<br />
<br />
==Connectedness==<br />
<br />
The electric field is made up. It's a lie. It's a concept that an English intellectual by the name of Michael Faraday made up centuries ago to think about the universe in a different way. But it this concept that is Faraday's greatest gift to the world. The electric field allows us to think about point charges, charge distributions, and current. It allows us to better understand electricity, a concept that would go on to spur some of the greatest inventions of the entire history of humankind. And now, with advances in areas like quantum computing and bioengineering where circuits are regularly employed to push the boundaries of science and engineering, we have Michael Faraday to thank. Devices that save lives or improve their quality, such as neuroprosthetics or pacemakers, rely on the principles theorized by Faraday long ago.<br />
<br />
==History==<br />
<br />
It was in 1831 that Hans Christian Oersted demonstrated that by applying electric current through a wire, a magnetic field could be produced. How was this verified? The needle from a nearby compass was deflected accordingly. Michael Faraday would go on to demonstrate electromagnetic induction, in which Faraday resolved the issue of whether magnetism could produce electricity (which it could, if the magnetic effect was set in motion, creating a resulting current). But it was not until 1864 that a Scottish physicist by the name of James Clerk Maxwell came along to provide a unifying statement for electromagnetism by way of his groundbreaking publication 'Dynamical Theory of the Electric Field'. Maxwell's equations were a set of four equations that expressed, mathematically, the behaviors in which electric and magnetic fields participated.<br />
<br />
== See also ==<br />
<br />
===External links===<br />
Interactive Electric Field [https://phet.colorado.edu/sims/charges-and-fields/charges-and-fields_en.html]<br />
<br />
Electric Field Simulator [http://www.flashphysics.org/electricField.html]<br />
<br />
==References==<br />
<br />
The following references were used while writing this page:<br />
<br />
http://www.rare-earth-magnets.com/history-of-magnetism-and-electricity<br />
<br />
https://en.wikipedia.org/wiki/Electric_field</div>
Daveed
http://www.physicsbook.gatech.edu/index.php?title=File:BarMagnetEfield.png&diff=23791
File:BarMagnetEfield.png
2016-11-23T04:18:50Z
<p>Daveed: </p>
<hr />
<div></div>
Daveed
http://www.physicsbook.gatech.edu/index.php?title=Electric_field&diff=23698
Electric field
2016-11-18T18:01:09Z
<p>Daveed: </p>
<hr />
<div>====Electric field====<br />
<br />
Claimed by David Gamero (Fall 2016)<br />
<div class="mw-collapsible-content"><br />
<br />
The electric field created by a charge is present throughout space at all times, whether or not there is another charge around to feel its effects. The electric field created by a charge penetrates through matter. The field permeates the neighboring space, biding its time until it can affect anything brought into its space of interaction. <br />
<br />
==The Main Idea==<br />
To be exact, the definition of the Electric Field is as follows: <br />
The electric field is a region around a charged particle or object within which a force would be exerted on other objects.<br />
If we put a charged particle at a location and it experiences a force, it would be logical to assume that there is something present that<br />
is interacting with the particle. This "virtual force" is in essence the electric field.<br />
===A Mathematical Model===<br />
<br />
The electric field can be expressed mathematically as follows:<br />
<br />
<math>{\vec{F_{net}} = 0 \Leftrightarrow \frac{d\vec{v}}{dt}} = 0</math><br />
<br />
<math>{\vec{F_{2}} = {q_{1}}{\vec{E_{1}}} \Leftrightarrow \frac{d\vec{v}}{dt}} </math><br />
<br />
which can be translated to postulate that the force on particle 2 is determined by the charge of particle 2 and the electric<br />
field.<br />
<br />
You can also visualize the electric field lines using a simulator[http://www.flashphysics.org/electricField.html].<br />
<br />
==Examples==<br />
<br />
The following examples are to test your basic understanding of the Electric Field. For more examples that test your knowledge of all three of the laws, peruse the class textbook.<br />
<br />
===Simple===<br />
Which way is the electric field going for a negatively charged particle?<br />
<br />
[[File:Simple111.png]]<br />
<br />
It's easy to see that the electric field is pointing toward the negatively charged particle. The electric field is tending<br />
toward the negatively charged particle.<br />
<br />
===Middling===<br />
Two charged objects are separated by a distance d. The first charge is larger in magnitude than the second charge:<br />
<br />
A) The first charge exerts a larger force on the second charge. <br />
<br />
B) The second charge exerts a larger force on the first charge. <br />
<br />
C) The charges exert forces on each other that are equal in magnitude and opposite in direction. <br />
<br />
D) The charges exert forces on each other equal in magnitude and pointing in the same direction. <br />
<br />
The answer is of course C, which can be reasoned even by an extension of Newton's Third Law. Using the simple equation in this page, it is also possible to derive and reason this result. Notice that the forces are opposite in direction! The equations above relate vectors, an important concept on physics.<br />
<br />
===Difficult===<br />
The number of electric field lines passing through a unit cross sectional area is indicative of:<br />
<br />
A)field direction<br />
<br />
B)charge density<br />
<br />
C)field strength<br />
<br />
D)charge motion<br />
<br />
E)rate of energy transfer<br />
<br />
The answer is C, since the number of electric field lines through area is how field strength can be qualitatively and quantitatively determined.<br />
<br />
==Connectedness==<br />
<br />
The electric field is made up. It's a lie. It's a concept that an English intellectual by the name of Michael Faraday made up centuries ago to think about the universe in a different way. But it this concept that is Faraday's greatest gift to the world. The electric field allows us to think about point charges, charge distributions, and current. It allows us to better understand electricity, a concept that would go on to spur some of the greatest inventions of the entire history of humankind. And now, with advances in areas like quantum computing and bioengineering where circuits are regularly employed to push the boundaries of science and engineering, we have Michael Faraday to thank. Devices that save lives or improve their quality, such as neuroprosthetics or pacemakers, rely on the principles theorized by Faraday long ago.<br />
<br />
==History==<br />
<br />
It was in 1831 that Hans Christian Oersted demonstrated that by applying electric current through a wire, a magnetic field could be produced. How was this verified? The needle from a nearby compass was deflected accordingly. Michael Faraday would go on to demonstrate electromagnetic induction, in which Faraday resolved the issue of whether magnetism could produce electricity (which it could, if the magnetic effect was set in motion, creating a resulting current). But it was not until 1864 that a Scottish physicist by the name of James Clerk Maxwell came along to provide a unifying statement for electromagnetism by way of his groundbreaking publication 'Dynamical Theory of the Electric Field'. Maxwell's equations were a set of four equations that expressed, mathematically, the behaviors in which electric and magnetic fields participated.<br />
<br />
== See also ==<br />
<br />
===External links===<br />
Interactive Electric Field [https://phet.colorado.edu/sims/charges-and-fields/charges-and-fields_en.html]<br />
<br />
Electric Field Simulator [http://www.flashphysics.org/electricField.html]<br />
<br />
==References==<br />
<br />
The following references were used while writing this page:<br />
<br />
http://www.rare-earth-magnets.com/history-of-magnetism-and-electricity<br />
<br />
https://en.wikipedia.org/wiki/Electric_field</div>
Daveed
http://www.physicsbook.gatech.edu/index.php?title=Electric_field&diff=23697
Electric field
2016-11-18T18:00:55Z
<p>Daveed: </p>
<hr />
<div>====Electric field====<br />
<div class="mw-collapsible-content"><br />
Claimed by David Gamero (Fall 2016)<br />
<br />
The electric field created by a charge is present throughout space at all times, whether or not there is another charge around to feel its effects. The electric field created by a charge penetrates through matter. The field permeates the neighboring space, biding its time until it can affect anything brought into its space of interaction. <br />
<br />
==The Main Idea==<br />
To be exact, the definition of the Electric Field is as follows: <br />
The electric field is a region around a charged particle or object within which a force would be exerted on other objects.<br />
If we put a charged particle at a location and it experiences a force, it would be logical to assume that there is something present that<br />
is interacting with the particle. This "virtual force" is in essence the electric field.<br />
===A Mathematical Model===<br />
<br />
The electric field can be expressed mathematically as follows:<br />
<br />
