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http://www.physicsbook.gatech.edu/api.php?action=feedcontributions&feedformat=atom&user=Swebster9 Physics Book - User contributions [en] 2026-04-12T10:48:59Z User contributions MediaWiki 1.42.7 http://www.physicsbook.gatech.edu/index.php?title=VPython_Modelling_of_Electric_and_Magnetic_Forces&diff=24413 VPython Modelling of Electric and Magnetic Forces 2016-11-27T00:48:54Z

<p>Swebster9: </p> <hr /> <div>VPython Modelling of Electric and Magnetic Forces<br /> claimed by Fall 2016: Sam Webster<br /> Spring 2016: Neil Acharya (nacharya)<br /> <br /> ==The Main Idea==<br /> <br /> State, in your own words, the main idea for this topic<br /> Electric Field of Capacitor<br /> <br /> ===A Mathematical Model===<br /> <br /> What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<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 /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=VPython_Modelling_of_Electric_and_Magnetic_Forces&diff=24412 VPython Modelling of Electric and Magnetic Forces 2016-11-27T00:48:20Z

<p>Swebster9: </p> <hr /> <div>VPython Modelling of Electric and Magnetic Forces<br /> claimed by Fall 2016: Sam Webster \n<br /> Spring 2016: Neil Acharya (nacharya)<br /> <br /> ==The Main Idea==<br /> <br /> State, in your own words, the main idea for this topic<br /> Electric Field of Capacitor<br /> <br /> ===A Mathematical Model===<br /> <br /> What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<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 /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=VPython_Modelling_of_Electric_and_Magnetic_Forces&diff=24411 VPython Modelling of Electric and Magnetic Forces 2016-11-27T00:47:28Z

<p>Swebster9: Claiming to Edit for Fall 2016</p> <hr /> <div>VPython Modelling of Electric and Magnetic Forces<br /> claimed by Sam Webster Fall 2016<br /> Spring 2016: Neil Acharya (nacharya)<br /> <br /> ==The Main Idea==<br /> <br /> State, in your own words, the main idea for this topic<br /> Electric Field of Capacitor<br /> <br /> ===A Mathematical Model===<br /> <br /> What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<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 /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Collisions&diff=23397 Collisions 2016-04-26T21:09:55Z

<p>Swebster9: </p> <hr /> <div>SECOND EDIT BY SUNGJAE HYUN IN 2016-04-16 ADDITIONS MADE BY Sam Webster 4-17-16<br /> <br /> This topic covers Collisions, a comprehensive way to combine the Momentum and Energy Principles.<br /> <br /> ==The Main Idea==<br /> <br /> Collisions are special types of contact interactions between objects. From a physics standpoint, collisions are a way to combine the Momentum and Energy Principles. In the case of collisions, if we choose a system of the two objects interacting, the change in momentum of the system and the change in energy of the system are both zero. With this in mind, calculations with collisions become very simple. We are able to choose a system of only the two objects (excluding external forces such as the Earth's gravity) because the collision takes place during such a short time that the external forces have a negligible effect. <br /> There are two types of collisions, [[Elastic Collisions]] and [[Inelastic Collisions]]. <br /> <br /> ===A Mathematical Model===<br /> <math>{E}_{f} = {E}_{i}</math> where <math>{E}_{f}</math> is the total final energy of the system and <math>{E}_{i}</math> is the total initial energy of the system.<br /> <br /> <math>{p}_{f} = {p}_{i}</math> where <math>{p}_{f}</math> is the total final momentum of the system and <math>{p}_{i}</math> is the total initial momentum of the system.<br /> <br /> ===A Computational Model===<br /> The following situation was used for this model created using python:<br /> <br /> Two objects are initially moving towards a third stationary object. Object 1 (in red) at position (-10,0,-2)m has a mass of 2kg and velocity (10,0,2)m/s. Object 2 (in blue) at position (0,6,3)m has a mass of 4kg and velocity (0,-6,3)m/s. Object 3 (in orange) at the origin has a mass of 5kg. The objects collide at the origin and after the collision it is observed that object 1 has embedded in object 3 (hence it is no longer visible in the model) and the combined object moves with velocity (5,-6,0)m/s (This is an example of a [[Maximally Inelastic Collision]]). The final velocity of object 2 is calculated and used in the rest of the simulation. (NOTE: the white sphere visible after the collision represents the origin to add dimension to the model and the delay during the collision is there to emphasis when and where the collision happens. Also use the link below the model for a more detailed explanation of the calculations and concepts.).<br /> <br /> [[File: CollisionsExample.gif]]<br /> <br /> Check out the code used for the simulation at [http://www.glowscript.org/#/user/samsaxlaxman/folder/Private/]. The code is commented pretty heavily (but it does assume some knowledge of python and python animations) in hopes that future students can modify some of the variables to experiment with creating different results.<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> Example 1)<br /> A 0.5 kg soccer ball is moving with a speed of 5 m/s directly toward to 0.7 kg basket ball which is at rest.<br /> When two balls collide and stick together what will their final velocity be?<br /> <br /> ___<br /> <br /> m1 = 0.5 kg,<br /> v1 init = 5 m/s,<br /> m2 = 0.7 kg,<br /> v2 init = 0 m/s<br /> <br /> So m1 * v1 + m2 * + v2 = (m1 + m2) * vfinal<br /> <br /> LHS = 0.5 * 5 + 0.7 * 0 = 2.5 kg*m/s<br /> RHS = (0.5 + 0.7) * vfinal = 1.2 * vfinal<br /> <br /> LHS = RHS in inelastic collision <br /> <br /> 2.5 = 1.2 * vfinal<br /> <br /> vfinal = 2.5 / 1.2 = 2.08333<br /> <br /> Thus, the final velocity is 2.08 m/s. Since the two balls stick together, this is an example of a [[Maximally Inelastic Collision]].<br /> <br /> ===Middling===<br /> Example 2)<br /> A bullet of 50 caliber machine gun is 42 grams. It strikes a wooden target block of mass 10 kg stationed on a friction-less surface. The wooden block gains velocity of 1.8 m/s after being embedded with the bullet.<br /> What was the velocity of the bullet before it collided with the target?<br /> <br /> <br /> ----<br /> <br /> m1 = 42/1000 = 0.042 kg,<br /> v1 init = ?,<br /> m2 = 10 kg,<br /> v2 init = 0,<br /> mfinal(m1+m2) = 0.042kg + 10kg,<br /> vfinal = 1.8 m/s<br /> <br /> m1 * v1 init + m2 * v2 init = (m1 + m2) * vfinal<br /> <br /> 0.042 kg * v1 init = (0.042 + 10) * 1.8 m/s<br /> v1 init = 18.0756 / 0.042 = 430.37 m/s<br /> <br /> Final Answer: The bullet's speed is 430.37 m/s.<br /> <br /> ===Difficult===<br /> Example 3) Two rocks in space are approaching a third stationary rock. Rock 1 has mass 30kg moves with velocity (13,-10,-2)m/s. Rock 2 has mass 60kg and moves with velocity (-3,23,3)m/s. Rock 3 has mass 35kg and is stationary. The rocks collide at rock 3's location. After the collision it is observed that Rock 1 has embedded into Rock 3, but a chunk of mass 15kg has broken off of the combined rock, Rock 3'. It is also noticed that Rock 2 is now moving with velocity (-2,12,2)m/s. (NOTE: due to the difficulty and use of three dimensions it is suggested to use a computer to solve this problem. Therefore the sample solution will involve code, but conceptually everything remains the same. Additionally some code is omitted for the sake of saving space, but the important calculations are included. See the entire code at [http://www.glowscript.org/#/user/samsaxlaxman/folder/Private/] with a model of the collision )<br /> <br /> '''First determine the momentum of Rock 3' plus the momentum of the 15kg chunk.''' <br /> <br /> <code><br /> Having defined the rocks as o1, o2, and o3 respectively, and defined there initial masses and velocities to calculate their individual momenta<br /> <br /> calculated the total momentum of the system by adding<br /> <br /> totalP = o1.p+o2.p+o3.p #total momentum of the system<br /> <br /> Next update the o1, o2 and o3 objects with the information observed after the collosions<br /> <br /> mChunk = 15 # in kg<br /> <br /> m1f = 0 #final mass object 1 in kg<br /> <br /> m2f = 60 #final mass object 2 in kg<br /> <br /> v2f = vector(-2,12,2) #final elocity object 2 in m/s<br /> <br /> m3f = o1.m + o2.m - mChunk #final mass object 3 in kg<br /> <br /> create a new sphere object with mass 15kg (code omitted)<br /> <br /> calculate the final momentum of rock 2<br /> <br /> o2.p = o2.v*o2.m<br /> <br /> finally determine the combined momentum of rock 3' and the chunk using the momentum principle<br /> <br /> pOfRock3PrimeAndChunk = totalP - o2.p #for now we are only calculating the combined momentum of rock 3' and the chunk<br /> </code><br /> <br /> ''The combined momentum of Rock 3' and the Chunk is <330, 360, 0>kg*m/s''<br /> <br /> '''Later Rock 3' is observed moving with velocity (3,5,2)m/s, what is the velocity of the 15kg chunk?'''<br /> <br /> <code><br /> Now we know the momentum of Rock 3' plus the chunk, AND we know the velocity and mass of Rock 3'<br /> <br /> pRock3Prime = m3f*vector(3,5,2) #calculate the momentum of Rock3'<br /> <br /> pChunk = pOfRock3PrimeAndChunk - pRock3Prime #calculate the momentum of the chunk<br /> <br /> chunk.v = pChunk/chunk.m #calculate the final velocity of the chunk<br /> </code><br /> <br /> ''The velocity of the chunk is <7, -1, -10>''<br /> <br /> '''With the information you know, determine the combined change in internal energy for all of the rocks.'''<br /> <br /> <code><br /> Start by calculating the total Kinetic Energy initial and the total Kinetic Energy final (In the actual program this has to go above the update statements for after the collision)<br /> <br /> o1.K = .5*o1.m*o1.v**2<br /> <br /> o2.K= .5*oK.m*o1.v**2<br /> <br /> o3.K = 0 #because it is stationary<br /> <br /> kTotInitial = o1.K+o2.K <br /> <br /> Now after the collision (in the actual program these go after the update statements for after the collision)<br /> <br /> o2.K = .5*o2.m*o2.v**2<br /> <br /> kRock3Prime = .5*m3f*mag(vector(3,5,2))**2<br /> <br /> chunk.K = .5*chunk.m*chunk.v**2<br /> <br /> kTotFinal = o2.K + kRock3Prime + chunk.K<br /> <br /> Now since there aren't any outside forces doing work and contributing energy, we know that change in internal energy equals -1*change in Kinetic energy, or kTotInitial - kTotFinal<br /> <br /> changeInInternalEnergy = kTotInitial - kTotFinal<br /> </code><br /> <br /> ''The change in internal energy is 5175J''<br /> <br /> ==Connectedness==<br /> Collisions are interesting phenomenons that are applicable to everyday situations. Some examples are when a bat collides with a baseball in your neighbor's backyard, two cars crashing in the highway in front of you, and two linebackers running into each-other at your local College's spring football game. Depending on the type of collision, you can predict if there will be a change in internal energy (thermal energy, chemical energy etc.). Another very interesting application of collisions is in the field of astronomy. The universe is ever-changing and we never know what might come our way. A large meteor could be flying at the Earth with a very high speed and we could use our knowledge of collisions to find out how the Earth will move after the collision, what the temperature change of the area would be, and how the rest of the Earth would be effected by the collision. By using our collision skills, we could evacuate anyone who is prone to harm during the collision. <br /> <br /> Knowledge of collisions is also a must for many engineering majors. Industrial engineers must take in collisions when they are trying to optimize complex systems. For instance, an Industrial engineer must make sure that the bridge he or she builds can withstand the forces the cars can exert on it. Architects and Civil engineers must design houses in a certain way so that slight collisions with other objects won't completely knock the house down. And of course, Mechanical engineers and Aerospace engineers must take into account collisions when designing and maintaining mechanical systems.<br /> <br /> ==History==<br /> In 1661, Christiaan Huygens, a Dutch physicist, concluded that when a moving body struck a stationary object of equal mass, the initial moving body would lose all of its momentum while the second object would pick up the same amount of velocity that the moving body had before the collision. He also stated that the total "quantity of motion" should be the same before and after the collision. This was the first thought of the conservation of momentum. <br /> <br /> In 1687, Sir Isaac Newtons went a little further and stated in his third law of motion that the forces of action and reaction between two bodies are opposite and equal. <br /> <br /> In Rutherford's Gold Foil Experiment in 1899, Rutherford found out that the plum pudding model of the atom was inaccurate and that there was actually a massive center of atoms. He did this through investigating atomic collisions between atoms and gold foil. Because some particles were scattered through angles larger than 90 degrees during the collisions, he was able to conclude that the atom had most of it's mass concentrated in a dense center rather than spread out evenly throughout the atom.<br /> <br /> == See also ==<br /> <br /> [[Maximally Inelastic Collision]] , [[Inelastic Collisions]] , [[Elastic Collisions]], [[Momentum Principle]], [[Net Force]].<br /> <br /> ===Further reading===<br /> <br /> Chabay, Ruth W., and Bruce A. Sherwood. Matter and Interactions. 4th ed. Vol. 1. Hoboken, NJ: Wiley, 2015. Print. Matter and Interactions.<br /> <br /> Ehrhardt, H., and L. A. Morgan. Electron Collisions with Molecules, Clusters, and Surfaces. New York: Plenum, 1994. Print.<br /> <br /> ===External links===<br /> "The Collision Theory - Boundless Open Textbook." Boundless. N.p., n.d. Web. 17 Apr. 2016.<br /> <br /> "Momentum and Collisions – Background Material." Momentum and Collisions. School of Physics Sydney, Australia, n.d. Web. 17 Apr. 2016.<br /> <br /> ==References==<br /> <br /> Chabay, Ruth W., and Bruce A. Sherwood. Matter and Interactions. 4th ed. Vol. 1. Hoboken, NJ: Wiley, 2015. Print. Matter and Interactions.<br /> <br /> "The Gold Foil Experiment." The Gold Foil Experiment. N.p., n.d. Web. 17 Apr. 2016.</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Collisions&diff=22664 Collisions 2016-04-17T23:43:27Z