<math>{\vec{F_{net}} = 0 \Leftrightarrow \frac{d\vec{v}}{dt}} = 0</math><br />
<br />
<math>{\vec{F_{2}} = {q_{1}}{\vec{E_{1}}} \Leftrightarrow \frac{d\vec{v}}{dt}} </math><br />
<br />
which can be translated to postulate that the force on particle 2 is determined by the charge of particle 2 and the electric<br />
field.<br />
<br />
You can also visualize the electric field lines using a simulator[http://www.flashphysics.org/electricField.html].<br />
<br />
==Examples==<br />
<br />
The following examples are to test your basic understanding of the Electric Field. For more examples that test your knowledge of all three of the laws, peruse the class textbook.<br />
<br />
===Simple===<br />
Which way is the electric field going for a negatively charged particle?<br />
<br />
[[File:Simple111.png]]<br />
<br />
It's easy to see that the electric field is pointing toward the negatively charged particle. The electric field is tending<br />
toward the negatively charged particle.<br />
<br />
===Middling===<br />
Two charged objects are separated by a distance d. The first charge is larger in magnitude than the second charge:<br />
<br />
A) The first charge exerts a larger force on the second charge. <br />
<br />
B) The second charge exerts a larger force on the first charge. <br />
<br />
C) The charges exert forces on each other that are equal in magnitude and opposite in direction. <br />
<br />
D) The charges exert forces on each other equal in magnitude and pointing in the same direction. <br />
<br />
The answer is of course C, which can be reasoned even by an extension of Newton's Third Law. Using the simple equation in this page, it is also possible to derive and reason this result. Notice that the forces are opposite in direction! The equations above relate vectors, an important concept on physics.<br />
<br />
===Difficult===<br />
The number of electric field lines passing through a unit cross sectional area is indicative of:<br />
<br />
A)field direction<br />
<br />
B)charge density<br />
<br />
C)field strength<br />
<br />
D)charge motion<br />
<br />
E)rate of energy transfer<br />
<br />
The answer is C, since the number of electric field lines through area is how field strength can be qualitatively and quantitatively determined.<br />
<br />
==Connectedness==<br />
<br />
The electric field is made up. It's a lie. It's a concept that an English intellectual by the name of Michael Faraday made up centuries ago to think about the universe in a different way. But it this concept that is Faraday's greatest gift to the world. The electric field allows us to think about point charges, charge distributions, and current. It allows us to better understand electricity, a concept that would go on to spur some of the greatest inventions of the entire history of humankind. And now, with advances in areas like quantum computing and bioengineering where circuits are regularly employed to push the boundaries of science and engineering, we have Michael Faraday to thank. Devices that save lives or improve their quality, such as neuroprosthetics or pacemakers, rely on the principles theorized by Faraday long ago.<br />
<br />
==History==<br />
<br />
It was in 1831 that Hans Christian Oersted demonstrated that by applying electric current through a wire, a magnetic field could be produced. How was this verified? The needle from a nearby compass was deflected accordingly. Michael Faraday would go on to demonstrate electromagnetic induction, in which Faraday resolved the issue of whether magnetism could produce electricity (which it could, if the magnetic effect was set in motion, creating a resulting current). But it was not until 1864 that a Scottish physicist by the name of James Clerk Maxwell came along to provide a unifying statement for electromagnetism by way of his groundbreaking publication 'Dynamical Theory of the Electric Field'. Maxwell's equations were a set of four equations that expressed, mathematically, the behaviors in which electric and magnetic fields participated.<br />
<br />
== See also ==<br />
<br />
===External links===<br />
Interactive Electric Field [https://phet.colorado.edu/sims/charges-and-fields/charges-and-fields_en.html]<br />
<br />
Electric Field Simulator [http://www.flashphysics.org/electricField.html]<br />
<br />
==References==<br />
<br />
The following references were used while writing this page:<br />
<br />
http://www.rare-earth-magnets.com/history-of-magnetism-and-electricity<br />
<br />
https://en.wikipedia.org/wiki/Electric_field</div>
Daveed
http://www.physicsbook.gatech.edu/index.php?title=Escape_Velocity&diff=21344
Escape Velocity
2016-04-14T18:27:37Z
<p>Daveed: </p>
<hr />
<div>Claimed by David Gamero<br />
created by Varun Rajagopal<br />
[[File:Spacex.jpg|600px|thumb|right|space x]]<br />
<br />
Escape velocity is defined as the minimum velocity required for an object to escape the gravitational force of a large object. The sum of an object's kinetic energy and its Gravitational potential energy is equal to zero. The gravitational potential energy is negative due to the fact that kinetic energy is always positive. The velocity of the object will be be zero at infinite distance from the centre of gravity. There is no net force on an object as it escapes and zero acceleration is perceived.<br />
<br />
<br />
<br />
==The Main Idea==<br />
<br />
The formula for escape velocity at a certain distance from a body is calculated by the formula {{cite book|last=Khatri, Poudel, Gautam|first=M.K. , P.R. , A.K.|title=Principles of Physics|year=2010|publisher=Ayam Publication|location=Kathmandu|isbn=9789937903844|pages=170, 171}}<br />
:<math>v_e = \sqrt{\frac{2GM}{r}},</math><br />
<br />
where ''G'' is the universal [[gravitational constant]] (''G''&nbsp;=&nbsp;6.67×10<sup>−11</sup>&nbsp;m<sup>3</sup>&nbsp;kg<sup>−1</sup>&nbsp;s<sup>−2</sup>), ''M'' is the mass of the large body to be escaped, and ''r'' the distance from the [[center of mass]] of the mass ''M'' to the object.<ref group="nb"> This equation assumes there is no atmospheric friction and is an ideal scenario with sending an object on a trajectory. In fact, the escape velocity stated here should actually be called escape speed due to the fact that the quantity to be calculated is completely independent of direction. Notice that the equation does not include the mass of the object escaping a large body as escape velocity is only dependent on gravitational force. We also assume that an object is escaping from a uniform body. <br />
<br />
===A Mathematical Model===<br />
<br />
When we model escape velocity or speed, we have to assume that an object must have a velocity an infinite distance away from a large body allowing us to find the very minimum speed to escape that large body a certain distance away. "Escape velocity" is the speed needed to go from some distance away from a large body to an infinite distance, ending at infinity with a final speed of zero. This dismisses any initial acceleration. This means that a modern spacecraft for example with propellers does not follow these assumptions.<br />
<br />
:<math>(K + U_g)_i = (K + U_g)_f \,</math><br />
<br />
''K''<sub>''ƒ''</sub> = 0 because final velocity is zero, and ''U''<sub>gƒ</sub> = 0 because its final distance is expressed as infinity, therefore<br />
<br />
:<math>\frac{1}{2}mv_e^2 + \frac{-GMm}{r} = 0 + 0</math><br />
<br />
<!-- extra space between two lines of "displayed" [[TeX]] that were crowding each other and impairing legibility --><br />
<br />
:<math>v_e = \sqrt{\frac{2GM}{r}}</math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<div style="width:100%;height:400px"><br />
In the following diagrams the differences highlight the energy needed to escape a gravitational field. When the total energy (kinetic plus gravitational) is equal to or greater than zero then the object can escape, this is called an unbound system (illustrated in left energy diagram). This comes from that there is at least enough kinetic energy to offset the negative potential energy, so the object ends at a distance of <math>r=\infty</math> with no gravitational potential energy, which means it has escaped and its initial velocity was equal to or greater than the escape velocity. On the other hand in the image on the right, kinetic energy reaches zero at a radius where potential energy is still negative, which means that the object has a velocity of zero but is still being pulled by gravity resulting in it getting dragged back in and never being able to escape. In this bound system the initial velocity was less than the escape velocity.<br />
[[File:Ediagram_MSPaint_UnboundSystemWithExtraEnergy.png|500px|thumb|left|EnergyDiagramUnboundSystem]][[File:EDiagram_MSPaint_BoundSystem.png|500px|thumb|right|EnergyDiagramBoundSystem]]<br />
</div><br />
==Examples==<br />
<br />
[[File:prob.jpg|600px|thumb|center|example]]<br />
<br />
===Escaping Jupiter's Atmosphere===<br />
The radius of Jupiter is 71500e3 m, and its mass is 1900e24 kg. What is the escape speed of an object launched straight up from just above the atmosphere of Jupiter?<br />
<br />
<div style=""><br />
System = Jupiter + object<br />
<math><br />
<br />
\Delta E = 0\\<br />
\\<br />
v_i = ?\\<br />
v_f = 0 m/s\\<br />
r_i = 71500e3 m\\<br />
r_f = \infty\\<br />
m = mObject\\<br />
M = mJupiter (1900e24 kg)\\<br />
<br />
</math><br />
<br />
Starting from the Energy Principle:<br />
<br />
<math><br />
<br />
\Delta E = W + Q\\<br />
\Delta E = (0) + (0)\\<br />
\Delta E = 0\\<br />
(\Delta K + \Delta U) = 0\\<br />
\frac{1}{2}m(v_f^2-v_i^2) + (\frac{-GMm}{r_f} - \frac{-GMm}{r_i}) = 0\\<br />
\frac{1}{2}m((0)-v_i^2) + ((0) - \frac{-GMm}{r_i}) = 0\\<br />
\frac{-1}{2}mv_i^2 + \frac{GMm}{r_i} = 0\\<br />
\frac{GMm}{r_i} = \frac{1}{2}mv_i^2\\<br />
\frac{GM}{r_i} = \frac{1}{2}v_i^2\\<br />
v_i = \sqrt{\frac{2GM}{r_i}}\\<br />
= \sqrt{\frac{2(6.7e-11)(1900e24)}{(71500e3)}}\\<br />
= 59672.767m/s<br />
</math><br />
<br />
</div><br />
<br />
==Connectedness==<br />
In space, a rocket will not actually be able to travel an infinite distance once it escapes the gravitational pull of Earth, but rather must escape the gravitational pull of the Sun, the planets in our solar system, and every other larger body. The calculation of escape velocity assumes many conditions and cannot be completely applied to real life. However, if a spacecraft does not overcome the gravitational force of Earth, it will not be able to escape Earth and would likely fall back to Earth with disaster as there are many other conditions of leaving the atmosphere. The concept of escape velocity is very closely tied to the energy principle, and it is a direct application of conversion from potential to kinetic energies that is easily observable and testable. Application of this principle is most tied to aerospace and specifically spaceflight, but the underlying principle is a cross-discipline, universal concept.<br />
<br />
<br />
<br />
===External links===<br />
http://www.scientificamerican.com/article/bring-science-home-reaction-time/<br />
<br />
https://www.youtube.com/watch?v=7w56rwAtUZU<br />
<br />
==References==<br />
"Escape Velocity | Physics." Encyclopedia Britannica Online. Encyclopedia Britannica, n.d. Web. 05 Dec. 2015. <br />
[http://www.britannica.com/science/escape-velocity]<br />
<br />
Giancoli, Douglas C. "Physics for Scientists and Engineers with Modern Physics." Google Books. Google, n.d. Web. 05 Dec. 2015. <br />
[https://books.google.com/books?id=xz-UEdtRmzkC&pg=PA199&dq=escape+velocity+gravitational+potential+energy&hl=en&sa=X&ved=0CC0Q6AEwA2oVChMI8_PO4_PBxwIVBJmICh3T6gGl#v=onepage&q=escape%20velocity%20gravitational%20potential%20energy&f=false]<br />
<br />
"Escape Velocity." Wikipedia. Wikimedia Foundation, n.d. Web. 05 Dec. 2015.<br />
[https://en.wikipedia.org/wiki/Escape_velocity]<br />
<br />
Velocity, Escape, and ©200. ESCAPE VELOCITY EXAMPLES (n.d.): n. pag. 13 June 2003. Web. 5 Dec. 2015.<br />
[http://www.beaconlearningcenter.com/documents/1483_01.pdf]</div>
Daveed
http://www.physicsbook.gatech.edu/index.php?title=Escape_Velocity&diff=20721
Escape Velocity
2016-04-03T19:07:57Z
<p>Daveed: </p>
<hr />
<div>Claimed by David Gamero<br />
created by Varun Rajagopal<br />
[[File:Spacex.jpg|600px|thumb|right|space x]]<br />
<br />
Escape velocity is defined as the minimum velocity required for an object to escape the gravitational force of a large object. The sum of an object's kinetic energy and its Gravitational potential energy is equal to zero. The gravitational potential energy is negative due to the fact that kinetic energy is always positive. The velocity of the object will be be zero at infinite distance from the centre of gravity. There is no net force on an object as it escapes and zero acceleration is perceived.<br />
<br />
<br />
<br />
==The Main Idea==<br />
<br />
The formula for escape velocity at a certain distance from a body is calculated by the formula {{cite book|last=Khatri, Poudel, Gautam|first=M.K. , P.R. , A.K.|title=Principles of Physics|year=2010|publisher=Ayam Publication|location=Kathmandu|isbn=9789937903844|pages=170, 171}}<br />
:<math>v_e = \sqrt{\frac{2GM}{r}},</math><br />
<br />
where ''G'' is the universal [[gravitational constant]] (''G''&nbsp;=&nbsp;6.67×10<sup>−11</sup>&nbsp;m<sup>3</sup>&nbsp;kg<sup>−1</sup>&nbsp;s<sup>−2</sup>), ''M'' is the mass of the large body to be escaped, and ''r'' the distance from the [[center of mass]] of the mass ''M'' to the object.<ref group="nb"> This equation assumes there is no atmospheric friction and is an ideal scenario with sending an object on a trajectory. In fact, the escape velocity stated here should actually be called escape speed due to the fact that the quantity to be calculated is completely independent of direction. Notice that the equation does not include the mass of the object escaping a large body as escape velocity is only dependent on gravitational force. We also assume that an object is escaping from a uniform body. <br />
<br />
===A Mathematical Model===<br />
<br />
When we model escape velocity or speed, we have to assume that an object must have a velocity an infinite distance away from a large body allowing us to find the very minimum speed to escape that large body a certain distance away. "Escape velocity" is the speed needed to go from some distance away from a large body to an infinite distance, ending at infinity with a final speed of zero. This dismisses any initial acceleration. This means that a modern spacecraft for example with propellers does not follow these assumptions.<br />
<br />
:<math>(K + U_g)_i = (K + U_g)_f \,</math><br />
<br />
''K''<sub>''ƒ''</sub> = 0 because final velocity is zero, and ''U''<sub>gƒ</sub> = 0 because its final distance is expressed as infinity, therefore<br />
<br />
:<math>\frac{1}{2}mv_e^2 + \frac{-GMm}{r} = 0 + 0</math><br />
<br />
<!-- extra space between two lines of "displayed" [[TeX]] that were crowding each other and impairing legibility --><br />
<br />
:<math>v_e = \sqrt{\frac{2GM}{r}}</math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<div style="width:100%;height:400px"><br />
In the following diagrams the differences highlight the energy needed to escape a gravitational field. When the total energy (kinetic plus gravitational) is equal to or greater than zero then the object can escape, this is called an unbound system (illustrated in left energy diagram). This comes from that there is at least enough kinetic energy to offset the negative potential energy, so the object ends at a distance of <math>r=\infty</math> with no gravitational potential energy, which means it has escaped and its initial velocity was equal to or greater than the escape velocity. On the other hand in the image on the right, kinetic energy reaches zero at a radius where potential energy is still negative, which means that the object has a velocity of zero but is still being pulled by gravity resulting in it getting dragged back in and never being able to escape. In this bound system the initial velocity was less than the escape velocity.<br />
[[File:Ediagram_MSPaint_UnboundSystemWithExtraEnergy.png|500px|thumb|left|EnergyDiagramUnboundSystem]][[File:EDiagram_MSPaint_BoundSystem.png|500px|thumb|right|EnergyDiagramBoundSystem]]<br />
</div><br />
==Examples==<br />
<br />
[[File:prob.jpg|600px|thumb|center|example]]<br />
<br />
===Escaping Jupiter's Atmosphere===<br />
The radius of Jupiter is 71500e3 m, and its mass is 1900e24 kg. What is the escape speed of an object launched straight up from just above the atmosphere of Jupiter?<br />
<br />
<div style=""><br />
System = Jupiter + object<br />
<math><br />
<br />
\Delta E = 0\\<br />
\\<br />
v_i = ?\\<br />
v_f = 0 m/s\\<br />
r_i = 71500e3 m\\<br />
r_f = \infty\\<br />
m = mObject\\<br />
M = mJupiter (1900e24 kg)\\<br />
<br />
</math><br />
<br />
Starting from the Energy Principle:<br />
<br />
<math><br />
<br />
\Delta E = W + Q\\<br />
\Delta E = (0) + (0)\\<br />
\Delta E = 0\\<br />
(\Delta K + \Delta U) = 0\\<br />
\frac{1}{2}m(v_f^2-v_i^2) + (\frac{-GMm}{r_f} - \frac{-GMm}{r_i}) = 0\\<br />
\frac{1}{2}m((0)-v_i^2) + ((0) - \frac{-GMm}{r_i}) = 0\\<br />
\frac{-1}{2}mv_i^2 + \frac{GMm}{r_i} = 0\\<br />
\frac{GMm}{r_i} = \frac{1}{2}mv_i^2\\<br />
\frac{GM}{r_i} = \frac{1}{2}v_i^2\\<br />
v_i = \sqrt{\frac{2GM}{r_i}}\\<br />
= \sqrt{\frac{2(6.7e-11)(1900e24)}{(71500e3)}}\\<br />
= 59672.767m/s<br />
</math><br />
<br />
</div><br />
<br />
==Connectedness==<br />
In space, a rocket will not actually be able to travel an infinite distance once it escapes the gravitational pull of Earth, but rather must escape the gravitational pull of the Sun, the planets in our solar system, and every other larger body. The calculation of escape velocity assumes many conditions and cannot be completely applied to real life. However, if a spacecraft does not overcome the gravitational force of Earth, it will not be able to escape Earth and would likely fall back to Earth with disaster as there are many other conditions of leaving the atmosphere. This equation shows the conservation of energy which is a very important principle that is universal for all physics and science.<br />
<br />
<br />
<br />
===External links===<br />
http://www.scientificamerican.com/article/bring-science-home-reaction-time/<br />
<br />
https://www.youtube.com/watch?v=7w56rwAtUZU<br />
<br />
==References==<br />
"Escape Velocity | Physics." Encyclopedia Britannica Online. Encyclopedia Britannica, n.d. Web. 05 Dec. 2015. <br />
[http://www.britannica.com/science/escape-velocity]<br />
<br />
Giancoli, Douglas C. "Physics for Scientists and Engineers with Modern Physics." Google Books. Google, n.d. Web. 05 Dec. 2015. <br />