<p>Swebster9: /* Difficult */</p> <hr /> <div>SECOND EDIT BY SUNGJAE HYUN IN 2016-04-16 ADDITIONS MADE BY (currently in progress, adding computational model and difficult problem) Sam Webster 4-17-16<br /> <br /> This topic covers Collisions, a comprehensive way to combine the Momentum and Energy Principles.<br /> <br /> ==The Main Idea==<br /> <br /> Collisions are special types of contact interactions between objects. From a physics standpoint, collisions are a way to combine the Momentum and Energy Principles. In the case of collisions, if we choose a system of the two objects interacting, the change in momentum of the system and the change in energy of the system are both zero. With this in mind, calculations with collisions become very simple. We are able to choose a system of only the two objects (excluding external forces such as the Earth's gravity) because the collision takes place during such a short time that the external forces have a negligible effect. <br /> There are two types of collisions, [[Elastic Collisions]] and [[Inelastic Collisions]]. <br /> <br /> ===A Mathematical Model===<br /> <math>{E}_{f} = {E}_{i}</math> where <math>{E}_{f}</math> is the total final energy of the system and <math>{E}_{i}</math> is the total initial energy of the system.<br /> <br /> <math>{p}_{f} = {p}_{i}</math> where <math>{p}_{f}</math> is the total final momentum of the system and <math>{p}_{i}</math> is the total initial momentum of the system.<br /> <br /> ===A Computational Model===<br /> The following situation was used for this model created using python:<br /> <br /> Two objects are initially moving towards a third stationary object. Object 1 (in red) at position (-10,0,-2)m has a mass of 2kg and velocity (10,0,2)m/s. Object 2 (in blue) at position (0,6,3)m has a mass of 4kg and velocity (0,-6,3)m/s. Object 3 (in orange) at the origin has a mass of 5kg. The objects collide at the origin and after the collision it is observed that object 1 has embedded in object 3 (hence it is no longer visible in the model) and the combined object moves with velocity (5,-6,0)m/s (This is an example of a [[Maximally Inelastic Collision]]). The final velocity of object 2 is calculated and used in the rest of the simulation. (NOTE: the white sphere visible after the collision represents the origin to add dimension to the model and the delay during the collision is there to emphasis when and where the collision happens. Also use the link below the model for a more detailed explanation of the calculations and concepts.).<br /> <br /> [[File: CollisionsExample.gif]]<br /> <br /> Check out the code used for the simulation at [http://www.glowscript.org/#/user/samsaxlaxman/folder/Private/]. The code is commented pretty heavily (but it does assume some knowledge of python and python animations) in hopes that future students can modify some of the variables to experiment with creating different results.<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> Example 1)<br /> A 0.5 kg soccer ball is moving with a speed of 5 m/s directly toward to 0.7 kg basket ball which is at rest.<br /> When two balls collide and stick together what will their final velocity be?<br /> <br /> ___<br /> <br /> m1 = 0.5 kg,<br /> v1 init = 5 m/s,<br /> m2 = 0.7 kg,<br /> v2 init = 0 m/s<br /> <br /> So m1 * v1 + m2 * + v2 = (m1 + m2) * vfinal<br /> <br /> LHS = 0.5 * 5 + 0.7 * 0 = 2.5 kg*m/s<br /> RHS = (0.5 + 0.7) * vfinal = 1.2 * vfinal<br /> <br /> LHS = RHS in inelastic collision <br /> <br /> 2.5 = 1.2 * vfinal<br /> <br /> vfinal = 2.5 / 1.2 = 2.08333<br /> <br /> Thus, the final velocity is 2.08 m/s. Since the two balls stick together, this is an example of a [[Maximally Inelastic Collision]].<br /> <br /> ===Middling===<br /> Example 2)<br /> A bullet of 50 caliber machine gun is 42 grams. It strikes a wooden target block of mass 10 kg stationed on a friction-less surface. The wooden block gains velocity of 1.8 m/s after being embedded with the bullet.<br /> What was the velocity of the bullet before it collided with the target?<br /> <br /> <br /> ----<br /> <br /> m1 = 42/1000 = 0.042 kg,<br /> v1 init = ?,<br /> m2 = 10 kg,<br /> v2 init = 0,<br /> mfinal(m1+m2) = 0.042kg + 10kg,<br /> vfinal = 1.8 m/s<br /> <br /> m1 * v1 init + m2 * v2 init = (m1 + m2) * vfinal<br /> <br /> 0.042 kg * v1 init = (0.042 + 10) * 1.8 m/s<br /> v1 init = 18.0756 / 0.042 = 430.37 m/s<br /> <br /> Final Answer: The bullet's speed is 430.37 m/s.<br /> <br /> ===Difficult===<br /> Example 3) Two rocks in space are approaching a third stationary rock. Rock 1 has mass 30kg moves with velocity (13,-10,-2)m/s. Rock 2 has mass 60kg and moves with velocity (-3,23,3)m/s. Rock 3 has mass 35kg and is stationary. The rocks collide at rock 3's location. After the collision it is observed that Rock 1 has embedded into Rock 3, but a chunk of mass 15kg has broken off of the combined rock, Rock 3'. It is also noticed that Rock 2 is now moving with velocity (-2,12,2)m/s. (NOTE: due to the difficulty and use of three dimensions it is suggested to use a computer to solve this problem. Therefore the sample solution will involve code, but conceptually everything remains the same. Additionally some code is omitted for the sake of saving space, but the important calculations are included. See the entire code at [http://www.glowscript.org/#/user/samsaxlaxman/folder/Private/] with a model of the collision )<br /> <br /> '''First determine the momentum of Rock 3' plus the momentum of the 15kg chunk.''' <br /> <br /> <code><br /> Having defined the rocks as o1, o2, and o3 respectively, and defined there initial masses and velocities to calculate their individual momenta<br /> <br /> calculated the total momentum of the system by adding<br /> <br /> totalP = o1.p+o2.p+o3.p #total momentum of the system<br /> <br /> Next update the o1, o2 and o3 objects with the information observed after the collosions<br /> <br /> mChunk = 15 # in kg<br /> <br /> m1f = 0 #final mass object 1 in kg<br /> <br /> m2f = 60 #final mass object 2 in kg<br /> <br /> v2f = vector(-2,12,2) #final elocity object 2 in m/s<br /> <br /> m3f = o1.m + o2.m - mChunk #final mass object 3 in kg<br /> <br /> create a new sphere object with mass 15kg (code omitted)<br /> <br /> calculate the final momentum of rock 2<br /> <br /> o2.p = o2.v*o2.m<br /> <br /> finally determine the combined momentum of rock 3' and the chunk using the momentum principle<br /> <br /> pOfRock3PrimeAndChunk = totalP - o2.p #for now we are only calculating the combined momentum of rock 3' and the chunk<br /> </code><br /> <br /> ''The combined momentum of Rock 3' and the Chunk is <330, 360, 0>kg*m/s''<br /> <br /> '''Later Rock 3' is observed moving with velocity (3,5,2)m/s, what is the velocity of the 15kg chunk?'''<br /> <br /> <code><br /> Now we know the momentum of Rock 3' plus the chunk, AND we know the velocity and mass of Rock 3'<br /> <br /> pRock3Prime = m3f*vector(3,5,2) #calculate the momentum of Rock3'<br /> <br /> pChunk = pOfRock3PrimeAndChunk - pRock3Prime #calculate the momentum of the chunk<br /> <br /> chunk.v = pChunk/chunk.m #calculate the final velocity of the chunk<br /> </code><br /> <br /> ''The velocity of the chunk is <7, -1, -10>''<br /> <br /> '''With the information you know, determine the combined change in internal energy for all of the rocks.'''<br /> <br /> <code><br /> Start by calculating the total Kinetic Energy initial and the total Kinetic Energy final (In the actual program this has to go above the update statements for after the collision)<br /> <br /> o1.K = .5*o1.m*o1.v**2<br /> <br /> o2.K= .5*oK.m*o1.v**2<br /> <br /> o3.K = 0 #because it is stationary<br /> <br /> kTotInitial = o1.K+o2.K <br /> <br /> Now after the collision (in the actual program these go after the update statements for after the collision)<br /> <br /> o2.K = .5*o2.m*o2.v**2<br /> <br /> kRock3Prime = .5*m3f*mag(vector(3,5,2))**2<br /> <br /> chunk.K = .5*chunk.m*chunk.v**2<br /> <br /> kTotFinal = o2.K + kRock3Prime + chunk.K<br /> <br /> Now since there aren't any outside forces doing work and contributing energy, we know that change in internal energy equals -1*change in Kinetic energy, or kTotInitial - kTotFinal<br /> <br /> changeInInternalEnergy = kTotInitial - kTotFinal<br /> </code><br /> <br /> ''The change in internal energy is 5175J''<br /> <br /> ==Connectedness==<br /> Collisions are interesting phenomenons that are applicable to everyday situations. Some examples are when a bat collides with a baseball in your neighbor's backyard, two cars crashing in the highway in front of you, and two linebackers running into each-other at your local College's spring football game. Depending on the type of collision, you can predict if there will be a change in internal energy (thermal energy, chemical energy etc.). Another very interesting application of collisions is in the field of astronomy. The universe is ever-changing and we never know what might come our way. A large meteor could be flying at the Earth with a very high speed and we could use our knowledge of collisions to find out how the Earth will move after the collision, what the temperature change of the area would be, and how the rest of the Earth would be effected by the collision. By using our collision skills, we could evacuate anyone who is prone to harm during the collision. <br /> <br /> Knowledge of collisions is also a must for many engineering majors. Industrial engineers must take in collisions when they are trying to optimize complex systems. For instance, an Industrial engineer must make sure that the bridge he or she builds can withstand the forces the cars can exert on it. Architects and Civil engineers must design houses in a certain way so that slight collisions with other objects won't completely knock the house down. And of course, Mechanical engineers and Aerospace engineers must take into account collisions when designing and maintaining mechanical systems.<br /> <br /> ==History==<br /> In Rutherford's Gold Foil Experiment in 1899, Rutherford found out that the plum pudding model of the atom was inaccurate through atomic collisions.<br /> <br /> == See also ==<br /> <br /> [[Maximally Inelastic Collision]] , [[Inelastic Collisions]] , [[Elastic Collisions]], [[Momentum Principle]], [[Net Force]].<br /> <br /> ===Further reading===<br /> <br /> Chabay, Ruth W., and Bruce A. Sherwood. Matter and Interactions. 4th ed. Vol. 1. Hoboken, NJ: Wiley, 2015. Print. Matter and Interactions.<br /> <br /> ===External links===<br /> "The Collision Theory - Boundless Open Textbook." Boundless. N.p., n.d. Web. 17 Apr. 2016.<br /> <br /> ==References==<br /> <br /> Chabay, Ruth W., and Bruce A. Sherwood. Matter and Interactions. 4th ed. Vol. 1. Hoboken, NJ: Wiley, 2015. Print. Matter and Interactions.</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Collisions&diff=22653 Collisions 2016-04-17T23:36:56Z

<p>Swebster9: /* Difficult */</p> <hr /> <div>SECOND EDIT BY SUNGJAE HYUN IN 2016-04-16 ADDITIONS MADE BY (currently in progress, adding computational model and difficult problem) Sam Webster 4-17-16<br /> <br /> This topic covers Collisions, a comprehensive way to combine the Momentum and Energy Principles.<br /> <br /> ==The Main Idea==<br /> <br /> Collisions are special types of contact interactions between objects. From a physics standpoint, collisions are a way to combine the Momentum and Energy Principles. In the case of collisions, if we choose a system of the two objects interacting, the change in momentum of the system and the change in energy of the system are both zero. With this in mind, calculations with collisions become very simple. We are able to choose a system of only the two objects (excluding external forces such as the Earth's gravity) because the collision takes place during such a short time that the external forces have a negligible effect. <br /> There are two types of collisions, [[Elastic Collisions]] and [[Inelastic Collisions]]. <br /> <br /> ===A Mathematical Model===<br /> <math>{E}_{f} = {E}_{i}</math> where <math>{E}_{f}</math> is the total final energy of the system and <math>{E}_{i}</math> is the total initial energy of the system.<br /> <br /> <math>{p}_{f} = {p}_{i}</math> where <math>{p}_{f}</math> is the total final momentum of the system and <math>{p}_{i}</math> is the total initial momentum of the system.<br /> <br /> ===A Computational Model===<br /> The following situation was used for this model created using python:<br /> <br /> Two objects are initially moving towards a third stationary object. Object 1 (in red) at position (-10,0,-2)m has a mass of 2kg and velocity (10,0,2)m/s. Object 2 (in blue) at position (0,6,3)m has a mass of 4kg and velocity (0,-6,3)m/s. Object 3 (in orange) at the origin has a mass of 5kg. The objects collide at the origin and after the collision it is observed that object 1 has embedded in object 3 (hence it is no longer visible in the model) and the combined object moves with velocity (5,-6,0)m/s (This is an example of a [[Maximally Inelastic Collision]]). The final velocity of object 2 is calculated and used in the rest of the simulation. (NOTE: the white sphere visible after the collision represents the origin to add dimension to the model and the delay during the collision is there to emphasis when and where the collision happens. Also use the link below the model for a more detailed explanation of the calculations and concepts.).<br /> <br /> [[File: CollisionsExample.gif]]<br /> <br /> Check out the code used for the simulation at [http://www.glowscript.org/#/user/samsaxlaxman/folder/Private/]. The code is commented pretty heavily (but it does assume some knowledge of python and python animations) in hopes that future students can modify some of the variables to experiment with creating different results.<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> Example 1)<br /> A 0.5 kg soccer ball is moving with a speed of 5 m/s directly toward to 0.7 kg basket ball which is at rest.<br /> When two balls collide and stick together what will their final velocity be?<br /> <br /> ___<br /> <br /> m1 = 0.5 kg,<br /> v1 init = 5 m/s,<br /> m2 = 0.7 kg,<br /> v2 init = 0 m/s<br /> <br /> So m1 * v1 + m2 * + v2 = (m1 + m2) * vfinal<br /> <br /> LHS = 0.5 * 5 + 0.7 * 0 = 2.5 kg*m/s<br /> RHS = (0.5 + 0.7) * vfinal = 1.2 * vfinal<br /> <br /> LHS = RHS in inelastic collision <br /> <br /> 2.5 = 1.2 * vfinal<br /> <br /> vfinal = 2.5 / 1.2 = 2.08333<br /> <br /> Thus, the final velocity is 2.08 m/s. Since the two balls stick together, this is an example of a [[Maximally Inelastic Collision]].<br /> <br /> ===Middling===<br /> Example 2)<br /> A bullet of 50 caliber machine gun is 42 grams. It strikes a wooden target block of mass 10 kg stationed on a friction-less surface. The wooden block gains velocity of 1.8 m/s after being embedded with the bullet.<br /> What was the velocity of the bullet before it collided with the target?<br /> <br /> <br /> ----<br /> <br /> m1 = 42/1000 = 0.042 kg,<br /> v1 init = ?,<br /> m2 = 10 kg,<br /> v2 init = 0,<br /> mfinal(m1+m2) = 0.042kg + 10kg,<br /> vfinal = 1.8 m/s<br /> <br /> m1 * v1 init + m2 * v2 init = (m1 + m2) * vfinal<br /> <br /> 0.042 kg * v1 init = (0.042 + 10) * 1.8 m/s<br /> v1 init = 18.0756 / 0.042 = 430.37 m/s<br /> <br /> Final Answer: The bullet's speed is 430.37 m/s.<br /> <br /> ===Difficult===<br /> Example 3) Two rocks in space are approaching a third stationary rock. Rock 1 has mass 30kg moves with velocity (13,-10,-2)m/s. Rock 2 has mass 60kg and moves with velocity (-3,23,3)m/s. Rock 3 has mass 35kg and is stationary. The rocks collide at rock 3's location. After the collision it is observed that Rock 1 has embedded into Rock 3, but a chunk of mass 15kg has broken off of the combined rock, Rock 3'. It is also noticed that Rock 2 is now moving with velocity (-2,12,2)m/s. (NOTE: due to the difficulty and use of three dimensions it is suggested to use a computer to solve this problem. Therefore the sample solution will involve code, but conceptually everything remains the same. Additionally some code is omitted for the sake of saving space, but the important calculations are included. See the entire code at . . . )<br /> <br /> '''First determine the momentum of Rock 3' plus the momentum of the 15kg chunk.''' <br /> <br /> <code><br /> Having defined the rocks as o1, o2, and o3 respectively, and defined there initial masses and velocities to calculate their individual momenta<br /> <br /> calculated the total momentum of the system by adding<br /> <br /> totalP = o1.p+o2.p+o3.p #total momentum of the system<br /> <br /> Next update the o1, o2 and o3 objects with the information observed after the collosions<br /> <br /> mChunk = 15 # in kg<br /> <br /> m1f = 0 #final mass object 1 in kg<br /> <br /> m2f = 60 #final mass object 2 in kg<br /> <br /> v2f = vector(-2,12,2) #final elocity object 2 in m/s<br /> <br /> m3f = o1.m + o2.m - mChunk #final mass object 3 in kg<br /> <br /> create a new sphere object with mass 15kg (code omitted)<br /> <br /> calculate the final momentum of rock 2<br /> <br /> o2.p = o2.v*o2.m<br /> <br /> finally determine the combined momentum of rock 3' and the chunk using the momentum principle<br /> <br /> pOfRock3PrimeAndChunk = totalP - o2.p #for now we are only calculating the combined momentum of rock 3' and the chunk<br /> </code><br /> <br /> ''The combined momentum of Rock 3' and the Chunk is <330, 360, 0>kg*m/s''<br /> <br /> '''Later Rock 3' is observed moving with velocity (3,5,2)m/s, what is the velocity of the 15kg chunk?'''<br /> <br /> <code><br /> Now we know the momentum of Rock 3' plus the chunk, AND we know the velocity and mass of Rock 3'<br /> <br /> pRock3Prime = m3f*vector(3,5,2) #calculate the momentum of Rock3'<br /> <br /> pChunk = pOfRock3PrimeAndChunk - pRock3Prime #calculate the momentum of the chunk<br /> <br /> chunk.v = pChunk/chunk.m #calculate the final velocity of the chunk<br /> </code><br /> <br /> ''The velocity of the chunk is <7, -1, -10>''<br /> <br /> '''With the information you know, determine the combined change in internal energy for all of the rocks.'''<br /> <br /> <code><br /> Start by calculating the total Kinetic Energy initial and the total Kinetic Energy final (In the actual program this has to go above the update statements for after the collision)<br /> <br /> o1.K = .5*o1.m*o1.v**2<br /> <br /> o2.K= .5*oK.m*o1.v**2<br /> <br /> o3.K = 0 #because it is stationary<br /> <br /> kTotInitial = o1.K+o2.K <br /> <br /> Now after the collision (in the actual program these go after the update statements for after the collision)<br /> <br /> o2.K = .5*o2.m*o2.v**2<br /> <br /> kRock3Prime = .5*m3f*mag(vector(3,5,2))**2<br /> <br /> chunk.K = .5*chunk.m*chunk.v**2<br /> <br /> kTotFinal = o2.K + kRock3Prime + chunk.K<br /> <br /> Now since there aren't any outside forces doing work and contributing energy, we know that change in internal energy equals -1*change in Kinetic energy, or kTotInitial - kTotFinal<br /> <br /> changeInInternalEnergy = kTotInitial - kTotFinal<br /> </code><br /> <br /> ''The change in internal energy is 5175J''<br /> <br /> ==Connectedness==<br /> Collisions are interesting phenomenons that are applicable to everyday situations. Some examples are when a bat collides with a baseball in your neighbor's backyard, two cars crashing in the highway in front of you, and two linebackers running into each-other at your local College's spring football game. Depending on the type of collision, you can predict if there will be a change in internal energy (thermal energy, chemical energy etc.). Another very interesting application of collisions is in the field of astronomy. The universe is ever-changing and we never know what might come our way. A large meteor could be flying at the Earth with a very high speed and we could use our knowledge of collisions to find out how the Earth will move after the collision, what the temperature change of the area would be, and how the rest of the Earth would be effected by the collision. By using our collision skills, we could evacuate anyone who is prone to harm during the collision. <br /> <br /> Knowledge of collisions is also a must for many engineering majors. Industrial engineers must take in collisions when they are trying to optimize complex systems. For instance, an Industrial engineer must make sure that the bridge he or she builds can withstand the forces the cars can exert on it. Architects and Civil engineers must design houses in a certain way so that slight collisions with other objects won't completely knock the house down. And of course, Mechanical engineers and Aerospace engineers must take into account collisions when designing and maintaining mechanical systems.<br /> <br /> ==History==<br /> In Rutherford's Gold Foil Experiment in 1899, Rutherford found out that the plum pudding model of the atom was inaccurate through atomic collisions.<br /> <br /> == See also ==<br /> <br /> [[Maximally Inelastic Collision]] , [[Inelastic Collisions]] , [[Elastic Collisions]], [[Momentum Principle]], [[Net Force]].<br /> <br /> ===Further reading===<br /> <br /> Chabay, Ruth W., and Bruce A. Sherwood. Matter and Interactions. 4th ed. Vol. 1. Hoboken, NJ: Wiley, 2015. Print. Matter and Interactions.<br /> <br /> ===External links===<br /> "The Collision Theory - Boundless Open Textbook." Boundless. N.p., n.d. Web. 17 Apr. 2016.<br /> <br /> ==References==<br /> <br /> Chabay, Ruth W., and Bruce A. Sherwood. Matter and Interactions. 4th ed. Vol. 1. Hoboken, NJ: Wiley, 2015. Print. Matter and Interactions.</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Collisions&diff=22635 Collisions 2016-04-17T23:29:22Z

<p>Swebster9: /* Difficult */</p> <hr /> <div>SECOND EDIT BY SUNGJAE HYUN IN 2016-04-16 ADDITIONS MADE BY (currently in progress, adding computational model and difficult problem) Sam Webster 4-17-16<br /> <br /> This topic covers Collisions, a comprehensive way to combine the Momentum and Energy Principles.<br /> <br /> ==The Main Idea==<br /> <br /> Collisions are special types of contact interactions between objects. From a physics standpoint, collisions are a way to combine the Momentum and Energy Principles. In the case of collisions, if we choose a system of the two objects interacting, the change in momentum of the system and the change in energy of the system are both zero. With this in mind, calculations with collisions become very simple. We are able to choose a system of only the two objects (excluding external forces such as the Earth's gravity) because the collision takes place during such a short time that the external forces have a negligible effect. <br /> There are two types of collisions, [[Elastic Collisions]] and [[Inelastic Collisions]]. <br /> <br /> ===A Mathematical Model===<br /> <math>{E}_{f} = {E}_{i}</math> where <math>{E}_{f}</math> is the total final energy of the system and <math>{E}_{i}</math> is the total initial energy of the system.<br /> <br /> <math>{p}_{f} = {p}_{i}</math> where <math>{p}_{f}</math> is the total final momentum of the system and <math>{p}_{i}</math> is the total initial momentum of the system.<br /> <br /> ===A Computational Model===<br /> The following situation was used for this model created using python:<br /> <br /> Two objects are initially moving towards a third stationary object. Object 1 (in red) at position (-10,0,-2)m has a mass of 2kg and velocity (10,0,2)m/s. Object 2 (in blue) at position (0,6,3)m has a mass of 4kg and velocity (0,-6,3)m/s. Object 3 (in orange) at the origin has a mass of 5kg. The objects collide at the origin and after the collision it is observed that object 1 has embedded in object 3 (hence it is no longer visible in the model) and the combined object moves with velocity (5,-6,0)m/s (This is an example of a [[Maximally Inelastic Collision]]). The final velocity of object 2 is calculated and used in the rest of the simulation. (NOTE: the white sphere visible after the collision represents the origin to add dimension to the model and the delay during the collision is there to emphasis when and where the collision happens. Also use the link below the model for a more detailed explanation of the calculations and concepts.).<br /> <br /> [[File: CollisionsExample.gif]]<br /> <br /> Check out the code used for the simulation at [http://www.glowscript.org/#/user/samsaxlaxman/folder/Private/]. The code is commented pretty heavily (but it does assume some knowledge of python and python animations) in hopes that future students can modify some of the variables to experiment with creating different results.<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> Example 1)<br /> A 0.5 kg soccer ball is moving with a speed of 5 m/s directly toward to 0.7 kg basket ball which is at rest.<br /> When two balls collide and stick together what will their final velocity be?<br /> <br /> ___<br /> <br /> m1 = 0.5 kg,<br /> v1 init = 5 m/s,<br /> m2 = 0.7 kg,<br /> v2 init = 0 m/s<br /> <br /> So m1 * v1 + m2 * + v2 = (m1 + m2) * vfinal<br /> <br /> LHS = 0.5 * 5 + 0.7 * 0 = 2.5 kg*m/s<br /> RHS = (0.5 + 0.7) * vfinal = 1.2 * vfinal<br /> <br /> LHS = RHS in inelastic collision <br /> <br /> 2.5 = 1.2 * vfinal<br /> <br /> vfinal = 2.5 / 1.2 = 2.08333<br /> <br /> Thus, the final velocity is 2.08 m/s. Since the two balls stick together, this is an example of a [[Maximally Inelastic Collision]].<br /> <br /> ===Middling===<br /> Example 2)<br /> A bullet of 50 caliber machine gun is 42 grams. It strikes a wooden target block of mass 10 kg stationed on a friction-less surface. The wooden block gains velocity of 1.8 m/s after being embedded with the bullet.<br /> What was the velocity of the bullet before it collided with the target?<br /> <br /> <br /> ----<br /> <br /> m1 = 42/1000 = 0.042 kg,<br /> v1 init = ?,<br /> m2 = 10 kg,<br /> v2 init = 0,<br /> mfinal(m1+m2) = 0.042kg + 10kg,<br /> vfinal = 1.8 m/s<br /> <br /> m1 * v1 init + m2 * v2 init = (m1 + m2) * vfinal<br /> <br /> 0.042 kg * v1 init = (0.042 + 10) * 1.8 m/s<br /> v1 init = 18.0756 / 0.042 = 430.37 m/s<br /> <br /> Final Answer: The bullet's speed is 430.37 m/s.<br /> <br /> ===Difficult===<br /> Example 3) Two rocks in space are approaching a third stationary rock. Rock 1 has mass 30kg moves with velocity (13,-10,-2)m/s. Rock 2 has mass 60kg and moves with velocity (-3,23,3)m/s. Rock 3 has mass 35kg and is stationary. The rocks collide at rock 3's location. After the collision it is observed that Rock 1 has embedded into Rock 3, but a chunk of mass 15kg has broken off of the combined rock, Rock 3'. It is also noticed that Rock 2 is now moving with velocity (-2,12,2)m/s. (NOTE: due to the difficulty and use of three dimensions it is suggested to use a computer to solve this problem. Therefore the sample solution will involve code, but conceptually everything remains the same. Additionally some code is omitted for the sake of saving space, but the important calculations are included. See the entire code at . . . )<br /> <br /> '''First determine the momentum of Rock 3' plus the momentum of the 15kg chunk.''' <br /> <br /> <code><br /> Having defined the rocks as o1, o2, and o3 respectively, and defined there initial masses and velocities to calculate their individual momenta<br /> <br /> calculated the total momentum of the system by adding<br /> <br /> totalP = o1.p+o2.p+o3.p #total momentum of the system<br /> <br /> Next update the o1, o2 and o3 objects with the information observed after the collosions<br /> <br /> mChunk = 15 # in kg<br /> <br /> m1f = 0 #final mass object 1 in kg<br /> <br /> m2f = 60 #final mass object 2 in kg<br /> <br /> v2f = vector(-2,12,2) #final elocity object 2 in m/s<br /> <br /> m3f = o1.m + o2.m - mChunk #final mass object 3 in kg<br /> <br /> create a new sphere object with mass 15kg (code omitted)<br /> <br /> calculate the final momentum of rock 2<br /> <br /> o2.p = o2.v*o2.m<br /> <br /> finally determine the combined momentum of rock 3' and the chunk using the momentum principle<br /> <br /> pOfRock3PrimeAndChunk = totalP - o2.p #for now we are only calculating the combined momentum of rock 3' and the chunk<br /> </code><br /> <br /> ''The combined momentum of Rock 3' and the Chunk is <330, 360, 0>kg*m/s''<br /> <br /> '''Later Rock 3' is observed moving with velocity (3,5,2)m/s, what is the velocity of the 15kg chunk?'''<br /> <br /> <code><br /> Now we know the momentum of Rock 3' plus the chunk, AND we know the velocity and mass of Rock 3'<br /> <br /> pRock3Prime = m3f*vector(3,5,2) #calculate the momentum of Rock3'<br /> <br /> pChunk = pOfRock3PrimeAndChunk - pRock3Prime #calculate the momentum of the chunk<br /> <br /> chunk.v = pChunk/chunk.m #calculate the final velocity of the chunk<br /> </code><br /> <br /> ''The velocity of the chunk is <7, -1, -10>''<br /> <br /> '''With the information you know, determine the combined change in internal energy for all of the rocks.'''<br /> <br /> <code><br /> Start by calculating the total Kinetic Energy initial and the total Kinetic Energy final (In the actual program this has to go above the update statements for after the collision)<br /> <br /> o1.K = .5*o1.m*o1.v**2<br /> <br /> o2.K= .5*oK.m*o1.v**2<br /> <br /> o3.K = 0 #because it is stationary<br /> <br /> kTotInitial = o1.K+o2.K <br /> <br /> Now after the collision (in the actual program these go after the update statements for after the collision)<br /> <br /> o2.K = .5*o2.m*o2.v**2<br /> <br /> kRock3Prime = .5*m3f*mag(vector(3,5,2))**2<br /> <br /> chunk.K = .5*chunk.m*chunk.v**2<br /> <br /> kTotFinal = o2.K + kRock3Prime + chunk.K<br /> <br /> Now since there aren't any outside forces doing work and contributing energy, we know that change in internal energy equals -1*change in Kinetic energy, or kTotInitial - kTotFinal<br /> <br /> changeInInternalEnergy = kTotInitial - kTotFinal<br /> </code><br /> <br /> ==Connectedness==<br /> Collisions are interesting phenomenons that are applicable to everyday situations. Some examples are when a bat collides with a baseball in your neighbor's backyard, two cars crashing in the highway in front of you, and two linebackers running into each-other at your local College's spring football game. Depending on the type of collision, you can predict if there will be a change in internal energy (thermal energy, chemical energy etc.). Another very interesting application of collisions is in the field of astronomy. The universe is ever-changing and we never know what might come our way. A large meteor could be flying at the Earth with a very high speed and we could use our knowledge of collisions to find out how the Earth will move after the collision, what the temperature change of the area would be, and how the rest of the Earth would be effected by the collision. By using our collision skills, we could evacuate anyone who is prone to harm during the collision. <br /> <br /> Knowledge of collisions is also a must for many engineering majors. Industrial engineers must take in collisions when they are trying to optimize complex systems. For instance, an Industrial engineer must make sure that the bridge he or she builds can withstand the forces the cars can exert on it. Architects and Civil engineers must design houses in a certain way so that slight collisions with other objects won't completely knock the house down. And of course, Mechanical engineers and Aerospace engineers must take into account collisions when designing and maintaining mechanical systems.<br /> <br /> ==History==<br /> In Rutherford's Gold Foil Experiment in 1899, Rutherford found out that the plum pudding model of the atom was inaccurate through atomic collisions.<br /> <br /> == See also ==<br /> <br /> [[Maximally Inelastic Collision]] , [[Inelastic Collisions]] , [[Elastic Collisions]], [[Momentum Principle]], [[Net Force]].<br /> <br /> ===Further reading===<br /> <br /> Chabay, Ruth W., and Bruce A. Sherwood. Matter and Interactions. 4th ed. Vol. 1. Hoboken, NJ: Wiley, 2015. Print. Matter and Interactions.<br /> <br /> ===External links===<br /> "The Collision Theory - Boundless Open Textbook." Boundless. N.p., n.d. Web. 17 Apr. 2016.<br /> <br /> ==References==<br /> <br /> Chabay, Ruth W., and Bruce A. Sherwood. Matter and Interactions. 4th ed. Vol. 1. Hoboken, NJ: Wiley, 2015. Print. Matter and Interactions.</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Collisions&diff=22616 Collisions 2016-04-17T23:18:27Z

<p>Swebster9: /* Difficult */</p> <hr /> <div>SECOND EDIT BY SUNGJAE HYUN IN 2016-04-16 ADDITIONS MADE BY (currently in progress, adding computational model and difficult problem) Sam Webster 4-17-16<br /> <br /> This topic covers Collisions, a comprehensive way to combine the Momentum and Energy Principles.<br /> <br /> ==The Main Idea==<br /> <br /> Collisions are special types of contact interactions between objects. From a physics standpoint, collisions are a way to combine the Momentum and Energy Principles. In the case of collisions, if we choose a system of the two objects interacting, the change in momentum of the system and the change in energy of the system are both zero. With this in mind, calculations with collisions become very simple. We are able to choose a system of only the two objects (excluding external forces such as the Earth's gravity) because the collision takes place during such a short time that the external forces have a negligible effect. <br /> There are two types of collisions, [[Elastic Collisions]] and [[Inelastic Collisions]]. <br /> <br /> ===A Mathematical Model===<br /> <math>{E}_{f} = {E}_{i}</math> where <math>{E}_{f}</math> is the total final energy of the system and <math>{E}_{i}</math> is the total initial energy of the system.<br /> <br /> <math>{p}_{f} = {p}_{i}</math> where <math>{p}_{f}</math> is the total final momentum of the system and <math>{p}_{i}</math> is the total initial momentum of the system.<br /> <br /> ===A Computational Model===<br /> The following situation was used for this model created using python:<br /> <br /> Two objects are initially moving towards a third stationary object. Object 1 (in red) at position (-10,0,-2)m has a mass of 2kg and velocity (10,0,2)m/s. Object 2 (in blue) at position (0,6,3)m has a mass of 4kg and velocity (0,-6,3)m/s. Object 3 (in orange) at the origin has a mass of 5kg. The objects collide at the origin and after the collision it is observed that object 1 has embedded in object 3 (hence it is no longer visible in the model) and the combined object moves with velocity (5,-6,0)m/s (This is an example of a [[Maximally Inelastic Collision]]). The final velocity of object 2 is calculated and used in the rest of the simulation. (NOTE: the white sphere visible after the collision represents the origin to add dimension to the model and the delay during the collision is there to emphasis when and where the collision happens. Also use the link below the model for a more detailed explanation of the calculations and concepts.).<br /> <br /> [[File: CollisionsExample.gif]]<br /> <br /> Check out the code used for the simulation at [http://www.glowscript.org/#/user/samsaxlaxman/folder/Private/]. The code is commented pretty heavily (but it does assume some knowledge of python and python animations) in hopes that future students can modify some of the variables to experiment with creating different results.<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> Example 1)<br /> A 0.5 kg soccer ball is moving with a speed of 5 m/s directly toward to 0.7 kg basket ball which is at rest.<br /> When two balls collide and stick together what will their final velocity be?<br /> <br /> ___<br /> <br /> m1 = 0.5 kg,<br /> v1 init = 5 m/s,<br /> m2 = 0.7 kg,<br /> v2 init = 0 m/s<br /> <br /> So m1 * v1 + m2 * + v2 = (m1 + m2) * vfinal<br /> <br /> LHS = 0.5 * 5 + 0.7 * 0 = 2.5 kg*m/s<br /> RHS = (0.5 + 0.7) * vfinal = 1.2 * vfinal<br /> <br /> LHS = RHS in inelastic collision <br /> <br /> 2.5 = 1.2 * vfinal<br /> <br /> vfinal = 2.5 / 1.2 = 2.08333<br /> <br /> Thus, the final velocity is 2.08 m/s. Since the two balls stick together, this is an example of a [[Maximally Inelastic Collision]].<br /> <br /> ===Middling===<br /> Example 2)<br /> A bullet of 50 caliber machine gun is 42 grams. It strikes a wooden target block of mass 10 kg stationed on a friction-less surface. The wooden block gains velocity of 1.8 m/s after being embedded with the bullet.<br /> What was the velocity of the bullet before it collided with the target?<br /> <br /> <br /> ----<br /> <br /> m1 = 42/1000 = 0.042 kg,<br /> v1 init = ?,<br /> m2 = 10 kg,<br /> v2 init = 0,<br /> mfinal(m1+m2) = 0.042kg + 10kg,<br /> vfinal = 1.8 m/s<br /> <br /> m1 * v1 init + m2 * v2 init = (m1 + m2) * vfinal<br /> <br /> 0.042 kg * v1 init = (0.042 + 10) * 1.8 m/s<br /> v1 init = 18.0756 / 0.042 = 430.37 m/s<br /> <br /> Final Answer: The bullet's speed is 430.37 m/s.<br /> <br /> ===Difficult===<br /> Example 3) Two rocks in space are approaching a third stationary rock. Rock 1 has mass 30kg moves with velocity (13,-10,-2)m/s. Rock 2 has mass 60kg and moves with velocity (-3,23,3)m/s. Rock 3 has mass 35kg and is stationary. The rocks collide at rock 3's location. After the collision it is observed that Rock 1 has embedded into Rock 3, but a chunk of mass 15kg has broken off of the combined rock, Rock 3'. It is also noticed that Rock 2 is now moving with velocity (-2,12,2)m/s. (NOTE: due to the difficulty and use of three dimensions it is suggested to use a computer to solve this problem. Therefore the sample solution will involve code, but conceptually everything remains the same. Additionally some code is omitted for the sake of saving space, but the important calculations are included. See the entire code at . . . )<br /> <br /> '''First determine the momentum of Rock 3' plus the momentum of the 15kg chunk.''' <br /> <br /> <code><br /> Having defined the rocks as o1, o2, and o3 respectively, and defined there initial masses and velocities to calculate their individual momenta<br /> <br /> calculated the total momentum of the system by adding<br /> <br /> totalP = o1.p+o2.p+o3.p #total momentum of the system<br /> <br /> Next update the o1, o2 and o3 objects with the information observed after the collosions<br /> <br /> mChunk = 15 # in kg<br /> <br /> m1f = 0 #final mass object 1 in kg<br /> <br /> m2f = 60 #final mass object 2 in kg<br /> <br /> v2f = vector(-2,12,2) #final elocity object 2 in m/s<br /> <br /> m3f = o1.m + o2.m - mChunk #final mass object 3 in kg<br /> <br /> create a new sphere object with mass 15kg (code omitted)<br /> <br /> calculate the final momentum of rock 2<br /> <br /> o2.p = o2.v*o2.m<br /> <br /> finally determine the combined momentum of rock 3' and the chunk using the momentum principle<br /> <br /> pOfRock3PrimeAndChunk = totalP - o2.p #for now we are only calculating the combined momentum of rock 3' and the chunk<br /> </code><br /> <br /> ''The combined momentum of Rock 3' and the Chunk is <330, 360, 0>kg*m/s''<br /> <br /> '''Later Rock 3' is observed moving with velocity (3,5,2), what is the velocity of the 15kg chunk?'''<br /> <br /> <code><br /> Now we know the momentum of Rock 3' plus the chunk, AND we know the velocity and mass of Rock 3'<br /> <br /> pRock3Prime = m3f*vector(3,5,2) #calculate the momentum of Rock3'<br /> <br /> pChunk = pOfRock3PrimeAndChunk - pRock3Prime #calculate the momentum of the chunk<br /> <br /> chunk.v = pChunk/chunk.m #calculate the final velocity of the chunk<br /> </code><br /> <br /> "The velocity of the chunk is <7, -1, -10>"<br /> <br /> <br /> '''With the information you know, determine the combined change in internal energy for all of the rocks.'''<br /> <br /> ==Connectedness==<br /> Collisions are interesting phenomenons that are applicable to everyday situations. Some examples are when a bat collides with a baseball in your neighbor's backyard, two cars crashing in the highway in front of you, and two linebackers running into each-other at your local College's spring football game. Depending on the type of collision, you can predict if there will be a change in internal energy (thermal energy, chemical energy etc.). Another very interesting application of collisions is in the field of astronomy. The universe is ever-changing and we never know what might come our way. A large meteor could be flying at the Earth with a very high speed and we could use our knowledge of collisions to find out how the Earth will move after the collision, what the temperature change of the area would be, and how the rest of the Earth would be effected by the collision. By using our collision skills, we could evacuate anyone who is prone to harm during the collision. <br /> <br /> Knowledge of collisions is also a must for many engineering majors. Industrial engineers must take in collisions when they are trying to optimize complex systems. For instance, an Industrial engineer must make sure that the bridge he or she builds can withstand the forces the cars can exert on it. Architects and Civil engineers must design houses in a certain way so that slight collisions with other objects won't completely knock the house down. And of course, Mechanical engineers and Aerospace engineers must take into account collisions when designing and maintaining mechanical systems.<br /> <br /> ==History==<br /> In Rutherford's Gold Foil Experiment in 1899, Rutherford found out that the plum pudding model of the atom was inaccurate through atomic collisions.<br /> <br /> == See also ==<br /> <br /> [[Maximally Inelastic Collision]] , [[Inelastic Collisions]] , [[Elastic Collisions]], [[Momentum Principle]], [[Net Force]].<br /> <br /> ===Further reading===<br /> <br /> Chabay, Ruth W., and Bruce A. Sherwood. Matter and Interactions. 4th ed. Vol. 1. Hoboken, NJ: Wiley, 2015. Print. Matter and Interactions.<br /> <br /> ===External links===<br /> "The Collision Theory - Boundless Open Textbook." Boundless. N.p., n.d. Web. 17 Apr. 2016.<br /> <br /> ==References==<br /> <br /> Chabay, Ruth W., and Bruce A. Sherwood. Matter and Interactions. 4th ed. Vol. 1. Hoboken, NJ: Wiley, 2015. Print. Matter and Interactions.</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Collisions&diff=22542 Collisions 2016-04-17T21:43:43Z