[https://books.google.com/books?id=xz-UEdtRmzkC&pg=PA199&dq=escape+velocity+gravitational+potential+energy&hl=en&sa=X&ved=0CC0Q6AEwA2oVChMI8_PO4_PBxwIVBJmICh3T6gGl#v=onepage&q=escape%20velocity%20gravitational%20potential%20energy&f=false]<br />
<br />
"Escape Velocity." Wikipedia. Wikimedia Foundation, n.d. Web. 05 Dec. 2015.<br />
[https://en.wikipedia.org/wiki/Escape_velocity]<br />
<br />
Velocity, Escape, and ©200. ESCAPE VELOCITY EXAMPLES (n.d.): n. pag. 13 June 2003. Web. 5 Dec. 2015.<br />
[http://www.beaconlearningcenter.com/documents/1483_01.pdf]</div>
Daveed
http://www.physicsbook.gatech.edu/index.php?title=Escape_Velocity&diff=20720
Escape Velocity
2016-04-03T19:06:59Z
<p>Daveed: </p>
<hr />
<div>Claimed by David Gamero<br />
created by Varun Rajagopal<br />
[[File:Spacex.jpg|600px|thumb|right|space x]]<br />
<br />
Escape velocity is defined as the minimum velocity required for an object to escape the gravitational force of a large object. The sum of an object's kinetic energy and its Gravitational potential energy is equal to zero. The gravitational potential energy is negative due to the fact that kinetic energy is always positive. The velocity of the object will be be zero at infinite distance from the centre of gravity. There is no net force on an object as it escapes and zero acceleration is perceived.<br />
<br />
<br />
<br />
==The Main Idea==<br />
<br />
The formula for escape velocity at a certain distance from a body is calculated by the formula {{cite book|last=Khatri, Poudel, Gautam|first=M.K. , P.R. , A.K.|title=Principles of Physics|year=2010|publisher=Ayam Publication|location=Kathmandu|isbn=9789937903844|pages=170, 171}}<br />
:<math>v_e = \sqrt{\frac{2GM}{r}},</math><br />
<br />
where ''G'' is the universal [[gravitational constant]] (''G''&nbsp;=&nbsp;6.67×10<sup>−11</sup>&nbsp;m<sup>3</sup>&nbsp;kg<sup>−1</sup>&nbsp;s<sup>−2</sup>), ''M'' is the mass of the large body to be escaped, and ''r'' the distance from the [[center of mass]] of the mass ''M'' to the object.<ref group="nb"> This equation assumes there is no atmospheric friction and is an ideal scenario with sending an object on a trajectory. In fact, the escape velocity stated here should actually be called escape speed due to the fact that the quantity to be calculated is completely independent of direction. Notice that the equation does not include the mass of the object escaping a large body as escape velocity is only dependent on gravitational force. We also assume that an object is escaping from a uniform body. <br />
<br />
===A Mathematical Model===<br />
<br />
When we model escape velocity or speed, we have to assume that an object must have a velocity an infinite distance away from a large body allowing us to find the very minimum speed to escape that large body a certain distance away. "Escape velocity" is the speed needed to go from some distance away from a large body to an infinite distance, ending at infinity with a final speed of zero. This dismisses any initial acceleration. This means that a modern spacecraft for example with propellers does not follow these assumptions.<br />
<br />
:<math>(K + U_g)_i = (K + U_g)_f \,</math><br />
<br />
''K''<sub>''ƒ''</sub> = 0 because final velocity is zero, and ''U''<sub>gƒ</sub> = 0 because its final distance is expressed as infinity, therefore<br />
<br />
:<math>\frac{1}{2}mv_e^2 + \frac{-GMm}{r} = 0 + 0</math><br />
<br />
<!-- extra space between two lines of "displayed" [[TeX]] that were crowding each other and impairing legibility --><br />
<br />
:<math>v_e = \sqrt{\frac{2GM}{r}}</math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<div style="width:100%;height:450px"><br />
In the following diagrams the differences highlight the energy needed to escape a gravitational field. When the total energy (kinetic plus gravitational) is equal to or greater than zero then the object can escape, this is called an unbound system (illustrated in left energy diagram). This comes from that there is at least enough kinetic energy to offset the negative potential energy, so the object ends at a distance of <math>r=\infty</math> with no gravitational potential energy, which means it has escaped and its initial velocity was equal to or greater than the escape velocity. On the other hand in the image on the right, kinetic energy reaches zero at a radius where potential energy is still negative, which means that the object has a velocity of zero but is still being pulled by gravity resulting in it getting dragged back in and never being able to escape. In this bound system the initial velocity was less than the escape velocity.<br />
[[File:Ediagram_MSPaint_UnboundSystemWithExtraEnergy.png|500px|thumb|left|EnergyDiagramUnboundSystem]][[File:EDiagram_MSPaint_BoundSystem.png|500px|thumb|right|EnergyDiagramBoundSystem]]<br />
</div><br />
==Examples==<br />
<br />
[[File:prob.jpg|600px|thumb|center|example]]<br />
<br />
===Escaping Jupiter's Atmosphere===<br />
The radius of Jupiter is 71500e3 m, and its mass is 1900e24 kg. What is the escape speed of an object launched straight up from just above the atmosphere of Jupiter?<br />
<br />
<div style=""><br />
System = Jupiter + object<br />
<math><br />
<br />
\Delta E = 0\\<br />
\\<br />
v_i = ?\\<br />
v_f = 0 m/s\\<br />
r_i = 71500e3 m\\<br />
r_f = \infty\\<br />
m = mObject\\<br />
M = mJupiter (1900e24 kg)\\<br />
<br />
</math><br />
<br />
Starting from the Energy Principle:<br />
<br />
<math><br />
<br />
\Delta E = W + Q\\<br />
\Delta E = (0) + (0)\\<br />
\Delta E = 0\\<br />
(\Delta K + \Delta U) = 0\\<br />
\frac{1}{2}m(v_f^2-v_i^2) + (\frac{-GMm}{r_f} - \frac{-GMm}{r_i}) = 0\\<br />
\frac{1}{2}m((0)-v_i^2) + ((0) - \frac{-GMm}{r_i}) = 0\\<br />
\frac{-1}{2}mv_i^2 + \frac{GMm}{r_i} = 0\\<br />
\frac{GMm}{r_i} = \frac{1}{2}mv_i^2\\<br />
\frac{GM}{r_i} = \frac{1}{2}v_i^2\\<br />
v_i = \sqrt{\frac{2GM}{r_i}}\\<br />
= \sqrt{\frac{2(6.7e-11)(1900e24)}{(71500e3)}}\\<br />
= 59672.767m/s<br />
</math><br />
<br />
</div><br />
<br />
==Connectedness==<br />
In space, a rocket will not actually be able to travel an infinite distance once it escapes the gravitational pull of Earth, but rather must escape the gravitational pull of the Sun, the planets in our solar system, and every other larger body. The calculation of escape velocity assumes many conditions and cannot be completely applied to real life. However, if a spacecraft does not overcome the gravitational force of Earth, it will not be able to escape Earth and would likely fall back to Earth with disaster as there are many other conditions of leaving the atmosphere. This equation shows the conservation of energy which is a very important principle that is universal for all physics and science.<br />
<br />
<br />
<br />
===External links===<br />
http://www.scientificamerican.com/article/bring-science-home-reaction-time/<br />
<br />
https://www.youtube.com/watch?v=7w56rwAtUZU<br />
<br />
==References==<br />
"Escape Velocity | Physics." Encyclopedia Britannica Online. Encyclopedia Britannica, n.d. Web. 05 Dec. 2015. <br />
[http://www.britannica.com/science/escape-velocity]<br />
<br />
Giancoli, Douglas C. "Physics for Scientists and Engineers with Modern Physics." Google Books. Google, n.d. Web. 05 Dec. 2015. <br />
[https://books.google.com/books?id=xz-UEdtRmzkC&pg=PA199&dq=escape+velocity+gravitational+potential+energy&hl=en&sa=X&ved=0CC0Q6AEwA2oVChMI8_PO4_PBxwIVBJmICh3T6gGl#v=onepage&q=escape%20velocity%20gravitational%20potential%20energy&f=false]<br />
<br />
"Escape Velocity." Wikipedia. Wikimedia Foundation, n.d. Web. 05 Dec. 2015.<br />
[https://en.wikipedia.org/wiki/Escape_velocity]<br />
<br />
Velocity, Escape, and ©200. ESCAPE VELOCITY EXAMPLES (n.d.): n. pag. 13 June 2003. Web. 5 Dec. 2015.<br />
[http://www.beaconlearningcenter.com/documents/1483_01.pdf]</div>
Daveed
http://www.physicsbook.gatech.edu/index.php?title=Escape_Velocity&diff=20719
Escape Velocity
2016-04-03T19:06:13Z
<p>Daveed: </p>
<hr />
<div>Claimed by David Gamero<br />
created by Varun Rajagopal<br />
[[File:Spacex.jpg|600px|thumb|right|space x]]<br />
<br />
Escape velocity is defined as the minimum velocity required for an object to escape the gravitational force of a large object. The sum of an object's kinetic energy and its Gravitational potential energy is equal to zero. The gravitational potential energy is negative due to the fact that kinetic energy is always positive. The velocity of the object will be be zero at infinite distance from the centre of gravity. There is no net force on an object as it escapes and zero acceleration is perceived.<br />
<br />
<br />
<br />
==The Main Idea==<br />
<br />
The formula for escape velocity at a certain distance from a body is calculated by the formula {{cite book|last=Khatri, Poudel, Gautam|first=M.K. , P.R. , A.K.|title=Principles of Physics|year=2010|publisher=Ayam Publication|location=Kathmandu|isbn=9789937903844|pages=170, 171}}<br />
:<math>v_e = \sqrt{\frac{2GM}{r}},</math><br />
<br />
where ''G'' is the universal [[gravitational constant]] (''G''&nbsp;=&nbsp;6.67×10<sup>−11</sup>&nbsp;m<sup>3</sup>&nbsp;kg<sup>−1</sup>&nbsp;s<sup>−2</sup>), ''M'' is the mass of the large body to be escaped, and ''r'' the distance from the [[center of mass]] of the mass ''M'' to the object.<ref group="nb"> This equation assumes there is no atmospheric friction and is an ideal scenario with sending an object on a trajectory. In fact, the escape velocity stated here should actually be called escape speed due to the fact that the quantity to be calculated is completely independent of direction. Notice that the equation does not include the mass of the object escaping a large body as escape velocity is only dependent on gravitational force. We also assume that an object is escaping from a uniform body. <br />