<p>Swebster9: /* Difficult */</p> <hr /> <div>SECOND EDIT BY SUNGJAE HYUN IN 2016-04-16 ADDITIONS MADE BY (currently in progress, adding computational model and difficult problem) Sam Webster 4-17-16<br /> <br /> This topic covers Collisions, a comprehensive way to combine the Momentum and Energy Principles.<br /> <br /> ==The Main Idea==<br /> <br /> Collisions are special types of contact interactions between objects. From a physics standpoint, collisions are a way to combine the Momentum and Energy Principles. In the case of collisions, if we choose a system of the two objects interacting, the change in momentum of the system and the change in energy of the system are both zero. With this in mind, calculations with collisions become very simple. We are able to choose a system of only the two objects (excluding external forces such as the Earth's gravity) because the collision takes place during such a short time that the external forces have a negligible effect. <br /> There are two types of collisions, [[Elastic Collisions]] and [[Inelastic Collisions]]. <br /> <br /> ===A Mathematical Model===<br /> <math>{E}_{f} = {E}_{i}</math> where <math>{E}_{f}</math> is the total final energy of the system and <math>{E}_{i}</math> is the total initial energy of the system.<br /> <br /> <math>{p}_{f} = {p}_{i}</math> where <math>{p}_{f}</math> is the total final momentum of the system and <math>{p}_{i}</math> is the total initial momentum of the system.<br /> <br /> ===A Computational Model===<br /> The following situation was used for this model created using python:<br /> <br /> Two objects are initially moving towards a third stationary object. Object 1 (in red) at position (-10,0,-2)m has a mass of 2kg and velocity (10,0,2)m/s. Object 2 (in blue) at position (0,6,3)m has a mass of 4kg and velocity (0,-6,3)m/s. Object 3 (in orange) at the origin has a mass of 5kg. The objects collide at the origin and after the collision it is observed that object 1 has embedded in object 3 (hence it is no longer visible in the model) and the combined object moves with velocity (5,-6,0)m/s (This is an example of a [[Maximally Inelastic Collision]]). The final velocity of object 2 is calculated and used in the rest of the simulation. (NOTE: the white sphere visible after the collision represents the origin to add dimension to the model and the delay during the collision is there to emphasis when and where the collision happens. Also use the link below the model for a more detailed explanation of the calculations and concepts.).<br /> <br /> [[File: CollisionsExample.gif]]<br /> <br /> Check out the code used for the simulation at [http://www.glowscript.org/#/user/samsaxlaxman/folder/Private/]. The code is commented pretty heavily (but it does assume some knowledge of python and python animations) in hopes that future students can modify some of the variables to experiment with creating different results.<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> Example 1)<br /> A 0.5 kg soccer ball is moving with a speed of 5 m/s directly toward to 0.7 kg basket ball which is at rest.<br /> When two balls collide and stick together what will their final velocity be?<br /> <br /> ___<br /> <br /> m1 = 0.5 kg,<br /> v1 init = 5 m/s,<br /> m2 = 0.7 kg,<br /> v2 init = 0 m/s<br /> <br /> So m1 * v1 + m2 * + v2 = (m1 + m2) * vfinal<br /> <br /> LHS = 0.5 * 5 + 0.7 * 0 = 2.5 kg*m/s<br /> RHS = (0.5 + 0.7) * vfinal = 1.2 * vfinal<br /> <br /> LHS = RHS in inelastic collision <br /> <br /> 2.5 = 1.2 * vfinal<br /> <br /> vfinal = 2.5 / 1.2 = 2.08333<br /> <br /> Thus, the final velocity is 2.08 m/s. Since the two balls stick together, this is an example of a [[Maximally Inelastic Collision]].<br /> <br /> ===Middling===<br /> Example 2)<br /> A bullet of 50 caliber machine gun is 42 grams. It strikes a wooden target block of mass 10 kg stationed on a friction-less surface. The wooden block gains velocity of 1.8 m/s after being embedded with the bullet.<br /> What was the velocity of the bullet before it collided with the target?<br /> <br /> <br /> ----<br /> <br /> m1 = 42/1000 = 0.042 kg,<br /> v1 init = ?,<br /> m2 = 10 kg,<br /> v2 init = 0,<br /> mfinal(m1+m2) = 0.042kg + 10kg,<br /> vfinal = 1.8 m/s<br /> <br /> m1 * v1 init + m2 * v2 init = (m1 + m2) * vfinal<br /> <br /> 0.042 kg * v1 init = (0.042 + 10) * 1.8 m/s<br /> v1 init = 18.0756 / 0.042 = 430.37 m/s<br /> <br /> Final Answer: The bullet's speed is 430.37 m/s.<br /> <br /> ===Difficult===<br /> Example 3) Two rocks in space are approaching a third stationary rock. Rock 1 has mass 30kg moves with velocity (13,-10,-2)m/s. Rock 2 has mass 60kg and moves with velocity (-3,23,3)m/s. Rock 3 has mass 35kg and is stationary. The rocks collide at rock 3's location. After the collision it is observed that Rock 1 has embedded into Rock 3, but a chunk of mass 15kg has broken off of the combined rock, Rock 3'. It is also noticed that Rock 2 is now moving with velocity (-2,12,2)m/s. (NOTE: due to the difficulty and use of three dimensions it is suggested to use a computer to solve this problem. Therefore the sample solution will involve code, but conceptually everything remains the same. Additionally some code is omitted for the sake of saving space, but the important calculations are included. See the entire code at . . . )<br /> <br /> '''First determine the momentum of Rock 3' plus the momentum of the 15kg chunk.''' <br /> <br /> <code><br /> Having defined the rocks as o1, o2, and o3 respectively, and defined there initial masses and velocities to calculate their individual momenta<br /> <br /> calculated the total momentum of the system by adding<br /> <br /> totalP = o1.p+o2.p+o3.p #total momentum of the system<br /> <br /> Next update the o1, o2 and o3 objects with the information observed after the collosions<br /> <br /> mChunk = 15 # in kg<br /> <br /> m1f = 0 #final mass object 1 in kg<br /> <br /> m2f = 60 #final mass object 2 in kg<br /> <br /> v2f = vector(-2,12,2) #final elocity object 2 in m/s<br /> <br /> m3f = o1.m + o2.m - mChunk #final mass object 3 in kg<br /> <br /> create a new sphere object with mass 15kg (code omitted)<br /> <br /> calculate the final momentum of rock 2<br /> <br /> o2.p = o2.v*o2.m<br /> <br /> finally determine the combined momentum of rock 3' and the chunk using the momentum principle<br /> <br /> pOfRock3PrimeAndChunk = totalP - o2.p #for now we are only calculating the combined momentum of rock 3' and the chunk<br /> </code><br /> <br /> ''The combined momentum of Rock 3' and the Chunk is <330, 360, 0>kg*m/s''<br /> <br /> '''Later Rock 3' is observed moving with velocity (x,y,z), what is the velocity of the 15kg chunk?'''<br /> <br /> <br /> '''With the information you know, determine the combined change in internal energy for all of the rocks.'''<br /> <br /> ==Connectedness==<br /> Collisions are interesting phenomenons that are applicable to everyday situations. Some examples are when a bat collides with a baseball in your neighbor's backyard, two cars crashing in the highway in front of you, and two linebackers running into each-other at your local College's spring football game. Depending on the type of collision, you can predict if there will be a change in internal energy (thermal energy, chemical energy etc.). Another very interesting application of collisions is in the field of astronomy. The universe is ever-changing and we never know what might come our way. A large meteor could be flying at the Earth with a very high speed and we could use our knowledge of collisions to find out how the Earth will move after the collision, what the temperature change of the area would be, and how the rest of the Earth would be effected by the collision. By using our collision skills, we could evacuate anyone who is prone to harm during the collision. <br /> <br /> Knowledge of collisions is also a must for many engineering majors. Industrial engineers must take in collisions when they are trying to optimize complex systems. For instance, an Industrial engineer must make sure that the bridge he or she builds can withstand the forces the cars can exert on it. Architects and Civil engineers must design houses in a certain way so that slight collisions with other objects won't completely knock the house down. And of course, Mechanical engineers and Aerospace engineers must take into account collisions when designing and maintaining mechanical systems.<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> [[Maximally Inelastic Collision]] , [[Inelastic Collisions]] , [[Elastic Collisions]], [[Momentum Principle]], [[Net Force]].<br /> <br /> ===Further reading===<br /> <br /> Chabay, Ruth W., and Bruce A. Sherwood. Matter and Interactions. 4th ed. Vol. 1. Hoboken, NJ: Wiley, 2015. Print. Matter and Interactions.<br /> <br /> ===External links===<br /> "The Collision Theory - Boundless Open Textbook." Boundless. N.p., n.d. Web. 17 Apr. 2016.<br /> <br /> ==References==<br /> <br /> Chabay, Ruth W., and Bruce A. Sherwood. Matter and Interactions. 4th ed. Vol. 1. Hoboken, NJ: Wiley, 2015. Print. Matter and Interactions.</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Collisions&diff=22540 Collisions 2016-04-17T21:42:40Z

<p>Swebster9: /* Difficult */</p> <hr /> <div>SECOND EDIT BY SUNGJAE HYUN IN 2016-04-16 ADDITIONS MADE BY (currently in progress, adding computational model and difficult problem) Sam Webster 4-17-16<br /> <br /> This topic covers Collisions, a comprehensive way to combine the Momentum and Energy Principles.<br /> <br /> ==The Main Idea==<br /> <br /> Collisions are special types of contact interactions between objects. From a physics standpoint, collisions are a way to combine the Momentum and Energy Principles. In the case of collisions, if we choose a system of the two objects interacting, the change in momentum of the system and the change in energy of the system are both zero. With this in mind, calculations with collisions become very simple. We are able to choose a system of only the two objects (excluding external forces such as the Earth's gravity) because the collision takes place during such a short time that the external forces have a negligible effect. <br /> There are two types of collisions, [[Elastic Collisions]] and [[Inelastic Collisions]]. <br /> <br /> ===A Mathematical Model===<br /> <math>{E}_{f} = {E}_{i}</math> where <math>{E}_{f}</math> is the total final energy of the system and <math>{E}_{i}</math> is the total initial energy of the system.<br /> <br /> <math>{p}_{f} = {p}_{i}</math> where <math>{p}_{f}</math> is the total final momentum of the system and <math>{p}_{i}</math> is the total initial momentum of the system.<br /> <br /> ===A Computational Model===<br /> The following situation was used for this model created using python:<br /> <br /> Two objects are initially moving towards a third stationary object. Object 1 (in red) at position (-10,0,-2)m has a mass of 2kg and velocity (10,0,2)m/s. Object 2 (in blue) at position (0,6,3)m has a mass of 4kg and velocity (0,-6,3)m/s. Object 3 (in orange) at the origin has a mass of 5kg. The objects collide at the origin and after the collision it is observed that object 1 has embedded in object 3 (hence it is no longer visible in the model) and the combined object moves with velocity (5,-6,0)m/s (This is an example of a [[Maximally Inelastic Collision]]). The final velocity of object 2 is calculated and used in the rest of the simulation. (NOTE: the white sphere visible after the collision represents the origin to add dimension to the model and the delay during the collision is there to emphasis when and where the collision happens. Also use the link below the model for a more detailed explanation of the calculations and concepts.).<br /> <br /> [[File: CollisionsExample.gif]]<br /> <br /> Check out the code used for the simulation at [http://www.glowscript.org/#/user/samsaxlaxman/folder/Private/]. The code is commented pretty heavily (but it does assume some knowledge of python and python animations) in hopes that future students can modify some of the variables to experiment with creating different results.<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> Example 1)<br /> A 0.5 kg soccer ball is moving with a speed of 5 m/s directly toward to 0.7 kg basket ball which is at rest.<br /> When two balls collide and stick together what will their final velocity be?<br /> <br /> ___<br /> <br /> m1 = 0.5 kg,<br /> v1 init = 5 m/s,<br /> m2 = 0.7 kg,<br /> v2 init = 0 m/s<br /> <br /> So m1 * v1 + m2 * + v2 = (m1 + m2) * vfinal<br /> <br /> LHS = 0.5 * 5 + 0.7 * 0 = 2.5 kg*m/s<br /> RHS = (0.5 + 0.7) * vfinal = 1.2 * vfinal<br /> <br /> LHS = RHS in inelastic collision <br /> <br /> 2.5 = 1.2 * vfinal<br /> <br /> vfinal = 2.5 / 1.2 = 2.08333<br /> <br /> Thus, the final velocity is 2.08 m/s. Since the two balls stick together, this is an example of a [[Maximally Inelastic Collision]].<br /> <br /> ===Middling===<br /> Example 2)<br /> A bullet of 50 caliber machine gun is 42 grams. It strikes a wooden target block of mass 10 kg stationed on a friction-less surface. The wooden block gains velocity of 1.8 m/s after being embedded with the bullet.<br /> What was the velocity of the bullet before it collided with the target?<br /> <br /> <br /> ----<br /> <br /> m1 = 42/1000 = 0.042 kg,<br /> v1 init = ?,<br /> m2 = 10 kg,<br /> v2 init = 0,<br /> mfinal(m1+m2) = 0.042kg + 10kg,<br /> vfinal = 1.8 m/s<br /> <br /> m1 * v1 init + m2 * v2 init = (m1 + m2) * vfinal<br /> <br /> 0.042 kg * v1 init = (0.042 + 10) * 1.8 m/s<br /> v1 init = 18.0756 / 0.042 = 430.37 m/s<br /> <br /> Final Answer: The bullet's speed is 430.37 m/s.<br /> <br /> ===Difficult===<br /> Example 3) Two rocks in space are approaching a third stationary rock. Rock 1 has mass 30kg moves with velocity (13,-10,-2)m/s. Rock 2 has mass 60kg and moves with velocity (-3,23,3)m/s. Rock 3 has mass 35kg and is stationary. The rocks collide at rock 3's location. After the collision it is observed that Rock 1 has embedded into Rock 3, but a chunk of mass 15kg has broken off of the combined rock, Rock 3'. It is also noticed that Rock 2 is now moving with velocity (-2,12,2)m/s. (NOTE: due to the difficulty and use of three dimensions it is suggested to use a computer to solve this problem. Therefore the sample solution will involve code, but conceptually everything remains the same.)<br /> <br /> '''First determine the momentum of Rock 3' plus the momentum of the 15kg chunk.''' <br /> <br /> <code><br /> Having defined the rocks as o1, o2, and o3 respectively, and defined there initial masses and velocities to calculate their individual momenta<br /> <br /> calculated the total momentum of the system by adding<br /> <br /> totalP = o1.p+o2.p+o3.p #total momentum of the system<br /> <br /> Next update the o1, o2 and o3 objects with the information observed after the collosions<br /> <br /> mChunk = 15 # in kg<br /> <br /> m1f = 0 #final mass object 1 in kg<br /> <br /> m2f = 60 #final mass object 2 in kg<br /> <br /> v2f = vector(-2,12,2) #final elocity object 2 in m/s<br /> <br /> m3f = o1.m + o2.m - mChunk #final mass object 3 in kg<br /> <br /> create a new sphere object with mass 15kg (code omitted)<br /> <br /> calculate the final momentum of rock 2<br /> <br /> o2.p = o2.v*o2.m<br /> <br /> finally determine the combined momentum of rock 3' and the chunk using the momentum principle<br /> <br /> pOfRock3PrimeAndChunk = totalP - o2.p #for now we are only calculating the combined momentum of rock 3' and the chunk<br /> </code><br /> <br /> ''The combined momentum of Rock 3' and the Chunk is <330, 360, 0>kg*m/s''<br /> <br /> '''Later Rock 3' is observed moving with velocity (x,y,z), what is the velocity of the 15kg chunk?'''<br /> <br /> <br /> '''With the information you know, determine the combined change in internal energy for all of the rocks.'''<br /> <br /> ==Connectedness==<br /> Collisions are interesting phenomenons that are applicable to everyday situations. Some examples are when a bat collides with a baseball in your neighbor's backyard, two cars crashing in the highway in front of you, and two linebackers running into each-other at your local College's spring football game. Depending on the type of collision, you can predict if there will be a change in internal energy (thermal energy, chemical energy etc.). Another very interesting application of collisions is in the field of astronomy. The universe is ever-changing and we never know what might come our way. A large meteor could be flying at the Earth with a very high speed and we could use our knowledge of collisions to find out how the Earth will move after the collision, what the temperature change of the area would be, and how the rest of the Earth would be effected by the collision. By using our collision skills, we could evacuate anyone who is prone to harm during the collision. <br /> <br /> Knowledge of collisions is also a must for many engineering majors. Industrial engineers must take in collisions when they are trying to optimize complex systems. For instance, an Industrial engineer must make sure that the bridge he or she builds can withstand the forces the cars can exert on it. Architects and Civil engineers must design houses in a certain way so that slight collisions with other objects won't completely knock the house down. And of course, Mechanical engineers and Aerospace engineers must take into account collisions when designing and maintaining mechanical systems.<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> [[Maximally Inelastic Collision]] , [[Inelastic Collisions]] , [[Elastic Collisions]], [[Momentum Principle]], [[Net Force]].<br /> <br /> ===Further reading===<br /> <br /> Chabay, Ruth W., and Bruce A. Sherwood. Matter and Interactions. 4th ed. Vol. 1. Hoboken, NJ: Wiley, 2015. Print. Matter and Interactions.<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> Chabay, Ruth W., and Bruce A. Sherwood. Matter and Interactions. 4th ed. Vol. 1. Hoboken, NJ: Wiley, 2015. Print. Matter and Interactions.</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Collisions&diff=22539 Collisions 2016-04-17T21:41:31Z

<p>Swebster9: /* Difficult */</p> <hr /> <div>SECOND EDIT BY SUNGJAE HYUN IN 2016-04-16 ADDITIONS MADE BY (currently in progress, adding computational model and difficult problem) Sam Webster 4-17-16<br /> <br /> This topic covers Collisions, a comprehensive way to combine the Momentum and Energy Principles.<br /> <br /> ==The Main Idea==<br /> <br /> Collisions are special types of contact interactions between objects. From a physics standpoint, collisions are a way to combine the Momentum and Energy Principles. In the case of collisions, if we choose a system of the two objects interacting, the change in momentum of the system and the change in energy of the system are both zero. With this in mind, calculations with collisions become very simple. We are able to choose a system of only the two objects (excluding external forces such as the Earth's gravity) because the collision takes place during such a short time that the external forces have a negligible effect. <br /> There are two types of collisions, [[Elastic Collisions]] and [[Inelastic Collisions]]. <br /> <br /> ===A Mathematical Model===<br /> <math>{E}_{f} = {E}_{i}</math> where <math>{E}_{f}</math> is the total final energy of the system and <math>{E}_{i}</math> is the total initial energy of the system.<br /> <br /> <math>{p}_{f} = {p}_{i}</math> where <math>{p}_{f}</math> is the total final momentum of the system and <math>{p}_{i}</math> is the total initial momentum of the system.<br /> <br /> ===A Computational Model===<br /> The following situation was used for this model created using python:<br /> <br /> Two objects are initially moving towards a third stationary object. Object 1 (in red) at position (-10,0,-2)m has a mass of 2kg and velocity (10,0,2)m/s. Object 2 (in blue) at position (0,6,3)m has a mass of 4kg and velocity (0,-6,3)m/s. Object 3 (in orange) at the origin has a mass of 5kg. The objects collide at the origin and after the collision it is observed that object 1 has embedded in object 3 (hence it is no longer visible in the model) and the combined object moves with velocity (5,-6,0)m/s (This is an example of a [[Maximally Inelastic Collision]]). The final velocity of object 2 is calculated and used in the rest of the simulation. (NOTE: the white sphere visible after the collision represents the origin to add dimension to the model and the delay during the collision is there to emphasis when and where the collision happens. Also use the link below the model for a more detailed explanation of the calculations and concepts.).<br /> <br /> [[File: CollisionsExample.gif]]<br /> <br /> Check out the code used for the simulation at [http://www.glowscript.org/#/user/samsaxlaxman/folder/Private/]. The code is commented pretty heavily (but it does assume some knowledge of python and python animations) in hopes that future students can modify some of the variables to experiment with creating different results.<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> Example 1)<br /> A 0.5 kg soccer ball is moving with a speed of 5 m/s directly toward to 0.7 kg basket ball which is at rest.<br /> When two balls collide and stick together what will their final velocity be?<br /> <br /> ___<br /> <br /> m1 = 0.5 kg,<br /> v1 init = 5 m/s,<br /> m2 = 0.7 kg,<br /> v2 init = 0 m/s<br /> <br /> So m1 * v1 + m2 * + v2 = (m1 + m2) * vfinal<br /> <br /> LHS = 0.5 * 5 + 0.7 * 0 = 2.5 kg*m/s<br /> RHS = (0.5 + 0.7) * vfinal = 1.2 * vfinal<br /> <br /> LHS = RHS in inelastic collision <br /> <br /> 2.5 = 1.2 * vfinal<br /> <br /> vfinal = 2.5 / 1.2 = 2.08333<br /> <br /> Thus, the final velocity is 2.08 m/s. Since the two balls stick together, this is an example of a [[Maximally Inelastic Collision]].<br /> <br /> ===Middling===<br /> Example 2)<br /> A bullet of 50 caliber machine gun is 42 grams. It strikes a wooden target block of mass 10 kg stationed on a friction-less surface. The wooden block gains velocity of 1.8 m/s after being embedded with the bullet.<br /> What was the velocity of the bullet before it collided with the target?<br /> <br /> <br /> ----<br /> <br /> m1 = 42/1000 = 0.042 kg,<br /> v1 init = ?,<br /> m2 = 10 kg,<br /> v2 init = 0,<br /> mfinal(m1+m2) = 0.042kg + 10kg,<br /> vfinal = 1.8 m/s<br /> <br /> m1 * v1 init + m2 * v2 init = (m1 + m2) * vfinal<br /> <br /> 0.042 kg * v1 init = (0.042 + 10) * 1.8 m/s<br /> v1 init = 18.0756 / 0.042 = 430.37 m/s<br /> <br /> Final Answer: The bullet's speed is 430.37 m/s.<br /> <br /> ===Difficult===<br /> Example 3) Two rocks in space are approaching a third stationary rock. Rock 1 has mass 30kg moves with velocity (13,-10,-2)m/s. Rock 2 has mass 60kg and moves with velocity (-3,23,3)m/s. Rock 3 has mass 35kg and is stationary. The rocks collide at rock 3's location. After the collision it is observed that Rock 1 has embedded into Rock 3, but a chunk of mass 15kg has broken off of the combined rock, Rock 3'. It is also noticed that Rock 2 is now moving with velocity (-2,12,2)m/s. (NOTE: due to the difficulty and use of three dimensions it is suggested to use a computer to solve this problem. Therefore the sample solution will involve code, but conceptually everything remains the same.)<br /> <br /> First determine the momentum of Rock 3' plus the momentum of the 15kg chunk. <br /> <br /> <code><br /> Having defined the rocks as o1, o2, and o3 respectively, and defined there initial masses and velocities to calculate their individual momenta<br /> <br /> calculated the total momentum of the system by adding<br /> <br /> totalP = o1.p+o2.p+o3.p #total momentum of the system<br /> <br /> Next update the o1, o2 and o3 objects with the information observed after the collosions<br /> <br /> mChunk = 15 # in kg<br /> <br /> m1f = 0 #final mass object 1 in kg<br /> <br /> m2f = 60 #final mass object 2 in kg<br /> <br /> v2f = vector(-2,12,2) #final elocity object 2 in m/s<br /> <br /> m3f = o1.m + o2.m - mChunk #final mass object 3 in kg<br /> <br /> create a new sphere object with mass 15kg (code omitted)<br /> <br /> calculate the final momentum of rock 2<br /> <br /> o2.p = o2.v*o2.m<br /> <br /> finally determine the combined momentum of rock 3' and the chunk using the momentum principle<br /> <br /> pOfRock3PrimeAndChunk = totalP - o2.p #for now we are only calculating the combined momentum of rock 3' and the chunk<br /> </code><br /> <br /> The combined momentum of Rock 3' and the Chunk is <330, 360, 0>kg*m/s<br /> <br /> Later Rock 3' is observed moving with velocity (x,y,z), what is the velocity of the 15kg chunk?<br /> <br /> <br /> With the information you know, determine the combined change in internal energy for all of the rocks.<br /> <br /> ==Connectedness==<br /> Collisions are interesting phenomenons that are applicable to everyday situations. Some examples are when a bat collides with a baseball in your neighbor's backyard, two cars crashing in the highway in front of you, and two linebackers running into each-other at your local College's spring football game. Depending on the type of collision, you can predict if there will be a change in internal energy (thermal energy, chemical energy etc.). Another very interesting application of collisions is in the field of astronomy. The universe is ever-changing and we never know what might come our way. A large meteor could be flying at the Earth with a very high speed and we could use our knowledge of collisions to find out how the Earth will move after the collision, what the temperature change of the area would be, and how the rest of the Earth would be effected by the collision. By using our collision skills, we could evacuate anyone who is prone to harm during the collision. <br /> <br /> Knowledge of collisions is also a must for many engineering majors. Industrial engineers must take in collisions when they are trying to optimize complex systems. For instance, an Industrial engineer must make sure that the bridge he or she builds can withstand the forces the cars can exert on it. Architects and Civil engineers must design houses in a certain way so that slight collisions with other objects won't completely knock the house down. And of course, Mechanical engineers and Aerospace engineers must take into account collisions when designing and maintaining mechanical systems.<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> [[Maximally Inelastic Collision]] , [[Inelastic Collisions]] , [[Elastic Collisions]], [[Momentum Principle]], [[Net Force]].<br /> <br /> ===Further reading===<br /> <br /> Chabay, Ruth W., and Bruce A. Sherwood. Matter and Interactions. 4th ed. Vol. 1. Hoboken, NJ: Wiley, 2015. Print. Matter and Interactions.<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> Chabay, Ruth W., and Bruce A. Sherwood. Matter and Interactions. 4th ed. Vol. 1. Hoboken, NJ: Wiley, 2015. Print. Matter and Interactions.</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Collisions&diff=22538 Collisions 2016-04-17T21:41:20Z

<p>Swebster9: /* Solution to Question 1 */</p> <hr /> <div>SECOND EDIT BY SUNGJAE HYUN IN 2016-04-16 ADDITIONS MADE BY (currently in progress, adding computational model and difficult problem) Sam Webster 4-17-16<br /> <br /> This topic covers Collisions, a comprehensive way to combine the Momentum and Energy Principles.<br /> <br /> ==The Main Idea==<br /> <br /> Collisions are special types of contact interactions between objects. From a physics standpoint, collisions are a way to combine the Momentum and Energy Principles. In the case of collisions, if we choose a system of the two objects interacting, the change in momentum of the system and the change in energy of the system are both zero. With this in mind, calculations with collisions become very simple. We are able to choose a system of only the two objects (excluding external forces such as the Earth's gravity) because the collision takes place during such a short time that the external forces have a negligible effect. <br /> There are two types of collisions, [[Elastic Collisions]] and [[Inelastic Collisions]]. <br /> <br /> ===A Mathematical Model===<br /> <math>{E}_{f} = {E}_{i}</math> where <math>{E}_{f}</math> is the total final energy of the system and <math>{E}_{i}</math> is the total initial energy of the system.<br /> <br /> <math>{p}_{f} = {p}_{i}</math> where <math>{p}_{f}</math> is the total final momentum of the system and <math>{p}_{i}</math> is the total initial momentum of the system.<br /> <br /> ===A Computational Model===<br /> The following situation was used for this model created using python:<br /> <br /> Two objects are initially moving towards a third stationary object. Object 1 (in red) at position (-10,0,-2)m has a mass of 2kg and velocity (10,0,2)m/s. Object 2 (in blue) at position (0,6,3)m has a mass of 4kg and velocity (0,-6,3)m/s. Object 3 (in orange) at the origin has a mass of 5kg. The objects collide at the origin and after the collision it is observed that object 1 has embedded in object 3 (hence it is no longer visible in the model) and the combined object moves with velocity (5,-6,0)m/s (This is an example of a [[Maximally Inelastic Collision]]). The final velocity of object 2 is calculated and used in the rest of the simulation. (NOTE: the white sphere visible after the collision represents the origin to add dimension to the model and the delay during the collision is there to emphasis when and where the collision happens. Also use the link below the model for a more detailed explanation of the calculations and concepts.).<br /> <br /> [[File: CollisionsExample.gif]]<br /> <br /> Check out the code used for the simulation at [http://www.glowscript.org/#/user/samsaxlaxman/folder/Private/]. The code is commented pretty heavily (but it does assume some knowledge of python and python animations) in hopes that future students can modify some of the variables to experiment with creating different results.<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> Example 1)<br /> A 0.5 kg soccer ball is moving with a speed of 5 m/s directly toward to 0.7 kg basket ball which is at rest.<br /> When two balls collide and stick together what will their final velocity be?<br /> <br /> ___<br /> <br /> m1 = 0.5 kg,<br /> v1 init = 5 m/s,<br /> m2 = 0.7 kg,<br /> v2 init = 0 m/s<br /> <br /> So m1 * v1 + m2 * + v2 = (m1 + m2) * vfinal<br /> <br /> LHS = 0.5 * 5 + 0.7 * 0 = 2.5 kg*m/s<br /> RHS = (0.5 + 0.7) * vfinal = 1.2 * vfinal<br /> <br /> LHS = RHS in inelastic collision <br /> <br /> 2.5 = 1.2 * vfinal<br /> <br /> vfinal = 2.5 / 1.2 = 2.08333<br /> <br /> Thus, the final velocity is 2.08 m/s. Since the two balls stick together, this is an example of a [[Maximally Inelastic Collision]].<br /> <br /> ===Middling===<br /> Example 2)<br /> A bullet of 50 caliber machine gun is 42 grams. It strikes a wooden target block of mass 10 kg stationed on a friction-less surface. The wooden block gains velocity of 1.8 m/s after being embedded with the bullet.<br /> What was the velocity of the bullet before it collided with the target?<br /> <br /> <br /> ----<br /> <br /> m1 = 42/1000 = 0.042 kg,<br /> v1 init = ?,<br /> m2 = 10 kg,<br /> v2 init = 0,<br /> mfinal(m1+m2) = 0.042kg + 10kg,<br /> vfinal = 1.8 m/s<br /> <br /> m1 * v1 init + m2 * v2 init = (m1 + m2) * vfinal<br /> <br /> 0.042 kg * v1 init = (0.042 + 10) * 1.8 m/s<br /> v1 init = 18.0756 / 0.042 = 430.37 m/s<br /> <br /> Final Answer: The bullet's speed is 430.37 m/s.<br /> <br /> ===Difficult===<br /> Example 3) Two rocks in space are approaching a third stationary rock. Rock 1 has mass 30kg moves with velocity (13,-10,-2)m/s. Rock 2 has mass 60kg and moves with velocity (-3,23,3)m/s. Rock 3 has mass 35kg and is stationary. The rocks collide at rock 3's location. After the collision it is observed that Rock 1 has embedded into Rock 3, but a chunk of mass 15kg has broken off of the combined rock, Rock 3'. It is also noticed that Rock 2 is now moving with velocity (-2,12,2)m/s. (NOTE: due to the difficulty and use of three dimensions it is suggested to use a computer to solve this problem. Therefore the sample solution will involve code, but conceptually everything remains the same.)<br /> <br /> First determine the momentum of Rock 3' plus the momentum of the 15kg chunk. <br /> ====Solution to Question 1====<br /> <br /> <code><br /> Having defined the rocks as o1, o2, and o3 respectively, and defined there initial masses and velocities to calculate their individual momenta<br /> <br /> calculated the total momentum of the system by adding<br /> <br /> totalP = o1.p+o2.p+o3.p #total momentum of the system<br /> <br /> Next update the o1, o2 and o3 objects with the information observed after the collosions<br /> <br /> mChunk = 15 # in kg<br /> <br /> m1f = 0 #final mass object 1 in kg<br /> <br /> m2f = 60 #final mass object 2 in kg<br /> <br /> v2f = vector(-2,12,2) #final elocity object 2 in m/s<br /> <br /> m3f = o1.m + o2.m - mChunk #final mass object 3 in kg<br /> <br /> create a new sphere object with mass 15kg (code omitted)<br /> <br /> calculate the final momentum of rock 2<br /> <br /> o2.p = o2.v*o2.m<br /> <br /> finally determine the combined momentum of rock 3' and the chunk using the momentum principle<br /> <br /> pOfRock3PrimeAndChunk = totalP - o2.p #for now we are only calculating the combined momentum of rock 3' and the chunk<br /> </code><br /> <br /> The combined momentum of Rock 3' and the Chunk is <330, 360, 0>kg*m/s<br /> <br /> Later Rock 3' is observed moving with velocity (x,y,z), what is the velocity of the 15kg chunk?<br /> <br /> <br /> With the information you know, determine the combined change in internal energy for all of the rocks.<br /> <br /> ==Connectedness==<br /> Collisions are interesting phenomenons that are applicable to everyday situations. Some examples are when a bat collides with a baseball in your neighbor's backyard, two cars crashing in the highway in front of you, and two linebackers running into each-other at your local College's spring football game. Depending on the type of collision, you can predict if there will be a change in internal energy (thermal energy, chemical energy etc.). Another very interesting application of collisions is in the field of astronomy. The universe is ever-changing and we never know what might come our way. A large meteor could be flying at the Earth with a very high speed and we could use our knowledge of collisions to find out how the Earth will move after the collision, what the temperature change of the area would be, and how the rest of the Earth would be effected by the collision. By using our collision skills, we could evacuate anyone who is prone to harm during the collision. <br /> <br /> Knowledge of collisions is also a must for many engineering majors. Industrial engineers must take in collisions when they are trying to optimize complex systems. For instance, an Industrial engineer must make sure that the bridge he or she builds can withstand the forces the cars can exert on it. Architects and Civil engineers must design houses in a certain way so that slight collisions with other objects won't completely knock the house down. And of course, Mechanical engineers and Aerospace engineers must take into account collisions when designing and maintaining mechanical systems.<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> [[Maximally Inelastic Collision]] , [[Inelastic Collisions]] , [[Elastic Collisions]], [[Momentum Principle]], [[Net Force]].<br /> <br /> ===Further reading===<br /> <br /> Chabay, Ruth W., and Bruce A. Sherwood. Matter and Interactions. 4th ed. Vol. 1. Hoboken, NJ: Wiley, 2015. Print. Matter and Interactions.<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> Chabay, Ruth W., and Bruce A. Sherwood. Matter and Interactions. 4th ed. Vol. 1. Hoboken, NJ: Wiley, 2015. Print. Matter and Interactions.</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Collisions&diff=22534 Collisions 2016-04-17T21:39:46Z

<p>Swebster9: /* Solution to Question 1 */</p> <hr /> <div>SECOND EDIT BY SUNGJAE HYUN IN 2016-04-16 ADDITIONS MADE BY (currently in progress, adding computational model and difficult problem) Sam Webster 4-17-16<br /> <br /> This topic covers Collisions, a comprehensive way to combine the Momentum and Energy Principles.<br /> <br /> ==The Main Idea==<br /> <br /> Collisions are special types of contact interactions between objects. From a physics standpoint, collisions are a way to combine the Momentum and Energy Principles. In the case of collisions, if we choose a system of the two objects interacting, the change in momentum of the system and the change in energy of the system are both zero. With this in mind, calculations with collisions become very simple. We are able to choose a system of only the two objects (excluding external forces such as the Earth's gravity) because the collision takes place during such a short time that the external forces have a negligible effect. <br /> There are two types of collisions, [[Elastic Collisions]] and [[Inelastic Collisions]]. <br /> <br /> ===A Mathematical Model===<br /> <math>{E}_{f} = {E}_{i}</math> where <math>{E}_{f}</math> is the total final energy of the system and <math>{E}_{i}</math> is the total initial energy of the system.<br /> <br /> <math>{p}_{f} = {p}_{i}</math> where <math>{p}_{f}</math> is the total final momentum of the system and <math>{p}_{i}</math> is the total initial momentum of the system.<br /> <br /> ===A Computational Model===<br /> The following situation was used for this model created using python:<br /> <br /> Two objects are initially moving towards a third stationary object. Object 1 (in red) at position (-10,0,-2)m has a mass of 2kg and velocity (10,0,2)m/s. Object 2 (in blue) at position (0,6,3)m has a mass of 4kg and velocity (0,-6,3)m/s. Object 3 (in orange) at the origin has a mass of 5kg. The objects collide at the origin and after the collision it is observed that object 1 has embedded in object 3 (hence it is no longer visible in the model) and the combined object moves with velocity (5,-6,0)m/s (This is an example of a [[Maximally Inelastic Collision]]). The final velocity of object 2 is calculated and used in the rest of the simulation. (NOTE: the white sphere visible after the collision represents the origin to add dimension to the model and the delay during the collision is there to emphasis when and where the collision happens. Also use the link below the model for a more detailed explanation of the calculations and concepts.).<br /> <br /> [[File: CollisionsExample.gif]]<br /> <br /> Check out the code used for the simulation at [http://www.glowscript.org/#/user/samsaxlaxman/folder/Private/]. The code is commented pretty heavily (but it does assume some knowledge of python and python animations) in hopes that future students can modify some of the variables to experiment with creating different results.<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> Example 1)<br /> A 0.5 kg soccer ball is moving with a speed of 5 m/s directly toward to 0.7 kg basket ball which is at rest.<br /> When two balls collide and stick together what will their final velocity be?<br /> <br /> ___<br /> <br /> m1 = 0.5 kg,<br /> v1 init = 5 m/s,<br /> m2 = 0.7 kg,<br /> v2 init = 0 m/s<br /> <br /> So m1 * v1 + m2 * + v2 = (m1 + m2) * vfinal<br /> <br /> LHS = 0.5 * 5 + 0.7 * 0 = 2.5 kg*m/s<br /> RHS = (0.5 + 0.7) * vfinal = 1.2 * vfinal<br /> <br /> LHS = RHS in inelastic collision <br /> <br /> 2.5 = 1.2 * vfinal<br /> <br /> vfinal = 2.5 / 1.2 = 2.08333<br /> <br /> Thus, the final velocity is 2.08 m/s. Since the two balls stick together, this is an example of a [[Maximally Inelastic Collision]].<br /> <br /> ===Middling===<br /> Example 2)<br /> A bullet of 50 caliber machine gun is 42 grams. It strikes a wooden target block of mass 10 kg stationed on a friction-less surface. The wooden block gains velocity of 1.8 m/s after being embedded with the bullet.<br /> What was the velocity of the bullet before it collided with the target?<br /> <br /> <br /> ----<br /> <br /> m1 = 42/1000 = 0.042 kg,<br /> v1 init = ?,<br /> m2 = 10 kg,<br /> v2 init = 0,<br /> mfinal(m1+m2) = 0.042kg + 10kg,<br /> vfinal = 1.8 m/s<br /> <br /> m1 * v1 init + m2 * v2 init = (m1 + m2) * vfinal<br /> <br /> 0.042 kg * v1 init = (0.042 + 10) * 1.8 m/s<br /> v1 init = 18.0756 / 0.042 = 430.37 m/s<br /> <br /> Final Answer: The bullet's speed is 430.37 m/s.<br /> <br /> ===Difficult===<br /> Example 3) Two rocks in space are approaching a third stationary rock. Rock 1 has mass 30kg moves with velocity (13,-10,-2)m/s. Rock 2 has mass 60kg and moves with velocity (-3,23,3)m/s. Rock 3 has mass 35kg and is stationary. The rocks collide at rock 3's location. After the collision it is observed that Rock 1 has embedded into Rock 3, but a chunk of mass 15kg has broken off of the combined rock, Rock 3'. It is also noticed that Rock 2 is now moving with velocity (-2,12,2)m/s. (NOTE: due to the difficulty and use of three dimensions it is suggested to use a computer to solve this problem. Therefore the sample solution will involve code, but conceptually everything remains the same.)<br /> <br /> First determine the momentum of Rock 3' plus the momentum of the 15kg chunk. <br /> ====Solution to Question 1====<br /> <br /> <code><br /> Having defined the rocks as o1, o2, and o3 respectively, and defined there initial masses and velocities to calculate their individual momenta<br /> <br /> calculated the total momentum of the system by adding<br /> <br /> totalP = o1.p+o2.p+o3.p #total momentum of the system<br /> <br /> Next update the o1, o2 and o3 objects with the information observed after the collosions<br /> <br /> mChunk = 15 # in kg<br /> <br /> m1f = 0 #final mass object 1 in kg<br /> <br /> m2f = 60 #final mass object 2 in kg<br /> <br /> v2f = vector(-2,12,2) #final elocity object 2 in m/s<br /> <br /> m3f = o1.m + o2.m - mChunk #final mass object 3 in kg<br /> <br /> create a new sphere object with mass 15kg (code omitted)<br /> <br /> calculate the final momentum of rock 2<br /> <br /> o2.p = o2.v*o2.m<br /> <br /> finally determine the combined momentum of rock 3' and the chunk using the momentum principle<br /> <br /> pOfRock3PrimeAndChunk = totalP - o2.p #for now we are only calculating the combined momentum of rock 3' and the chunk<br /> </code><br /> <br /> <br /> <br /> Later Rock 3' is observed moving with velocity (x,y,z), what is the velocity of the 15kg chunk?<br /> <br /> <br /> With the information you know, determine the combined change in internal energy for all of the rocks.<br /> <br /> ==Connectedness==<br /> Collisions are interesting phenomenons that are applicable to everyday situations. Some examples are when a bat collides with a baseball in your neighbor's backyard, two cars crashing in the highway in front of you, and two linebackers running into each-other at your local College's spring football game. Depending on the type of collision, you can predict if there will be a change in internal energy (thermal energy, chemical energy etc.). Another very interesting application of collisions is in the field of astronomy. The universe is ever-changing and we never know what might come our way. A large meteor could be flying at the Earth with a very high speed and we could use our knowledge of collisions to find out how the Earth will move after the collision, what the temperature change of the area would be, and how the rest of the Earth would be effected by the collision. By using our collision skills, we could evacuate anyone who is prone to harm during the collision. <br /> <br /> Knowledge of collisions is also a must for many engineering majors. Industrial engineers must take in collisions when they are trying to optimize complex systems. For instance, an Industrial engineer must make sure that the bridge he or she builds can withstand the forces the cars can exert on it. Architects and Civil engineers must design houses in a certain way so that slight collisions with other objects won't completely knock the house down. And of course, Mechanical engineers and Aerospace engineers must take into account collisions when designing and maintaining mechanical systems.<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> [[Maximally Inelastic Collision]] , [[Inelastic Collisions]] , [[Elastic Collisions]], [[Momentum Principle]], [[Net Force]].<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Collisions&diff=22532 Collisions 2016-04-17T21:39:14Z