<br />
===A Mathematical Model===<br />
<br />
When we model escape velocity or speed, we have to assume that an object must have a velocity an infinite distance away from a large body allowing us to find the very minimum speed to escape that large body a certain distance away. "Escape velocity" is the speed needed to go from some distance away from a large body to an infinite distance, ending at infinity with a final speed of zero. This dismisses any initial acceleration. This means that a modern spacecraft for example with propellers does not follow these assumptions.<br />
<br />
:<math>(K + U_g)_i = (K + U_g)_f \,</math><br />
<br />
''K''<sub>''ƒ''</sub> = 0 because final velocity is zero, and ''U''<sub>gƒ</sub> = 0 because its final distance is expressed as infinity, therefore<br />
<br />
:<math>\frac{1}{2}mv_e^2 + \frac{-GMm}{r} = 0 + 0</math><br />
<br />
<!-- extra space between two lines of "displayed" [[TeX]] that were crowding each other and impairing legibility --><br />
<br />
:<math>v_e = \sqrt{\frac{2GM}{r}}</math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<div style="width:100%;height:500px"><br />
In the following diagrams the differences highlight the energy needed to escape a gravitational field. When the total energy (kinetic plus gravitational) is equal to or greater than zero then the object can escape, this is called an unbound system (illustrated in left energy diagram). This comes from that there is at least enough kinetic energy to offset the negative potential energy, so the object ends at a distance of <math>r=\infty</math> with no gravitational potential energy, which means it has escaped and its initial velocity was equal to or greater than the escape velocity. On the other hand in the image on the right, kinetic energy reaches zero at a radius where potential energy is still negative, which means that the object has a velocity of zero but is still being pulled by gravity resulting in it getting dragged back in and never being able to escape. In this bound system the initial velocity was less than the escape velocity.<br />
[[File:Ediagram_MSPaint_UnboundSystemWithExtraEnergy.png|500px|thumb|left|EnergyDiagramUnboundSystem]][[File:EDiagram_MSPaint_BoundSystem.png|500px|thumb|right|EnergyDiagramBoundSystem]]<br />
</div><br />
==Examples==<br />
<br />
[[File:prob.jpg|600px|thumb|center|example]]<br />
<br />
===Escaping Jupiter's Atmosphere===<br />
The radius of Jupiter is 71500e3 m, and its mass is 1900e24 kg. What is the escape speed of an object launched straight up from just above the atmosphere of Jupiter?<br />
<br />
<div style=""><br />
System = Jupiter + object<br />
<math><br />
<br />
\Delta E = 0\\<br />
\\<br />
v_i = ?\\<br />
v_f = 0 m/s\\<br />
r_i = 71500e3 m\\<br />
r_f = \infty\\<br />
m = mObject\\<br />
M = mJupiter (1900e24 kg)\\<br />
<br />
</math><br />
<br />
Starting from the Energy Principle:<br />
<br />
<math><br />
<br />
\Delta E = W + Q\\<br />
\Delta E = (0) + (0)\\<br />
\Delta E = 0\\<br />
(\Delta K + \Delta U) = 0\\<br />
\frac{1}{2}m(v_f^2-v_i^2) + (\frac{-GMm}{r_f} - \frac{-GMm}{r_i}) = 0\\<br />
\frac{1}{2}m((0)-v_i^2) + ((0) - \frac{-GMm}{r_i}) = 0\\<br />
\frac{-1}{2}mv_i^2 + \frac{GMm}{r_i} = 0\\<br />
\frac{GMm}{r_i} = \frac{1}{2}mv_i^2\\<br />
\frac{GM}{r_i} = \frac{1}{2}v_i^2\\<br />
v_i = \sqrt{\frac{2GM}{r_i}}\\<br />
= \sqrt{\frac{2(6.7e-11)(1900e24)}{(71500e3)}}\\<br />
= 59672.767m/s<br />
</math><br />
<br />
</div><br />
<br />
==Connectedness==<br />
In space, a rocket will not actually be able to travel an infinite distance once it escapes the gravitational pull of Earth, but rather must escape the gravitational pull of the Sun, the planets in our solar system, and every other larger body. The calculation of escape velocity assumes many conditions and cannot be completely applied to real life. However, if a spacecraft does not overcome the gravitational force of Earth, it will not be able to escape Earth and would likely fall back to Earth with disaster as there are many other conditions of leaving the atmosphere. This equation shows the conservation of energy which is a very important principle that is universal for all physics and science.<br />
<br />
<br />
<br />
===External links===<br />
http://www.scientificamerican.com/article/bring-science-home-reaction-time/<br />
<br />
https://www.youtube.com/watch?v=7w56rwAtUZU<br />
<br />
==References==<br />
"Escape Velocity | Physics." Encyclopedia Britannica Online. Encyclopedia Britannica, n.d. Web. 05 Dec. 2015. <br />
[http://www.britannica.com/science/escape-velocity]<br />
<br />
Giancoli, Douglas C. "Physics for Scientists and Engineers with Modern Physics." Google Books. Google, n.d. Web. 05 Dec. 2015. <br />
[https://books.google.com/books?id=xz-UEdtRmzkC&pg=PA199&dq=escape+velocity+gravitational+potential+energy&hl=en&sa=X&ved=0CC0Q6AEwA2oVChMI8_PO4_PBxwIVBJmICh3T6gGl#v=onepage&q=escape%20velocity%20gravitational%20potential%20energy&f=false]<br />
<br />
"Escape Velocity." Wikipedia. Wikimedia Foundation, n.d. Web. 05 Dec. 2015.<br />
[https://en.wikipedia.org/wiki/Escape_velocity]<br />
<br />
Velocity, Escape, and ©200. ESCAPE VELOCITY EXAMPLES (n.d.): n. pag. 13 June 2003. Web. 5 Dec. 2015.<br />
[http://www.beaconlearningcenter.com/documents/1483_01.pdf]</div>
Daveed
http://www.physicsbook.gatech.edu/index.php?title=Escape_Velocity&diff=20718
Escape Velocity
2016-04-03T19:04:52Z
<p>Daveed: </p>
<hr />
<div>Claimed by David Gamero<br />
created by Varun Rajagopal<br />
[[File:Spacex.jpg|600px|thumb|right|space x]]<br />
<br />
Escape velocity is defined as the minimum velocity required for an object to escape the gravitational force of a large object. The sum of an object's kinetic energy and its Gravitational potential energy is equal to zero. The gravitational potential energy is negative due to the fact that kinetic energy is always positive. The velocity of the object will be be zero at infinite distance from the centre of gravity. There is no net force on an object as it escapes and zero acceleration is perceived.<br />
<br />
<br />
<br />
==The Main Idea==<br />
<br />
The formula for escape velocity at a certain distance from a body is calculated by the formula {{cite book|last=Khatri, Poudel, Gautam|first=M.K. , P.R. , A.K.|title=Principles of Physics|year=2010|publisher=Ayam Publication|location=Kathmandu|isbn=9789937903844|pages=170, 171}}<br />
:<math>v_e = \sqrt{\frac{2GM}{r}},</math><br />
<br />
where ''G'' is the universal [[gravitational constant]] (''G''&nbsp;=&nbsp;6.67×10<sup>−11</sup>&nbsp;m<sup>3</sup>&nbsp;kg<sup>−1</sup>&nbsp;s<sup>−2</sup>), ''M'' is the mass of the large body to be escaped, and ''r'' the distance from the [[center of mass]] of the mass ''M'' to the object.<ref group="nb"> This equation assumes there is no atmospheric friction and is an ideal scenario with sending an object on a trajectory. In fact, the escape velocity stated here should actually be called escape speed due to the fact that the quantity to be calculated is completely independent of direction. Notice that the equation does not include the mass of the object escaping a large body as escape velocity is only dependent on gravitational force. We also assume that an object is escaping from a uniform body. <br />
<br />
===A Mathematical Model===<br />
<br />
When we model escape velocity or speed, we have to assume that an object must have a velocity an infinite distance away from a large body allowing us to find the very minimum speed to escape that large body a certain distance away. "Escape velocity" is the speed needed to go from some distance away from a large body to an infinite distance, ending at infinity with a final speed of zero. This dismisses any initial acceleration. This means that a modern spacecraft for example with propellers does not follow these assumptions.<br />
<br />
:<math>(K + U_g)_i = (K + U_g)_f \,</math><br />
<br />
''K''<sub>''ƒ''</sub> = 0 because final velocity is zero, and ''U''<sub>gƒ</sub> = 0 because its final distance is expressed as infinity, therefore<br />
<br />
:<math>\frac{1}{2}mv_e^2 + \frac{-GMm}{r} = 0 + 0</math><br />
<br />
<!-- extra space between two lines of "displayed" [[TeX]] that were crowding each other and impairing legibility --><br />
<br />
:<math>v_e = \sqrt{\frac{2GM}{r}}</math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<div style="width:100%;height:300px"><br />
In the following diagrams the differences highlight the energy needed to escape a gravitational field. When the total energy (kinetic plus gravitational) is equal to or greater than zero then the object can escape, this is called an unbound system (illustrated in left energy diagram). This comes from that there is at least enough kinetic energy to offset the negative potential energy, so the object ends at a distance of <math>r=\infty</math> with no gravitational potential energy, which means it has escaped and its initial velocity was equal to or greater than the escape velocity. On the other hand in the image on the right, kinetic energy reaches zero at a radius where potential energy is still negative, which means that the object has a velocity of zero but is still being pulled by gravity resulting in it getting dragged back in and never being able to escape. In this bound system the initial velocity was less than the escape velocity.<br />
[[File:Ediagram_MSPaint_UnboundSystemWithExtraEnergy.png|500px|thumb|left|EnergyDiagramUnboundSystem]][[File:EDiagram_MSPaint_BoundSystem.png|500px|thumb|right|EnergyDiagramBoundSystem]]<br />
</div><br />
==Examples==<br />
<br />
[[File:prob.jpg|600px|thumb|center|example]]<br />
<br />
===Escaping Jupiter's Atmosphere===<br />
The radius of Jupiter is 71500e3 m, and its mass is 1900e24 kg. What is the escape speed of an object launched straight up from just above the atmosphere of Jupiter?<br />
<br />
<div style=""><br />
System = Jupiter + object<br />
<math><br />
<br />
\Delta E = 0\\<br />
\\<br />
v_i = ?\\<br />
v_f = 0 m/s\\<br />
r_i = 71500e3 m\\<br />
r_f = \infty\\<br />
m = mObject\\<br />
M = mJupiter (1900e24 kg)\\<br />
<br />
</math><br />
<br />
Starting from the Energy Principle:<br />
<br />
<math><br />
<br />
\Delta E = W + Q\\<br />
\Delta E = (0) + (0)\\<br />
\Delta E = 0\\<br />
(\Delta K + \Delta U) = 0\\<br />
\frac{1}{2}m(v_f^2-v_i^2) + (\frac{-GMm}{r_f} - \frac{-GMm}{r_i}) = 0\\<br />
\frac{1}{2}m((0)-v_i^2) + ((0) - \frac{-GMm}{r_i}) = 0\\<br />
\frac{-1}{2}mv_i^2 + \frac{GMm}{r_i} = 0\\<br />
\frac{GMm}{r_i} = \frac{1}{2}mv_i^2\\<br />
\frac{GM}{r_i} = \frac{1}{2}v_i^2\\<br />
v_i = \sqrt{\frac{2GM}{r_i}}\\<br />
= \sqrt{\frac{2(6.7e-11)(1900e24)}{(71500e3)}}\\<br />
= 59672.767m/s<br />
</math><br />
<br />
</div><br />
<br />
==Connectedness==<br />
In space, a rocket will not actually be able to travel an infinite distance once it escapes the gravitational pull of Earth, but rather must escape the gravitational pull of the Sun, the planets in our solar system, and every other larger body. The calculation of escape velocity assumes many conditions and cannot be completely applied to real life. However, if a spacecraft does not overcome the gravitational force of Earth, it will not be able to escape Earth and would likely fall back to Earth with disaster as there are many other conditions of leaving the atmosphere. This equation shows the conservation of energy which is a very important principle that is universal for all physics and science.<br />
<br />
<br />
<br />
===External links===<br />
http://www.scientificamerican.com/article/bring-science-home-reaction-time/<br />
<br />
https://www.youtube.com/watch?v=7w56rwAtUZU<br />
<br />
==References==<br />
"Escape Velocity | Physics." Encyclopedia Britannica Online. Encyclopedia Britannica, n.d. Web. 05 Dec. 2015. <br />
[http://www.britannica.com/science/escape-velocity]<br />
<br />
Giancoli, Douglas C. "Physics for Scientists and Engineers with Modern Physics." Google Books. Google, n.d. Web. 05 Dec. 2015. <br />
[https://books.google.com/books?id=xz-UEdtRmzkC&pg=PA199&dq=escape+velocity+gravitational+potential+energy&hl=en&sa=X&ved=0CC0Q6AEwA2oVChMI8_PO4_PBxwIVBJmICh3T6gGl#v=onepage&q=escape%20velocity%20gravitational%20potential%20energy&f=false]<br />
<br />
"Escape Velocity." Wikipedia. Wikimedia Foundation, n.d. Web. 05 Dec. 2015.<br />
[https://en.wikipedia.org/wiki/Escape_velocity]<br />
<br />
Velocity, Escape, and ©200. ESCAPE VELOCITY EXAMPLES (n.d.): n. pag. 13 June 2003. Web. 5 Dec. 2015.<br />
[http://www.beaconlearningcenter.com/documents/1483_01.pdf]</div>
Daveed
http://www.physicsbook.gatech.edu/index.php?title=Escape_Velocity&diff=20715
Escape Velocity
2016-04-03T02:58:16Z
<p>Daveed: </p>
<hr />
<div>Claimed by David Gamero<br />
created by Varun Rajagopal<br />
[[File:Spacex.jpg|600px|thumb|right|space x]]<br />
<br />
Escape velocity is defined as the minimum velocity required for an object to escape the gravitational force of a large object. The sum of an object's kinetic energy and its Gravitational potential energy is equal to zero. The gravitational potential energy is negative due to the fact that kinetic energy is always positive. The velocity of the object will be be zero at infinite distance from the centre of gravity. There is no net force on an object as it escapes and zero acceleration is perceived.<br />
<br />
<br />
<br />
==The Main Idea==<br />
<br />
The formula for escape velocity at a certain distance from a body is calculated by the formula {{cite book|last=Khatri, Poudel, Gautam|first=M.K. , P.R. , A.K.|title=Principles of Physics|year=2010|publisher=Ayam Publication|location=Kathmandu|isbn=9789937903844|pages=170, 171}}<br />
:<math>v_e = \sqrt{\frac{2GM}{r}},</math><br />
<br />
where ''G'' is the universal [[gravitational constant]] (''G''&nbsp;=&nbsp;6.67×10<sup>−11</sup>&nbsp;m<sup>3</sup>&nbsp;kg<sup>−1</sup>&nbsp;s<sup>−2</sup>), ''M'' is the mass of the large body to be escaped, and ''r'' the distance from the [[center of mass]] of the mass ''M'' to the object.<ref group="nb"> This equation assumes there is no atmospheric friction and is an ideal scenario with sending an object on a trajectory. In fact, the escape velocity stated here should actually be called escape speed due to the fact that the quantity to be calculated is completely independent of direction. Notice that the equation does not include the mass of the object escaping a large body as escape velocity is only dependent on gravitational force. We also assume that an object is escaping from a uniform body. <br />
<br />
===A Mathematical Model===<br />
<br />
When we model escape velocity or speed, we have to assume that an object must have a velocity an infinite distance away from a large body allowing us to find the very minimum speed to escape that large body a certain distance away. "Escape velocity" is the speed needed to go from some distance away from a large body to an infinite distance, ending at infinity with a final speed of zero. This dismisses any initial acceleration. This means that a modern spacecraft for example with propellers does not follow these assumptions.<br />
<br />
:<math>(K + U_g)_i = (K + U_g)_f \,</math><br />
<br />
''K''<sub>''ƒ''</sub> = 0 because final velocity is zero, and ''U''<sub>gƒ</sub> = 0 because its final distance is expressed as infinity, therefore<br />
<br />
:<math>\frac{1}{2}mv_e^2 + \frac{-GMm}{r} = 0 + 0</math><br />
<br />
<!-- extra space between two lines of "displayed" [[TeX]] that were crowding each other and impairing legibility --><br />
<br />
:<math>v_e = \sqrt{\frac{2GM}{r}}</math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<div style="width:100%;height:300px"><br />
[[File:Ediagram_MSPaint_UnboundSystemWithExtraEnergy.png|500px|thumb|left|EnergyDiagramUnboundSystem]][[File:EDiagram_MSPaint_BoundSystem.png|500px|thumb|right|EnergyDiagramBoundSystem]]<br />
</div><br />
==Examples==<br />
<br />
[[File:prob.jpg|600px|thumb|center|example]]<br />
<br />
===Escaping Jupiter's Atmosphere===<br />
The radius of Jupiter is 71500e3 m, and its mass is 1900e24 kg. What is the escape speed of afn object launched straight up from just above the atmosphere of Jupiter?<br />
<br />
<div style=""><br />
System = Jupiter + object<br />
<math><br />
<br />
\Delta E = 0\\<br />
\\<br />
v_i = ?\\<br />
v_f = 0 m/s\\<br />
r_i = 71500e3 m\\<br />
r_f = \infty\\<br />
m = mObject\\<br />
M = mJupiter (1900e24 kg)\\<br />
<br />
</math><br />
<br />
Starting from the Energy Principle:<br />
<br />
<math><br />
<br />
\Delta E = W + Q\\<br />
\Delta E = (0) + (0)\\<br />
\Delta E = 0\\<br />
(\Delta K + \Delta U) = 0\\<br />
\frac{1}{2}m(v_f^2-v_i^2) + (\frac{-GMm}{r_f} - \frac{-GMm}{r_i}) = 0\\<br />
\frac{1}{2}m((0)-v_i^2) + ((0) - \frac{-GMm}{r_i}) = 0\\<br />
\frac{-1}{2}mv_i^2 + \frac{GMm}{r_i} = 0\\<br />
\frac{GMm}{r_i} = \frac{1}{2}mv_i^2\\<br />
\frac{GM}{r_i} = \frac{1}{2}v_i^2\\<br />
v_i = \sqrt{\frac{2GM}{r_i}}\\<br />
= \sqrt{\frac{2(6.7e-11)(1900e24)}{(71500e3)}}\\<br />
= 59672.767m/s<br />
</math><br />
<br />
</div><br />
<br />
==Connectedness==<br />
In space, a rocket will not actually be able to travel an infinite distance once it escapes the gravitational pull of Earth, but rather must escape the gravitational pull of the Sun, the planets in our solar system, and every other larger body. The calculation of escape velocity assumes many conditions and cannot be completely applied to real life. However, if a spacecraft does not overcome the gravitational force of Earth, it will not be able to escape Earth and would likely fall back to Earth with disaster as there are many other conditions of leaving the atmosphere. This equation shows the conservation of energy which is a very important principle that is universal for all physics and science.<br />
<br />
<br />
<br />
===External links===<br />
http://www.scientificamerican.com/article/bring-science-home-reaction-time/<br />
<br />
https://www.youtube.com/watch?v=7w56rwAtUZU<br />
<br />
==References==<br />
"Escape Velocity | Physics." Encyclopedia Britannica Online. Encyclopedia Britannica, n.d. Web. 05 Dec. 2015. <br />
[http://www.britannica.com/science/escape-velocity]<br />
<br />
Giancoli, Douglas C. "Physics for Scientists and Engineers with Modern Physics." Google Books. Google, n.d. Web. 05 Dec. 2015. <br />