<p>Swebster9: /* Solution to Question 1 */</p> <hr /> <div>SECOND EDIT BY SUNGJAE HYUN IN 2016-04-16 ADDITIONS MADE BY (currently in progress, adding computational model and difficult problem) Sam Webster 4-17-16<br /> <br /> This topic covers Collisions, a comprehensive way to combine the Momentum and Energy Principles.<br /> <br /> ==The Main Idea==<br /> <br /> Collisions are special types of contact interactions between objects. From a physics standpoint, collisions are a way to combine the Momentum and Energy Principles. In the case of collisions, if we choose a system of the two objects interacting, the change in momentum of the system and the change in energy of the system are both zero. With this in mind, calculations with collisions become very simple. We are able to choose a system of only the two objects (excluding external forces such as the Earth's gravity) because the collision takes place during such a short time that the external forces have a negligible effect. <br /> There are two types of collisions, [[Elastic Collisions]] and [[Inelastic Collisions]]. <br /> <br /> ===A Mathematical Model===<br /> <math>{E}_{f} = {E}_{i}</math> where <math>{E}_{f}</math> is the total final energy of the system and <math>{E}_{i}</math> is the total initial energy of the system.<br /> <br /> <math>{p}_{f} = {p}_{i}</math> where <math>{p}_{f}</math> is the total final momentum of the system and <math>{p}_{i}</math> is the total initial momentum of the system.<br /> <br /> ===A Computational Model===<br /> The following situation was used for this model created using python:<br /> <br /> Two objects are initially moving towards a third stationary object. Object 1 (in red) at position (-10,0,-2)m has a mass of 2kg and velocity (10,0,2)m/s. Object 2 (in blue) at position (0,6,3)m has a mass of 4kg and velocity (0,-6,3)m/s. Object 3 (in orange) at the origin has a mass of 5kg. The objects collide at the origin and after the collision it is observed that object 1 has embedded in object 3 (hence it is no longer visible in the model) and the combined object moves with velocity (5,-6,0)m/s (This is an example of a [[Maximally Inelastic Collision]]). The final velocity of object 2 is calculated and used in the rest of the simulation. (NOTE: the white sphere visible after the collision represents the origin to add dimension to the model and the delay during the collision is there to emphasis when and where the collision happens. Also use the link below the model for a more detailed explanation of the calculations and concepts.).<br /> <br /> [[File: CollisionsExample.gif]]<br /> <br /> Check out the code used for the simulation at [http://www.glowscript.org/#/user/samsaxlaxman/folder/Private/]. The code is commented pretty heavily (but it does assume some knowledge of python and python animations) in hopes that future students can modify some of the variables to experiment with creating different results.<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> Example 1)<br /> A 0.5 kg soccer ball is moving with a speed of 5 m/s directly toward to 0.7 kg basket ball which is at rest.<br /> When two balls collide and stick together what will their final velocity be?<br /> <br /> ___<br /> <br /> m1 = 0.5 kg,<br /> v1 init = 5 m/s,<br /> m2 = 0.7 kg,<br /> v2 init = 0 m/s<br /> <br /> So m1 * v1 + m2 * + v2 = (m1 + m2) * vfinal<br /> <br /> LHS = 0.5 * 5 + 0.7 * 0 = 2.5 kg*m/s<br /> RHS = (0.5 + 0.7) * vfinal = 1.2 * vfinal<br /> <br /> LHS = RHS in inelastic collision <br /> <br /> 2.5 = 1.2 * vfinal<br /> <br /> vfinal = 2.5 / 1.2 = 2.08333<br /> <br /> Thus, the final velocity is 2.08 m/s. Since the two balls stick together, this is an example of a [[Maximally Inelastic Collision]].<br /> <br /> ===Middling===<br /> Example 2)<br /> A bullet of 50 caliber machine gun is 42 grams. It strikes a wooden target block of mass 10 kg stationed on a friction-less surface. The wooden block gains velocity of 1.8 m/s after being embedded with the bullet.<br /> What was the velocity of the bullet before it collided with the target?<br /> <br /> <br /> ----<br /> <br /> m1 = 42/1000 = 0.042 kg,<br /> v1 init = ?,<br /> m2 = 10 kg,<br /> v2 init = 0,<br /> mfinal(m1+m2) = 0.042kg + 10kg,<br /> vfinal = 1.8 m/s<br /> <br /> m1 * v1 init + m2 * v2 init = (m1 + m2) * vfinal<br /> <br /> 0.042 kg * v1 init = (0.042 + 10) * 1.8 m/s<br /> v1 init = 18.0756 / 0.042 = 430.37 m/s<br /> <br /> Final Answer: The bullet's speed is 430.37 m/s.<br /> <br /> ===Difficult===<br /> Example 3) Two rocks in space are approaching a third stationary rock. Rock 1 has mass 30kg moves with velocity (13,-10,-2)m/s. Rock 2 has mass 60kg and moves with velocity (-3,23,3)m/s. Rock 3 has mass 35kg and is stationary. The rocks collide at rock 3's location. After the collision it is observed that Rock 1 has embedded into Rock 3, but a chunk of mass 15kg has broken off of the combined rock, Rock 3'. It is also noticed that Rock 2 is now moving with velocity (-2,12,2)m/s. (NOTE: due to the difficulty and use of three dimensions it is suggested to use a computer to solve this problem. Therefore the sample solution will involve code, but conceptually everything remains the same.)<br /> <br /> First determine the momentum of Rock 3' plus the momentum of the 15kg chunk. <br /> ====Solution to Question 1====<br /> <br /> <code><br /> #Having defined the rocks as o1, o2, and o3 respectively, and defined there initial masses and velocities to calculate their individual momenta<br /> <br /> #calculated the total momentum of the system by adding<br /> <br /> totalP = o1.p+o2.p+o3.p #total momentum of the system<br /> <br /> #Next update the o1, o2 and o3 objects with the information observed after the collosions<br /> <br /> mChunk = 15 # in kg<br /> <br /> m1f = 0 #final mass object 1 in kg<br /> <br /> m2f = 60 #final mass object 2 in kg<br /> <br /> v2f = vector(-2,12,2) #final elocity object 2 in m/s<br /> <br /> m3f = o1.m + o2.m - mChunk #final mass object 3 in kg<br /> <br /> #create a new sphere object with mass 15kg (code omitted)<br /> <br /> #calculate the final momentum of rock 2<br /> <br /> o2.p = o2.v*o2.m<br /> <br /> #finally determine the combined momentum of rock 3' and the chunk using the momentum principle<br /> <br /> pOfRock3PrimeAndChunk = totalP - o2.p #for now we are only calculating the combined momentum of rock 3' and the chunk<br /> </code><br /> <br /> <br /> <br /> Later Rock 3' is observed moving with velocity (x,y,z), what is the velocity of the 15kg chunk?<br /> <br /> <br /> With the information you know, determine the combined change in internal energy for all of the rocks.<br /> <br /> ==Connectedness==<br /> Collisions are interesting phenomenons that are applicable to everyday situations. Some examples are when a bat collides with a baseball in your neighbor's backyard, two cars crashing in the highway in front of you, and two linebackers running into each-other at your local College's spring football game. Depending on the type of collision, you can predict if there will be a change in internal energy (thermal energy, chemical energy etc.). Another very interesting application of collisions is in the field of astronomy. The universe is ever-changing and we never know what might come our way. A large meteor could be flying at the Earth with a very high speed and we could use our knowledge of collisions to find out how the Earth will move after the collision, what the temperature change of the area would be, and how the rest of the Earth would be effected by the collision. By using our collision skills, we could evacuate anyone who is prone to harm during the collision. <br /> <br /> Knowledge of collisions is also a must for many engineering majors. Industrial engineers must take in collisions when they are trying to optimize complex systems. For instance, an Industrial engineer must make sure that the bridge he or she builds can withstand the forces the cars can exert on it. Architects and Civil engineers must design houses in a certain way so that slight collisions with other objects won't completely knock the house down. And of course, Mechanical engineers and Aerospace engineers must take into account collisions when designing and maintaining mechanical systems.<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> [[Maximally Inelastic Collision]] , [[Inelastic Collisions]] , [[Elastic Collisions]], [[Momentum Principle]], [[Net Force]].<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Collisions&diff=22521 Collisions 2016-04-17T21:30:44Z

<p>Swebster9: /* Solution to Question 1 */</p> <hr /> <div>SECOND EDIT BY SUNGJAE HYUN IN 2016-04-16 ADDITIONS MADE BY (currently in progress, adding computational model and difficult problem) Sam Webster 4-17-16<br /> <br /> This topic covers Collisions, a comprehensive way to combine the Momentum and Energy Principles.<br /> <br /> ==The Main Idea==<br /> <br /> Collisions are special types of contact interactions between objects. From a physics standpoint, collisions are a way to combine the Momentum and Energy Principles. In the case of collisions, if we choose a system of the two objects interacting, the change in momentum of the system and the change in energy of the system are both zero. With this in mind, calculations with collisions become very simple. We are able to choose a system of only the two objects (excluding external forces such as the Earth's gravity) because the collision takes place during such a short time that the external forces have a negligible effect. <br /> There are two types of collisions, [[Elastic Collisions]] and [[Inelastic Collisions]]. <br /> <br /> ===A Mathematical Model===<br /> <math>{E}_{f} = {E}_{i}</math> where <math>{E}_{f}</math> is the total final energy of the system and <math>{E}_{i}</math> is the total initial energy of the system.<br /> <br /> <math>{p}_{f} = {p}_{i}</math> where <math>{p}_{f}</math> is the total final momentum of the system and <math>{p}_{i}</math> is the total initial momentum of the system.<br /> <br /> ===A Computational Model===<br /> The following situation was used for this model created using python:<br /> <br /> Two objects are initially moving towards a third stationary object. Object 1 (in red) at position (-10,0,-2)m has a mass of 2kg and velocity (10,0,2)m/s. Object 2 (in blue) at position (0,6,3)m has a mass of 4kg and velocity (0,-6,3)m/s. Object 3 (in orange) at the origin has a mass of 5kg. The objects collide at the origin and after the collision it is observed that object 1 has embedded in object 3 (hence it is no longer visible in the model) and the combined object moves with velocity (5,-6,0)m/s (This is an example of a [[Maximally Inelastic Collision]]). The final velocity of object 2 is calculated and used in the rest of the simulation. (NOTE: the white sphere visible after the collision represents the origin to add dimension to the model and the delay during the collision is there to emphasis when and where the collision happens. Also use the link below the model for a more detailed explanation of the calculations and concepts.).<br /> <br /> [[File: CollisionsExample.gif]]<br /> <br /> Check out the code used for the simulation at [http://www.glowscript.org/#/user/samsaxlaxman/folder/Private/]. The code is commented pretty heavily (but it does assume some knowledge of python and python animations) in hopes that future students can modify some of the variables to experiment with creating different results.<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> Example 1)<br /> A 0.5 kg soccer ball is moving with a speed of 5 m/s directly toward to 0.7 kg basket ball which is at rest.<br /> When two balls collide and stick together what will their final velocity be?<br /> <br /> ___<br /> <br /> m1 = 0.5 kg,<br /> v1 init = 5 m/s,<br /> m2 = 0.7 kg,<br /> v2 init = 0 m/s<br /> <br /> So m1 * v1 + m2 * + v2 = (m1 + m2) * vfinal<br /> <br /> LHS = 0.5 * 5 + 0.7 * 0 = 2.5 kg*m/s<br /> RHS = (0.5 + 0.7) * vfinal = 1.2 * vfinal<br /> <br /> LHS = RHS in inelastic collision <br /> <br /> 2.5 = 1.2 * vfinal<br /> <br /> vfinal = 2.5 / 1.2 = 2.08333<br /> <br /> Thus, the final velocity is 2.08 m/s. Since the two balls stick together, this is an example of a [[Maximally Inelastic Collision]].<br /> <br /> ===Middling===<br /> Example 2)<br /> A bullet of 50 caliber machine gun is 42 grams. It strikes a wooden target block of mass 10 kg stationed on a friction-less surface. The wooden block gains velocity of 1.8 m/s after being embedded with the bullet.<br /> What was the velocity of the bullet before it collided with the target?<br /> <br /> <br /> ----<br /> <br /> m1 = 42/1000 = 0.042 kg,<br /> v1 init = ?,<br /> m2 = 10 kg,<br /> v2 init = 0,<br /> mfinal(m1+m2) = 0.042kg + 10kg,<br /> vfinal = 1.8 m/s<br /> <br /> m1 * v1 init + m2 * v2 init = (m1 + m2) * vfinal<br /> <br /> 0.042 kg * v1 init = (0.042 + 10) * 1.8 m/s<br /> v1 init = 18.0756 / 0.042 = 430.37 m/s<br /> <br /> Final Answer: The bullet's speed is 430.37 m/s.<br /> <br /> ===Difficult===<br /> Example 3) Two rocks in space are approaching a third stationary rock. Rock 1 has mass 30kg moves with velocity (13,-10,-2)m/s. Rock 2 has mass 60kg and moves with velocity (-3,23,3)m/s. Rock 3 has mass 35kg and is stationary. The rocks collide at rock 3's location. After the collision it is observed that Rock 1 has embedded into Rock 3, but a chunk of mass 15kg has broken off of the combined rock, Rock 3'. It is also noticed that Rock 2 is now moving with velocity (-2,12,2)m/s. (NOTE: due to the difficulty and use of three dimensions it is suggested to use a computer to solve this problem. Therefore the sample solution will involve code, but conceptually everything remains the same.)<br /> <br /> First determine the momentum of Rock 3' plus the momentum of the 15kg chunk. <br /> ====Solution to Question 1====<br /> <br /> <code>#KNOWNS<br /> <br /> m1i = 30 #initial mass object 1 in kg<br /> <br /> v1i = vector(13,-10,-2) #initial velocity object1 in m/s<br /> <br /> m2i = 60 #initial mass object 2 in kg<br /> <br /> v2i = vector(-3,23,3) #vinitial elocity object 2 in m/s<br /> <br /> m3i = 35 #initial mass object 3 in kg<br /> <br /> v3i = vector(0,0,0) #initial velocity object 3 in m/s<br /> <br /> #OBJECTS (Spheres representing the point particle col<br /> <br /> o1 = sphere(pos = vector(-13,10,2), radius = .5, color = color.red) #object 1<br /> <br /> o1.v = v1i<br /> <br /> o1.m = m1i<br /> <br /> o1.p = o1.v*o1.m<br /> <br /> o2 = sphere(pos = vector(3,-23,-3), radius = 1, color = color.blue) #object 2<br /> <br /> o2.v = v2i<br /> <br /> o2.m = m2i<br /> <br /> o2.p = o2.v*o2.m<br /> <br /> o3 = sphere(pos = vector(0,0,0), radius = .55, color = color.orange) #object 3<br /> <br /> o3.v = v3i<br /> <br /> o3.m = m3i<br /> <br /> o3.p = o3.m*o3.v<br /> <br /> </code><br /> <br /> <br /> <br /> Later Rock 3' is observed moving with velocity (x,y,z), what is the velocity of the 15kg chunk?<br /> <br /> <br /> With the information you know, determine the combined change in internal energy for all of the rocks.<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Collisions&diff=22518 Collisions 2016-04-17T21:29:16Z