[https://books.google.com/books?id=xz-UEdtRmzkC&pg=PA199&dq=escape+velocity+gravitational+potential+energy&hl=en&sa=X&ved=0CC0Q6AEwA2oVChMI8_PO4_PBxwIVBJmICh3T6gGl#v=onepage&q=escape%20velocity%20gravitational%20potential%20energy&f=false]<br />
<br />
"Escape Velocity." Wikipedia. Wikimedia Foundation, n.d. Web. 05 Dec. 2015.<br />
[https://en.wikipedia.org/wiki/Escape_velocity]<br />
<br />
Velocity, Escape, and ©200. ESCAPE VELOCITY EXAMPLES (n.d.): n. pag. 13 June 2003. Web. 5 Dec. 2015.<br />
[http://www.beaconlearningcenter.com/documents/1483_01.pdf]</div>
Daveed
http://www.physicsbook.gatech.edu/index.php?title=File:EDiagram_MSPaint_BoundSystem.png&diff=20714
File:EDiagram MSPaint BoundSystem.png
2016-04-03T02:57:56Z
<p>Daveed: Daveed uploaded a new version of &quot;File:EDiagram MSPaint BoundSystem.png&quot;</p>
<hr />
<div>An energy diagram of a bound system made in the highest MSPaint quality. Very rare and valuable.</div>
Daveed
http://www.physicsbook.gatech.edu/index.php?title=File:Ediagram_MSPaint_UnboundSystemWithExtraEnergy.png&diff=20713
File:Ediagram MSPaint UnboundSystemWithExtraEnergy.png
2016-04-03T02:38:07Z
<p>Daveed: An energy diagram for an unbound system with enough energy to have significant velocity after escaping. Highest MSPaint quality, appraised at 5k dogecoin.</p>
<hr />
<div>An energy diagram for an unbound system with enough energy to have significant velocity after escaping. Highest MSPaint quality, appraised at 5k dogecoin.</div>
Daveed
http://www.physicsbook.gatech.edu/index.php?title=File:EDiagram_MSPaint_BoundSystem.png&diff=20712
File:EDiagram MSPaint BoundSystem.png
2016-04-03T02:36:47Z
<p>Daveed: An energy diagram of a bound system made in the highest MSPaint quality. Very rare and valuable.</p>
<hr />
<div>An energy diagram of a bound system made in the highest MSPaint quality. Very rare and valuable.</div>
Daveed
http://www.physicsbook.gatech.edu/index.php?title=Escape_Velocity&diff=20711
Escape Velocity
2016-04-03T02:21:36Z
<p>Daveed: </p>
<hr />
<div>Claimed by David Gamero<br />
created by Varun Rajagopal<br />
[[File:Spacex.jpg|600px|thumb|right|space x]]<br />
<br />
Escape velocity is defined as the minimum velocity required for an object to escape the gravitational force of a large object. The sum of an object's kinetic energy and its Gravitational potential energy is equal to zero. The gravitational potential energy is negative due to the fact that kinetic energy is always positive. The velocity of the object will be be zero at infinite distance from the centre of gravity. There is no net force on an object as it escapes and zero acceleration is perceived.<br />
<br />
<br />
<br />
==The Main Idea==<br />
<br />
The formula for escape velocity at a certain distance from a body is calculated by the formula {{cite book|last=Khatri, Poudel, Gautam|first=M.K. , P.R. , A.K.|title=Principles of Physics|year=2010|publisher=Ayam Publication|location=Kathmandu|isbn=9789937903844|pages=170, 171}}<br />
:<math>v_e = \sqrt{\frac{2GM}{r}},</math><br />
<br />
where ''G'' is the universal [[gravitational constant]] (''G''&nbsp;=&nbsp;6.67×10<sup>−11</sup>&nbsp;m<sup>3</sup>&nbsp;kg<sup>−1</sup>&nbsp;s<sup>−2</sup>), ''M'' is the mass of the large body to be escaped, and ''r'' the distance from the [[center of mass]] of the mass ''M'' to the object.<ref group="nb"> This equation assumes there is no atmospheric friction and is an ideal scenario with sending an object on a trajectory. In fact, the escape velocity stated here should actually be called escape speed due to the fact that the quantity to be calculated is completely independent of direction. Notice that the equation does not include the mass of the object escaping a large body as escape velocity is only dependent on gravitational force. We also assume that an object is escaping from a uniform body. <br />
<br />
===A Mathematical Model===<br />
<br />
When we model escape velocity or speed, we have to assume that an object must have a velocity an infinite distance away from a large body allowing us to find the very minimum speed to escape that large body a certain distance away. "Escape velocity" is the speed needed to go from some distance away from a large body to an infinite distance, ending at infinity with a final speed of zero. This dismisses any initial acceleration. This means that a modern spacecraft for example with propellers does not follow these assumptions.<br />
<br />
:<math>(K + U_g)_i = (K + U_g)_f \,</math><br />
<br />
''K''<sub>''ƒ''</sub> = 0 because final velocity is zero, and ''U''<sub>gƒ</sub> = 0 because its final distance is expressed as infinity, therefore<br />
<br />
:<math>\frac{1}{2}mv_e^2 + \frac{-GMm}{r} = 0 + 0</math><br />
<br />
<!-- extra space between two lines of "displayed" [[TeX]] that were crowding each other and impairing legibility --><br />
<br />
:<math>v_e = \sqrt{\frac{2GM}{r}}</math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
[[File:prob.jpg|600px|thumb|center|example]]<br />
<br />
===Escaping Jupiter's Atmosphere===<br />
The radius of Jupiter is 71500e3 m, and its mass is 1900e24 kg. What is the escape speed of afn object launched straight up from just above the atmosphere of Jupiter?<br />
<br />
<div style=""><br />
System = Jupiter + object<br />
<math><br />
<br />
\Delta E = 0\\<br />
\\<br />
v_i = ?\\<br />
v_f = 0 m/s\\<br />
r_i = 71500e3 m\\<br />
r_f = \infty\\<br />
m = mObject\\<br />
M = mJupiter (1900e24 kg)\\<br />
<br />
</math><br />
<br />
Starting from the Energy Principle:<br />
<br />
<math><br />
<br />
\Delta E = W + Q\\<br />
\Delta E = (0) + (0)\\<br />
\Delta E = 0\\<br />
(\Delta K + \Delta U) = 0\\<br />
\frac{1}{2}m(v_f^2-v_i^2) + (\frac{-GMm}{r_f} - \frac{-GMm}{r_i}) = 0\\<br />
\frac{1}{2}m((0)-v_i^2) + ((0) - \frac{-GMm}{r_i}) = 0\\<br />
\frac{-1}{2}mv_i^2 + \frac{GMm}{r_i} = 0\\<br />
\frac{GMm}{r_i} = \frac{1}{2}mv_i^2\\<br />
\frac{GM}{r_i} = \frac{1}{2}v_i^2\\<br />
v_i = \sqrt{\frac{2GM}{r_i}}\\<br />
= \sqrt{\frac{2(6.7e-11)(1900e24)}{(71500e3)}}\\<br />
= 59672.767m/s<br />
</math><br />
<br />
</div><br />
<br />
==Connectedness==<br />
In space, a rocket will not actually be able to travel an infinite distance once it escapes the gravitational pull of Earth, but rather must escape the gravitational pull of the Sun, the planets in our solar system, and every other larger body. The calculation of escape velocity assumes many conditions and cannot be completely applied to real life. However, if a spacecraft does not overcome the gravitational force of Earth, it will not be able to escape Earth and would likely fall back to Earth with disaster as there are many other conditions of leaving the atmosphere. This equation shows the conservation of energy which is a very important principle that is universal for all physics and science.<br />
<br />
<br />
<br />
===External links===<br />
http://www.scientificamerican.com/article/bring-science-home-reaction-time/<br />
<br />
https://www.youtube.com/watch?v=7w56rwAtUZU<br />
<br />
==References==<br />
"Escape Velocity | Physics." Encyclopedia Britannica Online. Encyclopedia Britannica, n.d. Web. 05 Dec. 2015. <br />
[http://www.britannica.com/science/escape-velocity]<br />
<br />
Giancoli, Douglas C. "Physics for Scientists and Engineers with Modern Physics." Google Books. Google, n.d. Web. 05 Dec. 2015. <br />
[https://books.google.com/books?id=xz-UEdtRmzkC&pg=PA199&dq=escape+velocity+gravitational+potential+energy&hl=en&sa=X&ved=0CC0Q6AEwA2oVChMI8_PO4_PBxwIVBJmICh3T6gGl#v=onepage&q=escape%20velocity%20gravitational%20potential%20energy&f=false]<br />
<br />
"Escape Velocity." Wikipedia. Wikimedia Foundation, n.d. Web. 05 Dec. 2015.<br />
[https://en.wikipedia.org/wiki/Escape_velocity]<br />
<br />
Velocity, Escape, and ©200. ESCAPE VELOCITY EXAMPLES (n.d.): n. pag. 13 June 2003. Web. 5 Dec. 2015.<br />
[http://www.beaconlearningcenter.com/documents/1483_01.pdf]</div>
Daveed
http://www.physicsbook.gatech.edu/index.php?title=Escape_Velocity&diff=20710
Escape Velocity
2016-04-03T02:16:19Z
<p>Daveed: </p>
<hr />
<div>Claimed by David Gamero<br />
created by Varun Rajagopal<br />
[[File:Spacex.jpg|600px|thumb|right|space x]]<br />
<br />
Escape velocity is defined as the minimum velocity required for an object to escape the gravitational force of a large object. The sum of an object's kinetic energy and its Gravitational potential energy is equal to zero. The gravitational potential energy is negative due to the fact that kinetic energy is always positive. The velocity of the object will be be zero at infinite distance from the centre of gravity. There is no net force on an object as it escapes and zero acceleration is perceived.<br />
<br />
<br />
<br />
==The Main Idea==<br />
<br />
The formula for escape velocity at a certain distance from a body is calculated by the formula {{cite book|last=Khatri, Poudel, Gautam|first=M.K. , P.R. , A.K.|title=Principles of Physics|year=2010|publisher=Ayam Publication|location=Kathmandu|isbn=9789937903844|pages=170, 171}}<br />
:<math>v_e = \sqrt{\frac{2GM}{r}},</math><br />
<br />
where ''G'' is the universal [[gravitational constant]] (''G''&nbsp;=&nbsp;6.67×10<sup>−11</sup>&nbsp;m<sup>3</sup>&nbsp;kg<sup>−1</sup>&nbsp;s<sup>−2</sup>), ''M'' is the mass of the large body to be escaped, and ''r'' the distance from the [[center of mass]] of the mass ''M'' to the object.<ref group="nb"> This equation assumes there is no atmospheric friction and is an ideal scenario with sending an object on a trajectory. In fact, the escape velocity stated here should actually be called escape speed due to the fact that the quantity to be calculated is completely independent of direction. Notice that the equation does not include the mass of the object escaping a large body as escape velocity is only dependent on gravitational force. We also assume that an object is escaping from a uniform body. <br />
<br />
===A Mathematical Model===<br />
<br />
When we model escape velocity or speed, we have to assume that an object must have a velocity an infinite distance away from a large body allowing us to find the very minimum speed to escape that large body a certain distance away. "Escape velocity" is the speed needed to go from some distance away from a large body to an infinite distance, ending at infinity with a final speed of zero. This dismisses any initial acceleration. This means that a modern spacecraft for example with propellers does not follow these assumptions.<br />
<br />
:<math>(K + U_g)_i = (K + U_g)_f \,</math><br />
<br />
''K''<sub>''ƒ''</sub> = 0 because final velocity is zero, and ''U''<sub>gƒ</sub> = 0 because its final distance is expressed as infinity, therefore<br />
<br />
:<math>\frac{1}{2}mv_e^2 + \frac{-GMm}{r} = 0 + 0</math><br />
<br />
<!-- extra space between two lines of "displayed" [[TeX]] that were crowding each other and impairing legibility --><br />
<br />
:<math>v_e = \sqrt{\frac{2GM}{r}}</math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
[[File:prob.jpg|600px|thumb|center|example]]<br />
<br />
===Escaping Jupiter's Atmosphere===<br />
The radius of Jupiter is 71500e3 m, and its mass is 1900e24 kg. What is the escape speed of afn object launched straight up from just above the atmosphere of Jupiter?<br />
<br />
System = Jupiter + object<br />
<math><br />
\Delta E = 0\\<br />
\\<br />
v_i = ?\\<br />
v_f = 0 m/s\\<br />
r_i = 71500e3 m\\<br />
r_f = \infty\\<br />
m = mObject\\<br />
M = mJupiter (1900e24 kg)\\<br />
</math><br />
<br />
Starting from the Energy Principle:<br />
<br />
<math><br />
\Delta E = W + Q\\<br />
\Delta E = (0) + (0)\\<br />
\Delta E = 0\\<br />
(\Delta K + \Delta U) = 0\\<br />
\frac{1}{2}m(v_f^2-v_i^2) + (\frac{-GMm}{r_f} - \frac{-GMm}{r_i}) = 0\\<br />
\frac{1}{2}m((0)-v_i^2) + ((0) - \frac{-GMm}{r_i}) = 0\\<br />
\frac{-1}{2}mv_i^2 + \frac{GMm}{r_i} = 0\\<br />
\frac{GMm}{r_i} = \frac{1}{2}mv_i^2\\<br />
\frac{GM}{r_i} = \frac{1}{2}v_i^2\\<br />
v_i = \sqrt{\frac{2GM}{r_i}}\\<br />
= \sqrt{\frac{2(6.7e-11)(1900e24)}{(71500e3)}}\\<br />
= 59672.767m/s<br />
</math><br />
<br />
==Connectedness==<br />
In space, a rocket will not actually be able to travel an infinite distance once it escapes the gravitational pull of Earth, but rather must escape the gravitational pull of the Sun, the planets in our solar system, and every other larger body. The calculation of escape velocity assumes many conditions and cannot be completely applied to real life. However, if a spacecraft does not overcome the gravitational force of Earth, it will not be able to escape Earth and would likely fall back to Earth with disaster as there are many other conditions of leaving the atmosphere. This equation shows the conservation of energy which is a very important principle that is universal for all physics and science.<br />
<br />
<br />
<br />
===External links===<br />
http://www.scientificamerican.com/article/bring-science-home-reaction-time/<br />
<br />
https://www.youtube.com/watch?v=7w56rwAtUZU<br />
<br />
==References==<br />
"Escape Velocity | Physics." Encyclopedia Britannica Online. Encyclopedia Britannica, n.d. Web. 05 Dec. 2015. <br />
[http://www.britannica.com/science/escape-velocity]<br />
<br />
Giancoli, Douglas C. "Physics for Scientists and Engineers with Modern Physics." Google Books. Google, n.d. Web. 05 Dec. 2015. <br />
[https://books.google.com/books?id=xz-UEdtRmzkC&pg=PA199&dq=escape+velocity+gravitational+potential+energy&hl=en&sa=X&ved=0CC0Q6AEwA2oVChMI8_PO4_PBxwIVBJmICh3T6gGl#v=onepage&q=escape%20velocity%20gravitational%20potential%20energy&f=false]<br />
<br />
"Escape Velocity." Wikipedia. Wikimedia Foundation, n.d. Web. 05 Dec. 2015.<br />
[https://en.wikipedia.org/wiki/Escape_velocity]<br />
<br />
Velocity, Escape, and ©200. ESCAPE VELOCITY EXAMPLES (n.d.): n. pag. 13 June 2003. Web. 5 Dec. 2015.<br />
[http://www.beaconlearningcenter.com/documents/1483_01.pdf]</div>
Daveed
http://www.physicsbook.gatech.edu/index.php?title=Escape_Velocity&diff=20643
Escape Velocity
2016-03-17T18:31:02Z
<p>Daveed: </p>
<hr />
<div>Claimed by David Gamero<br />
created by Varun Rajagopal<br />
[[File:Spacex.jpg|600px|thumb|right|space x]]<br />
<br />
Escape velocity is defined as the minimum velocity required for an object to escape the gravitational force of a large object. The sum of an object's kinetic energy and its Gravitational potential energy is equal to zero. The gravitational potential energy is negative due to the fact that kinetic energy is always positive. The velocity of the object will be be zero at infinite distance from the centre of gravity. There is no net force on an object as it escapes and zero acceleration is perceived.<br />
<br />
<br />
<br />
==The Main Idea==<br />
<br />
The formula for escape velocity at a certain distance from a body is calculated by the formula {{cite book|last=Khatri, Poudel, Gautam|first=M.K. , P.R. , A.K.|title=Principles of Physics|year=2010|publisher=Ayam Publication|location=Kathmandu|isbn=9789937903844|pages=170, 171}}<br />
:<math>v_e = \sqrt{\frac{2GM}{r}},</math><br />
<br />
where ''G'' is the universal [[gravitational constant]] (''G''&nbsp;=&nbsp;6.67×10<sup>−11</sup>&nbsp;m<sup>3</sup>&nbsp;kg<sup>−1</sup>&nbsp;s<sup>−2</sup>), ''M'' is the mass of the large body to be escaped, and ''r'' the distance from the [[center of mass]] of the mass ''M'' to the object.<ref group="nb"> This equation assumes there is no atmospheric friction and is an ideal scenario with sending an object on a trajectory. In fact, the escape velocity stated here should actually be called escape speed due to the fact that the quantity to be calculated is completely independent of direction. Notice that the equation does not include the mass of the object escaping a large body as escape velocity is only dependent on gravitational force. We also assume that an object is escaping from a uniform body. <br />
<br />
===A Mathematical Model===<br />
<br />
When we model escape velocity or speed, we have to assume that an object must have a velocity an infinite distance away from a large body allowing us to find the very minimum speed to escape that large body a certain distance away. "Escape velocity" is the speed needed to go from some distance away from a large body to an infinite distance, ending at infinity with a final speed of zero. This dismisses any initial acceleration. This means that a modern spacecraft for example with propellers does not follow these assumptions.<br />
<br />
:<math>(K + U_g)_i = (K + U_g)_f \,</math><br />
<br />
''K''<sub>''ƒ''</sub> = 0 because final velocity is zero, and ''U''<sub>gƒ</sub> = 0 because its final distance is expressed as infinity, therefore<br />
<br />
:<math>\frac{1}{2}mv_e^2 + \frac{-GMm}{r} = 0 + 0</math><br />
<br />
<!-- extra space between two lines of "displayed" [[TeX]] that were crowding each other and impairing legibility --><br />
<br />
:<math>v_e = \sqrt{\frac{2GM}{r}}</math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
[[File:prob.jpg|600px|thumb|center|example]]<br />
<br />
==Connectedness==<br />
In space, a rocket will not actually be able to travel an infinite distance once it escapes the gravitational pull of Earth, but rather must escape the gravitational pull of the Sun, the planets in our solar system, and every other larger body. The calculation of escape velocity assumes many conditions and cannot be completely applied to real life. However, if a spacecraft does not overcome the gravitational force of Earth, it will not be able to escape Earth and would likely fall back to Earth with disaster as there are many other conditions of leaving the atmosphere. This equation shows the conservation of energy which is a very important principle that is universal for all physics and science.<br />
<br />
<br />
<br />
===External links===<br />
http://www.scientificamerican.com/article/bring-science-home-reaction-time/<br />
<br />
https://www.youtube.com/watch?v=7w56rwAtUZU<br />
<br />
==References==<br />
"Escape Velocity | Physics." Encyclopedia Britannica Online. Encyclopedia Britannica, n.d. Web. 05 Dec. 2015. <br />
[http://www.britannica.com/science/escape-velocity]<br />
<br />
Giancoli, Douglas C. "Physics for Scientists and Engineers with Modern Physics." Google Books. Google, n.d. Web. 05 Dec. 2015. <br />
[https://books.google.com/books?id=xz-UEdtRmzkC&pg=PA199&dq=escape+velocity+gravitational+potential+energy&hl=en&sa=X&ved=0CC0Q6AEwA2oVChMI8_PO4_PBxwIVBJmICh3T6gGl#v=onepage&q=escape%20velocity%20gravitational%20potential%20energy&f=false]<br />
<br />
"Escape Velocity." Wikipedia. Wikimedia Foundation, n.d. Web. 05 Dec. 2015.<br />
[https://en.wikipedia.org/wiki/Escape_velocity]<br />
<br />
Velocity, Escape, and ©200. ESCAPE VELOCITY EXAMPLES (n.d.): n. pag. 13 June 2003. Web. 5 Dec. 2015.<br />
[http://www.beaconlearningcenter.com/documents/1483_01.pdf]</div>
Daveed