<p>Swebster9: /* Solution to Question 1 */</p> <hr /> <div>SECOND EDIT BY SUNGJAE HYUN IN 2016-04-16 ADDITIONS MADE BY (currently in progress, adding computational model and difficult problem) Sam Webster 4-17-16<br /> <br /> This topic covers Collisions, a comprehensive way to combine the Momentum and Energy Principles.<br /> <br /> ==The Main Idea==<br /> <br /> Collisions are special types of contact interactions between objects. From a physics standpoint, collisions are a way to combine the Momentum and Energy Principles. In the case of collisions, if we choose a system of the two objects interacting, the change in momentum of the system and the change in energy of the system are both zero. With this in mind, calculations with collisions become very simple. We are able to choose a system of only the two objects (excluding external forces such as the Earth's gravity) because the collision takes place during such a short time that the external forces have a negligible effect. <br /> There are two types of collisions, [[Elastic Collisions]] and [[Inelastic Collisions]]. <br /> <br /> ===A Mathematical Model===<br /> <math>{E}_{f} = {E}_{i}</math> where <math>{E}_{f}</math> is the total final energy of the system and <math>{E}_{i}</math> is the total initial energy of the system.<br /> <br /> <math>{p}_{f} = {p}_{i}</math> where <math>{p}_{f}</math> is the total final momentum of the system and <math>{p}_{i}</math> is the total initial momentum of the system.<br /> <br /> ===A Computational Model===<br /> The following situation was used for this model created using python:<br /> <br /> Two objects are initially moving towards a third stationary object. Object 1 (in red) at position (-10,0,-2)m has a mass of 2kg and velocity (10,0,2)m/s. Object 2 (in blue) at position (0,6,3)m has a mass of 4kg and velocity (0,-6,3)m/s. Object 3 (in orange) at the origin has a mass of 5kg. The objects collide at the origin and after the collision it is observed that object 1 has embedded in object 3 (hence it is no longer visible in the model) and the combined object moves with velocity (5,-6,0)m/s (This is an example of a [[Maximally Inelastic Collision]]). The final velocity of object 2 is calculated and used in the rest of the simulation. (NOTE: the white sphere visible after the collision represents the origin to add dimension to the model and the delay during the collision is there to emphasis when and where the collision happens. Also use the link below the model for a more detailed explanation of the calculations and concepts.).<br /> <br /> [[File: CollisionsExample.gif]]<br /> <br /> Check out the code used for the simulation at [http://www.glowscript.org/#/user/samsaxlaxman/folder/Private/]. The code is commented pretty heavily (but it does assume some knowledge of python and python animations) in hopes that future students can modify some of the variables to experiment with creating different results.<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> Example 1)<br /> A 0.5 kg soccer ball is moving with a speed of 5 m/s directly toward to 0.7 kg basket ball which is at rest.<br /> When two balls collide and stick together what will their final velocity be?<br /> <br /> ___<br /> <br /> m1 = 0.5 kg,<br /> v1 init = 5 m/s,<br /> m2 = 0.7 kg,<br /> v2 init = 0 m/s<br /> <br /> So m1 * v1 + m2 * + v2 = (m1 + m2) * vfinal<br /> <br /> LHS = 0.5 * 5 + 0.7 * 0 = 2.5 kg*m/s<br /> RHS = (0.5 + 0.7) * vfinal = 1.2 * vfinal<br /> <br /> LHS = RHS in inelastic collision <br /> <br /> 2.5 = 1.2 * vfinal<br /> <br /> vfinal = 2.5 / 1.2 = 2.08333<br /> <br /> Thus, the final velocity is 2.08 m/s. Since the two balls stick together, this is an example of a [[Maximally Inelastic Collision]].<br /> <br /> ===Middling===<br /> Example 2)<br /> A bullet of 50 caliber machine gun is 42 grams. It strikes a wooden target block of mass 10 kg stationed on a friction-less surface. The wooden block gains velocity of 1.8 m/s after being embedded with the bullet.<br /> What was the velocity of the bullet before it collided with the target?<br /> <br /> <br /> ----<br /> <br /> m1 = 42/1000 = 0.042 kg,<br /> v1 init = ?,<br /> m2 = 10 kg,<br /> v2 init = 0,<br /> mfinal(m1+m2) = 0.042kg + 10kg,<br /> vfinal = 1.8 m/s<br /> <br /> m1 * v1 init + m2 * v2 init = (m1 + m2) * vfinal<br /> <br /> 0.042 kg * v1 init = (0.042 + 10) * 1.8 m/s<br /> v1 init = 18.0756 / 0.042 = 430.37 m/s<br /> <br /> Final Answer: The bullet's speed is 430.37 m/s.<br /> <br /> ===Difficult===<br /> Example 3) Two rocks in space are approaching a third stationary rock. Rock 1 has mass 30kg moves with velocity (13,-10,-2)m/s. Rock 2 has mass 60kg and moves with velocity (-3,23,3)m/s. Rock 3 has mass 35kg and is stationary. The rocks collide at rock 3's location. After the collision it is observed that Rock 1 has embedded into Rock 3, but a chunk of mass 15kg has broken off of the combined rock, Rock 3'. It is also noticed that Rock 2 is now moving with velocity (-2,12,2)m/s. (NOTE: due to the difficulty and use of three dimensions it is suggested to use a computer to solve this problem. Therefore the sample solution will involve code, but conceptually everything remains the same.)<br /> <br /> First determine the momentum of Rock 3' plus the momentum of the 15kg chunk. <br /> ====Solution to Question 1====<br /> <br /> <code>#KNOWNS<br /> <br /> dT = .1<br /> <br /> m1i = 30 #initial mass object 1 in kg<br /> <br /> v1i = vector(13,-10,-2) #initial velocity object1 in m/s<br /> <br /> m2i = 60 #initial mass object 2 in kg<br /> <br /> v2i = vector(-3,23,3) #vinitial elocity object 2 in m/s<br /> <br /> m3i = 35 #initial mass object 3 in kg<br /> <br /> v3i = vector(0,0,0) #initial velocity object 3 in m/s]<br /> </code><br /> <br /> <br /> <br /> <br /> Later Rock 3' is observed moving with velocity (x,y,z), what is the velocity of the 15kg chunk?<br /> <br /> <br /> With the information you know, determine the combined change in internal energy for all of the rocks.<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Collisions&diff=22517 Collisions 2016-04-17T21:28:46Z

<p>Swebster9: /* Solution to Question 1 */</p> <hr /> <div>SECOND EDIT BY SUNGJAE HYUN IN 2016-04-16 ADDITIONS MADE BY (currently in progress, adding computational model and difficult problem) Sam Webster 4-17-16<br /> <br /> This topic covers Collisions, a comprehensive way to combine the Momentum and Energy Principles.<br /> <br /> ==The Main Idea==<br /> <br /> Collisions are special types of contact interactions between objects. From a physics standpoint, collisions are a way to combine the Momentum and Energy Principles. In the case of collisions, if we choose a system of the two objects interacting, the change in momentum of the system and the change in energy of the system are both zero. With this in mind, calculations with collisions become very simple. We are able to choose a system of only the two objects (excluding external forces such as the Earth's gravity) because the collision takes place during such a short time that the external forces have a negligible effect. <br /> There are two types of collisions, [[Elastic Collisions]] and [[Inelastic Collisions]]. <br /> <br /> ===A Mathematical Model===<br /> <math>{E}_{f} = {E}_{i}</math> where <math>{E}_{f}</math> is the total final energy of the system and <math>{E}_{i}</math> is the total initial energy of the system.<br /> <br /> <math>{p}_{f} = {p}_{i}</math> where <math>{p}_{f}</math> is the total final momentum of the system and <math>{p}_{i}</math> is the total initial momentum of the system.<br /> <br /> ===A Computational Model===<br /> The following situation was used for this model created using python:<br /> <br /> Two objects are initially moving towards a third stationary object. Object 1 (in red) at position (-10,0,-2)m has a mass of 2kg and velocity (10,0,2)m/s. Object 2 (in blue) at position (0,6,3)m has a mass of 4kg and velocity (0,-6,3)m/s. Object 3 (in orange) at the origin has a mass of 5kg. The objects collide at the origin and after the collision it is observed that object 1 has embedded in object 3 (hence it is no longer visible in the model) and the combined object moves with velocity (5,-6,0)m/s (This is an example of a [[Maximally Inelastic Collision]]). The final velocity of object 2 is calculated and used in the rest of the simulation. (NOTE: the white sphere visible after the collision represents the origin to add dimension to the model and the delay during the collision is there to emphasis when and where the collision happens. Also use the link below the model for a more detailed explanation of the calculations and concepts.).<br /> <br /> [[File: CollisionsExample.gif]]<br /> <br /> Check out the code used for the simulation at [http://www.glowscript.org/#/user/samsaxlaxman/folder/Private/]. The code is commented pretty heavily (but it does assume some knowledge of python and python animations) in hopes that future students can modify some of the variables to experiment with creating different results.<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> Example 1)<br /> A 0.5 kg soccer ball is moving with a speed of 5 m/s directly toward to 0.7 kg basket ball which is at rest.<br /> When two balls collide and stick together what will their final velocity be?<br /> <br /> ___<br /> <br /> m1 = 0.5 kg,<br /> v1 init = 5 m/s,<br /> m2 = 0.7 kg,<br /> v2 init = 0 m/s<br /> <br /> So m1 * v1 + m2 * + v2 = (m1 + m2) * vfinal<br /> <br /> LHS = 0.5 * 5 + 0.7 * 0 = 2.5 kg*m/s<br /> RHS = (0.5 + 0.7) * vfinal = 1.2 * vfinal<br /> <br /> LHS = RHS in inelastic collision <br /> <br /> 2.5 = 1.2 * vfinal<br /> <br /> vfinal = 2.5 / 1.2 = 2.08333<br /> <br /> Thus, the final velocity is 2.08 m/s. Since the two balls stick together, this is an example of a [[Maximally Inelastic Collision]].<br /> <br /> ===Middling===<br /> Example 2)<br /> A bullet of 50 caliber machine gun is 42 grams. It strikes a wooden target block of mass 10 kg stationed on a friction-less surface. The wooden block gains velocity of 1.8 m/s after being embedded with the bullet.<br /> What was the velocity of the bullet before it collided with the target?<br /> <br /> <br /> ----<br /> <br /> m1 = 42/1000 = 0.042 kg,<br /> v1 init = ?,<br /> m2 = 10 kg,<br /> v2 init = 0,<br /> mfinal(m1+m2) = 0.042kg + 10kg,<br /> vfinal = 1.8 m/s<br /> <br /> m1 * v1 init + m2 * v2 init = (m1 + m2) * vfinal<br /> <br /> 0.042 kg * v1 init = (0.042 + 10) * 1.8 m/s<br /> v1 init = 18.0756 / 0.042 = 430.37 m/s<br /> <br /> Final Answer: The bullet's speed is 430.37 m/s.<br /> <br /> ===Difficult===<br /> Example 3) Two rocks in space are approaching a third stationary rock. Rock 1 has mass 30kg moves with velocity (13,-10,-2)m/s. Rock 2 has mass 60kg and moves with velocity (-3,23,3)m/s. Rock 3 has mass 35kg and is stationary. The rocks collide at rock 3's location. After the collision it is observed that Rock 1 has embedded into Rock 3, but a chunk of mass 15kg has broken off of the combined rock, Rock 3'. It is also noticed that Rock 2 is now moving with velocity (-2,12,2)m/s. (NOTE: due to the difficulty and use of three dimensions it is suggested to use a computer to solve this problem. Therefore the sample solution will involve code, but conceptually everything remains the same.)<br /> <br /> First determine the momentum of Rock 3' plus the momentum of the 15kg chunk. <br /> ====Solution to Question 1====<br /> <br /> <code>#KNOWNS<br /> dT = .1<br /> m1i = 30 #initial mass object 1 in kg<br /> v1i = vector(13,-10,-2) #initial velocity object1 in m/s<br /> m2i = 60 #initial mass object 2 in kg<br /> v2i = vector(-3,23,3) #vinitial elocity object 2 in m/s<br /> m3i = 35 #initial mass object 3 in kg<br /> v3i = vector(0,0,0) #initial velocity object 3 in m/s]<br /> </code><br /> <br /> <br /> <br /> <br /> Later Rock 3' is observed moving with velocity (x,y,z), what is the velocity of the 15kg chunk?<br /> <br /> <br /> With the information you know, determine the combined change in internal energy for all of the rocks.<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Collisions&diff=22516 Collisions 2016-04-17T21:26:35Z

<p>Swebster9: /* Solution to Question 1 */</p> <hr /> <div>SECOND EDIT BY SUNGJAE HYUN IN 2016-04-16 ADDITIONS MADE BY (currently in progress, adding computational model and difficult problem) Sam Webster 4-17-16<br /> <br /> This topic covers Collisions, a comprehensive way to combine the Momentum and Energy Principles.<br /> <br /> ==The Main Idea==<br /> <br /> Collisions are special types of contact interactions between objects. From a physics standpoint, collisions are a way to combine the Momentum and Energy Principles. In the case of collisions, if we choose a system of the two objects interacting, the change in momentum of the system and the change in energy of the system are both zero. With this in mind, calculations with collisions become very simple. We are able to choose a system of only the two objects (excluding external forces such as the Earth's gravity) because the collision takes place during such a short time that the external forces have a negligible effect. <br /> There are two types of collisions, [[Elastic Collisions]] and [[Inelastic Collisions]]. <br /> <br /> ===A Mathematical Model===<br /> <math>{E}_{f} = {E}_{i}</math> where <math>{E}_{f}</math> is the total final energy of the system and <math>{E}_{i}</math> is the total initial energy of the system.<br /> <br /> <math>{p}_{f} = {p}_{i}</math> where <math>{p}_{f}</math> is the total final momentum of the system and <math>{p}_{i}</math> is the total initial momentum of the system.<br /> <br /> ===A Computational Model===<br /> The following situation was used for this model created using python:<br /> <br /> Two objects are initially moving towards a third stationary object. Object 1 (in red) at position (-10,0,-2)m has a mass of 2kg and velocity (10,0,2)m/s. Object 2 (in blue) at position (0,6,3)m has a mass of 4kg and velocity (0,-6,3)m/s. Object 3 (in orange) at the origin has a mass of 5kg. The objects collide at the origin and after the collision it is observed that object 1 has embedded in object 3 (hence it is no longer visible in the model) and the combined object moves with velocity (5,-6,0)m/s (This is an example of a [[Maximally Inelastic Collision]]). The final velocity of object 2 is calculated and used in the rest of the simulation. (NOTE: the white sphere visible after the collision represents the origin to add dimension to the model and the delay during the collision is there to emphasis when and where the collision happens. Also use the link below the model for a more detailed explanation of the calculations and concepts.).<br /> <br /> [[File: CollisionsExample.gif]]<br /> <br /> Check out the code used for the simulation at [http://www.glowscript.org/#/user/samsaxlaxman/folder/Private/]. The code is commented pretty heavily (but it does assume some knowledge of python and python animations) in hopes that future students can modify some of the variables to experiment with creating different results.<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> Example 1)<br /> A 0.5 kg soccer ball is moving with a speed of 5 m/s directly toward to 0.7 kg basket ball which is at rest.<br /> When two balls collide and stick together what will their final velocity be?<br /> <br /> ___<br /> <br /> m1 = 0.5 kg,<br /> v1 init = 5 m/s,<br /> m2 = 0.7 kg,<br /> v2 init = 0 m/s<br /> <br /> So m1 * v1 + m2 * + v2 = (m1 + m2) * vfinal<br /> <br /> LHS = 0.5 * 5 + 0.7 * 0 = 2.5 kg*m/s<br /> RHS = (0.5 + 0.7) * vfinal = 1.2 * vfinal<br /> <br /> LHS = RHS in inelastic collision <br /> <br /> 2.5 = 1.2 * vfinal<br /> <br /> vfinal = 2.5 / 1.2 = 2.08333<br /> <br /> Thus, the final velocity is 2.08 m/s. Since the two balls stick together, this is an example of a [[Maximally Inelastic Collision]].<br /> <br /> ===Middling===<br /> Example 2)<br /> A bullet of 50 caliber machine gun is 42 grams. It strikes a wooden target block of mass 10 kg stationed on a friction-less surface. The wooden block gains velocity of 1.8 m/s after being embedded with the bullet.<br /> What was the velocity of the bullet before it collided with the target?<br /> <br /> <br /> ----<br /> <br /> m1 = 42/1000 = 0.042 kg,<br /> v1 init = ?,<br /> m2 = 10 kg,<br /> v2 init = 0,<br /> mfinal(m1+m2) = 0.042kg + 10kg,<br /> vfinal = 1.8 m/s<br /> <br /> m1 * v1 init + m2 * v2 init = (m1 + m2) * vfinal<br /> <br /> 0.042 kg * v1 init = (0.042 + 10) * 1.8 m/s<br /> v1 init = 18.0756 / 0.042 = 430.37 m/s<br /> <br /> Final Answer: The bullet's speed is 430.37 m/s.<br /> <br /> ===Difficult===<br /> Example 3) Two rocks in space are approaching a third stationary rock. Rock 1 has mass 30kg moves with velocity (13,-10,-2)m/s. Rock 2 has mass 60kg and moves with velocity (-3,23,3)m/s. Rock 3 has mass 35kg and is stationary. The rocks collide at rock 3's location. After the collision it is observed that Rock 1 has embedded into Rock 3, but a chunk of mass 15kg has broken off of the combined rock, Rock 3'. It is also noticed that Rock 2 is now moving with velocity (-2,12,2)m/s. (NOTE: due to the difficulty and use of three dimensions it is suggested to use a computer to solve this problem. Therefore the sample solution will involve code, but conceptually everything remains the same.)<br /> <br /> First determine the momentum of Rock 3' plus the momentum of the 15kg chunk. <br /> ====Solution to Question 1====<br /> <br /> [#KNOWNS<br /> dT = .1<br /> m1i = 30 #initial mass object 1 in kg<br /> v1i = vector(13,-10,-2) #initial velocity object1 in m/s<br /> m2i = 60 #initial mass object 2 in kg<br /> v2i = vector(-3,23,3) #vinitial elocity object 2 in m/s<br /> m3i = 35 #initial mass object 3 in kg<br /> v3i = vector(0,0,0) #initial velocity object 3 in m/s]<br /> <br /> <br /> <br /> <br /> Later Rock 3' is observed moving with velocity (x,y,z), what is the velocity of the 15kg chunk?<br /> <br /> <br /> With the information you know, determine the combined change in internal energy for all of the rocks.<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Collisions&diff=22514 Collisions 2016-04-17T21:25:02Z

<p>Swebster9: /* Solution to Question 1 */</p> <hr /> <div>SECOND EDIT BY SUNGJAE HYUN IN 2016-04-16 ADDITIONS MADE BY (currently in progress, adding computational model and difficult problem) Sam Webster 4-17-16<br /> <br /> This topic covers Collisions, a comprehensive way to combine the Momentum and Energy Principles.<br /> <br /> ==The Main Idea==<br /> <br /> Collisions are special types of contact interactions between objects. From a physics standpoint, collisions are a way to combine the Momentum and Energy Principles. In the case of collisions, if we choose a system of the two objects interacting, the change in momentum of the system and the change in energy of the system are both zero. With this in mind, calculations with collisions become very simple. We are able to choose a system of only the two objects (excluding external forces such as the Earth's gravity) because the collision takes place during such a short time that the external forces have a negligible effect. <br /> There are two types of collisions, [[Elastic Collisions]] and [[Inelastic Collisions]]. <br /> <br /> ===A Mathematical Model===<br /> <math>{E}_{f} = {E}_{i}</math> where <math>{E}_{f}</math> is the total final energy of the system and <math>{E}_{i}</math> is the total initial energy of the system.<br /> <br /> <math>{p}_{f} = {p}_{i}</math> where <math>{p}_{f}</math> is the total final momentum of the system and <math>{p}_{i}</math> is the total initial momentum of the system.<br /> <br /> ===A Computational Model===<br /> The following situation was used for this model created using python:<br /> <br /> Two objects are initially moving towards a third stationary object. Object 1 (in red) at position (-10,0,-2)m has a mass of 2kg and velocity (10,0,2)m/s. Object 2 (in blue) at position (0,6,3)m has a mass of 4kg and velocity (0,-6,3)m/s. Object 3 (in orange) at the origin has a mass of 5kg. The objects collide at the origin and after the collision it is observed that object 1 has embedded in object 3 (hence it is no longer visible in the model) and the combined object moves with velocity (5,-6,0)m/s (This is an example of a [[Maximally Inelastic Collision]]). The final velocity of object 2 is calculated and used in the rest of the simulation. (NOTE: the white sphere visible after the collision represents the origin to add dimension to the model and the delay during the collision is there to emphasis when and where the collision happens. Also use the link below the model for a more detailed explanation of the calculations and concepts.).<br /> <br /> [[File: CollisionsExample.gif]]<br /> <br /> Check out the code used for the simulation at [http://www.glowscript.org/#/user/samsaxlaxman/folder/Private/]. The code is commented pretty heavily (but it does assume some knowledge of python and python animations) in hopes that future students can modify some of the variables to experiment with creating different results.<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> Example 1)<br /> A 0.5 kg soccer ball is moving with a speed of 5 m/s directly toward to 0.7 kg basket ball which is at rest.<br /> When two balls collide and stick together what will their final velocity be?<br /> <br /> ___<br /> <br /> m1 = 0.5 kg,<br /> v1 init = 5 m/s,<br /> m2 = 0.7 kg,<br /> v2 init = 0 m/s<br /> <br /> So m1 * v1 + m2 * + v2 = (m1 + m2) * vfinal<br /> <br /> LHS = 0.5 * 5 + 0.7 * 0 = 2.5 kg*m/s<br /> RHS = (0.5 + 0.7) * vfinal = 1.2 * vfinal<br /> <br /> LHS = RHS in inelastic collision <br /> <br /> 2.5 = 1.2 * vfinal<br /> <br /> vfinal = 2.5 / 1.2 = 2.08333<br /> <br /> Thus, the final velocity is 2.08 m/s. Since the two balls stick together, this is an example of a [[Maximally Inelastic Collision]].<br /> <br /> ===Middling===<br /> Example 2)<br /> A bullet of 50 caliber machine gun is 42 grams. It strikes a wooden target block of mass 10 kg stationed on a friction-less surface. The wooden block gains velocity of 1.8 m/s after being embedded with the bullet.<br /> What was the velocity of the bullet before it collided with the target?<br /> <br /> <br /> ----<br /> <br /> m1 = 42/1000 = 0.042 kg,<br /> v1 init = ?,<br /> m2 = 10 kg,<br /> v2 init = 0,<br /> mfinal(m1+m2) = 0.042kg + 10kg,<br /> vfinal = 1.8 m/s<br /> <br /> m1 * v1 init + m2 * v2 init = (m1 + m2) * vfinal<br /> <br /> 0.042 kg * v1 init = (0.042 + 10) * 1.8 m/s<br /> v1 init = 18.0756 / 0.042 = 430.37 m/s<br /> <br /> Final Answer: The bullet's speed is 430.37 m/s.<br /> <br /> ===Difficult===<br /> Example 3) Two rocks in space are approaching a third stationary rock. Rock 1 has mass 30kg moves with velocity (13,-10,-2)m/s. Rock 2 has mass 60kg and moves with velocity (-3,23,3)m/s. Rock 3 has mass 35kg and is stationary. The rocks collide at rock 3's location. After the collision it is observed that Rock 1 has embedded into Rock 3, but a chunk of mass 15kg has broken off of the combined rock, Rock 3'. It is also noticed that Rock 2 is now moving with velocity (-2,12,2)m/s. (NOTE: due to the difficulty and use of three dimensions it is suggested to use a computer to solve this problem. Therefore the sample solution will involve code, but conceptually everything remains the same.)<br /> <br /> First determine the momentum of Rock 3' plus the momentum of the 15kg chunk. <br /> ====Solution to Question 1====<br /> <br /> #KNOWNS<br /> dT = .1<br /> m1i = 30 #initial mass object 1 in kg<br /> v1i = vector(13,-10,-2) #initial velocity object1 in m/s<br /> m2i = 60 #initial mass object 2 in kg<br /> v2i = vector(-3,23,3) #vinitial elocity object 2 in m/s<br /> m3i = 35 #initial mass object 3 in kg<br /> v3i = vector(0,0,0) #initial velocity object 3 in m/s<br /> <br /> <br /> <br /> <br /> Later Rock 3' is observed moving with velocity (x,y,z), what is the velocity of the 15kg chunk?<br /> <br /> <br /> With the information you know, determine the combined change in internal energy for all of the rocks.<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Collisions&diff=22512 Collisions 2016-04-17T21:23:50Z

<p>Swebster9: /* Solution to Question 1 */</p> <hr /> <div>SECOND EDIT BY SUNGJAE HYUN IN 2016-04-16 ADDITIONS MADE BY (currently in progress, adding computational model and difficult problem) Sam Webster 4-17-16<br /> <br /> This topic covers Collisions, a comprehensive way to combine the Momentum and Energy Principles.<br /> <br /> ==The Main Idea==<br /> <br /> Collisions are special types of contact interactions between objects. From a physics standpoint, collisions are a way to combine the Momentum and Energy Principles. In the case of collisions, if we choose a system of the two objects interacting, the change in momentum of the system and the change in energy of the system are both zero. With this in mind, calculations with collisions become very simple. We are able to choose a system of only the two objects (excluding external forces such as the Earth's gravity) because the collision takes place during such a short time that the external forces have a negligible effect. <br /> There are two types of collisions, [[Elastic Collisions]] and [[Inelastic Collisions]]. <br /> <br /> ===A Mathematical Model===<br /> <math>{E}_{f} = {E}_{i}</math> where <math>{E}_{f}</math> is the total final energy of the system and <math>{E}_{i}</math> is the total initial energy of the system.<br /> <br /> <math>{p}_{f} = {p}_{i}</math> where <math>{p}_{f}</math> is the total final momentum of the system and <math>{p}_{i}</math> is the total initial momentum of the system.<br /> <br /> ===A Computational Model===<br /> The following situation was used for this model created using python:<br /> <br /> Two objects are initially moving towards a third stationary object. Object 1 (in red) at position (-10,0,-2)m has a mass of 2kg and velocity (10,0,2)m/s. Object 2 (in blue) at position (0,6,3)m has a mass of 4kg and velocity (0,-6,3)m/s. Object 3 (in orange) at the origin has a mass of 5kg. The objects collide at the origin and after the collision it is observed that object 1 has embedded in object 3 (hence it is no longer visible in the model) and the combined object moves with velocity (5,-6,0)m/s (This is an example of a [[Maximally Inelastic Collision]]). The final velocity of object 2 is calculated and used in the rest of the simulation. (NOTE: the white sphere visible after the collision represents the origin to add dimension to the model and the delay during the collision is there to emphasis when and where the collision happens. Also use the link below the model for a more detailed explanation of the calculations and concepts.).<br /> <br /> [[File: CollisionsExample.gif]]<br /> <br /> Check out the code used for the simulation at [http://www.glowscript.org/#/user/samsaxlaxman/folder/Private/]. The code is commented pretty heavily (but it does assume some knowledge of python and python animations) in hopes that future students can modify some of the variables to experiment with creating different results.<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> Example 1)<br /> A 0.5 kg soccer ball is moving with a speed of 5 m/s directly toward to 0.7 kg basket ball which is at rest.<br /> When two balls collide and stick together what will their final velocity be?<br /> <br /> ___<br /> <br /> m1 = 0.5 kg,<br /> v1 init = 5 m/s,<br /> m2 = 0.7 kg,<br /> v2 init = 0 m/s<br /> <br /> So m1 * v1 + m2 * + v2 = (m1 + m2) * vfinal<br /> <br /> LHS = 0.5 * 5 + 0.7 * 0 = 2.5 kg*m/s<br /> RHS = (0.5 + 0.7) * vfinal = 1.2 * vfinal<br /> <br /> LHS = RHS in inelastic collision <br /> <br /> 2.5 = 1.2 * vfinal<br /> <br /> vfinal = 2.5 / 1.2 = 2.08333<br /> <br /> Thus, the final velocity is 2.08 m/s. Since the two balls stick together, this is an example of a [[Maximally Inelastic Collision]].<br /> <br /> ===Middling===<br /> Example 2)<br /> A bullet of 50 caliber machine gun is 42 grams. It strikes a wooden target block of mass 10 kg stationed on a friction-less surface. The wooden block gains velocity of 1.8 m/s after being embedded with the bullet.<br /> What was the velocity of the bullet before it collided with the target?<br /> <br /> <br /> ----<br /> <br /> m1 = 42/1000 = 0.042 kg,<br /> v1 init = ?,<br /> m2 = 10 kg,<br /> v2 init = 0,<br /> mfinal(m1+m2) = 0.042kg + 10kg,<br /> vfinal = 1.8 m/s<br /> <br /> m1 * v1 init + m2 * v2 init = (m1 + m2) * vfinal<br /> <br /> 0.042 kg * v1 init = (0.042 + 10) * 1.8 m/s<br /> v1 init = 18.0756 / 0.042 = 430.37 m/s<br /> <br /> Final Answer: The bullet's speed is 430.37 m/s.<br /> <br /> ===Difficult===<br /> Example 3) Two rocks in space are approaching a third stationary rock. Rock 1 has mass 30kg moves with velocity (13,-10,-2)m/s. Rock 2 has mass 60kg and moves with velocity (-3,23,3)m/s. Rock 3 has mass 35kg and is stationary. The rocks collide at rock 3's location. After the collision it is observed that Rock 1 has embedded into Rock 3, but a chunk of mass 15kg has broken off of the combined rock, Rock 3'. It is also noticed that Rock 2 is now moving with velocity (-2,12,2)m/s. (NOTE: due to the difficulty and use of three dimensions it is suggested to use a computer to solve this problem. Therefore the sample solution will involve code, but conceptually everything remains the same.)<br /> <br /> First determine the momentum of Rock 3' plus the momentum of the 15kg chunk. <br /> ====Solution to Question 1====<br /> <source lang="python"><br /> <br /> #KNOWNS<br /> dT = .1<br /> m1i = 30 #initial mass object 1 in kg<br /> v1i = vector(13,-10,-2) #initial velocity object1 in m/s<br /> m2i = 60 #initial mass object 2 in kg<br /> v2i = vector(-3,23,3) #vinitial elocity object 2 in m/s<br /> m3i = 35 #initial mass object 3 in kg<br /> v3i = vector(0,0,0) #initial velocity object 3 in m/s<br /> <br /> </source><br /> <br /> <br /> <br /> Later Rock 3' is observed moving with velocity (x,y,z), what is the velocity of the 15kg chunk?<br /> <br /> <br /> With the information you know, determine the combined change in internal energy for all of the rocks.<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Collisions&diff=22509 Collisions 2016-04-17T21:23:12Z

<p>Swebster9: /* Difficult */</p> <hr /> <div>SECOND EDIT BY SUNGJAE HYUN IN 2016-04-16 ADDITIONS MADE BY (currently in progress, adding computational model and difficult problem) Sam Webster 4-17-16<br /> <br /> This topic covers Collisions, a comprehensive way to combine the Momentum and Energy Principles.<br /> <br /> ==The Main Idea==<br /> <br /> Collisions are special types of contact interactions between objects. From a physics standpoint, collisions are a way to combine the Momentum and Energy Principles. In the case of collisions, if we choose a system of the two objects interacting, the change in momentum of the system and the change in energy of the system are both zero. With this in mind, calculations with collisions become very simple. We are able to choose a system of only the two objects (excluding external forces such as the Earth's gravity) because the collision takes place during such a short time that the external forces have a negligible effect. <br /> There are two types of collisions, [[Elastic Collisions]] and [[Inelastic Collisions]]. <br /> <br /> ===A Mathematical Model===<br /> <math>{E}_{f} = {E}_{i}</math> where <math>{E}_{f}</math> is the total final energy of the system and <math>{E}_{i}</math> is the total initial energy of the system.<br /> <br /> <math>{p}_{f} = {p}_{i}</math> where <math>{p}_{f}</math> is the total final momentum of the system and <math>{p}_{i}</math> is the total initial momentum of the system.<br /> <br /> ===A Computational Model===<br /> The following situation was used for this model created using python:<br /> <br /> Two objects are initially moving towards a third stationary object. Object 1 (in red) at position (-10,0,-2)m has a mass of 2kg and velocity (10,0,2)m/s. Object 2 (in blue) at position (0,6,3)m has a mass of 4kg and velocity (0,-6,3)m/s. Object 3 (in orange) at the origin has a mass of 5kg. The objects collide at the origin and after the collision it is observed that object 1 has embedded in object 3 (hence it is no longer visible in the model) and the combined object moves with velocity (5,-6,0)m/s (This is an example of a [[Maximally Inelastic Collision]]). The final velocity of object 2 is calculated and used in the rest of the simulation. (NOTE: the white sphere visible after the collision represents the origin to add dimension to the model and the delay during the collision is there to emphasis when and where the collision happens. Also use the link below the model for a more detailed explanation of the calculations and concepts.).<br /> <br /> [[File: CollisionsExample.gif]]<br /> <br /> Check out the code used for the simulation at [http://www.glowscript.org/#/user/samsaxlaxman/folder/Private/]. The code is commented pretty heavily (but it does assume some knowledge of python and python animations) in hopes that future students can modify some of the variables to experiment with creating different results.<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> Example 1)<br /> A 0.5 kg soccer ball is moving with a speed of 5 m/s directly toward to 0.7 kg basket ball which is at rest.<br /> When two balls collide and stick together what will their final velocity be?<br /> <br /> ___<br /> <br /> m1 = 0.5 kg,<br /> v1 init = 5 m/s,<br /> m2 = 0.7 kg,<br /> v2 init = 0 m/s<br /> <br /> So m1 * v1 + m2 * + v2 = (m1 + m2) * vfinal<br /> <br /> LHS = 0.5 * 5 + 0.7 * 0 = 2.5 kg*m/s<br /> RHS = (0.5 + 0.7) * vfinal = 1.2 * vfinal<br /> <br /> LHS = RHS in inelastic collision <br /> <br /> 2.5 = 1.2 * vfinal<br /> <br /> vfinal = 2.5 / 1.2 = 2.08333<br /> <br /> Thus, the final velocity is 2.08 m/s. Since the two balls stick together, this is an example of a [[Maximally Inelastic Collision]].<br /> <br /> ===Middling===<br /> Example 2)<br /> A bullet of 50 caliber machine gun is 42 grams. It strikes a wooden target block of mass 10 kg stationed on a friction-less surface. The wooden block gains velocity of 1.8 m/s after being embedded with the bullet.<br /> What was the velocity of the bullet before it collided with the target?<br /> <br /> <br /> ----<br /> <br /> m1 = 42/1000 = 0.042 kg,<br /> v1 init = ?,<br /> m2 = 10 kg,<br /> v2 init = 0,<br /> mfinal(m1+m2) = 0.042kg + 10kg,<br /> vfinal = 1.8 m/s<br /> <br /> m1 * v1 init + m2 * v2 init = (m1 + m2) * vfinal<br /> <br /> 0.042 kg * v1 init = (0.042 + 10) * 1.8 m/s<br /> v1 init = 18.0756 / 0.042 = 430.37 m/s<br /> <br /> Final Answer: The bullet's speed is 430.37 m/s.<br /> <br /> ===Difficult===<br /> Example 3) Two rocks in space are approaching a third stationary rock. Rock 1 has mass 30kg moves with velocity (13,-10,-2)m/s. Rock 2 has mass 60kg and moves with velocity (-3,23,3)m/s. Rock 3 has mass 35kg and is stationary. The rocks collide at rock 3's location. After the collision it is observed that Rock 1 has embedded into Rock 3, but a chunk of mass 15kg has broken off of the combined rock, Rock 3'. It is also noticed that Rock 2 is now moving with velocity (-2,12,2)m/s. (NOTE: due to the difficulty and use of three dimensions it is suggested to use a computer to solve this problem. Therefore the sample solution will involve code, but conceptually everything remains the same.)<br /> <br /> First determine the momentum of Rock 3' plus the momentum of the 15kg chunk. <br /> ====Solution to Question 1====<br /> <source lang="python"><br /> #KNOWNS<br /> dT = .1<br /> m1i = 30 #initial mass object 1 in kg<br /> v1i = vector(13,-10,-2) #initial velocity object1 in m/s<br /> m2i = 60 #initial mass object 2 in kg<br /> v2i = vector(-3,23,3) #vinitial elocity object 2 in m/s<br /> m3i = 35 #initial mass object 3 in kg<br /> v3i = vector(0,0,0) #initial velocity object 3 in m/s<br /> </source><br /> <br /> <br /> <br /> Later Rock 3' is observed moving with velocity (x,y,z), what is the velocity of the 15kg chunk?<br /> <br /> <br /> With the information you know, determine the combined change in internal energy for all of the rocks.<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Collisions&diff=22489 Collisions 2016-04-17T21:11:12Z

<p>Swebster9: /* Difficult */</p> <hr /> <div>SECOND EDIT BY SUNGJAE HYUN IN 2016-04-16 ADDITIONS MADE BY (currently in progress, adding computational model and difficult problem) Sam Webster 4-17-16<br /> <br /> This topic covers Collisions, a comprehensive way to combine the Momentum and Energy Principles.<br /> <br /> ==The Main Idea==<br /> <br /> Collisions are special types of contact interactions between objects. From a physics standpoint, collisions are a way to combine the Momentum and Energy Principles. In the case of collisions, if we choose a system of the two objects interacting, the change in momentum of the system and the change in energy of the system are both zero. With this in mind, calculations with collisions become very simple. We are able to choose a system of only the two objects (excluding external forces such as the Earth's gravity) because the collision takes place during such a short time that the external forces have a negligible effect. <br /> There are two types of collisions, [[Elastic Collisions]] and [[Inelastic Collisions]]. <br /> <br /> ===A Mathematical Model===<br /> <math>{E}_{f} = {E}_{i}</math> where <math>{E}_{f}</math> is the total final energy of the system and <math>{E}_{i}</math> is the total initial energy of the system.<br /> <br /> <math>{p}_{f} = {p}_{i}</math> where <math>{p}_{f}</math> is the total final momentum of the system and <math>{p}_{i}</math> is the total initial momentum of the system.<br /> <br /> ===A Computational Model===<br /> The following situation was used for this model created using python:<br /> <br /> Two objects are initially moving towards a third stationary object. Object 1 (in red) at position (-10,0,-2)m has a mass of 2kg and velocity (10,0,2)m/s. Object 2 (in blue) at position (0,6,3)m has a mass of 4kg and velocity (0,-6,3)m/s. Object 3 (in orange) at the origin has a mass of 5kg. The objects collide at the origin and after the collision it is observed that object 1 has embedded in object 3 (hence it is no longer visible in the model) and the combined object moves with velocity (5,-6,0)m/s (This is an example of a [[Maximally Inelastic Collision]]). The final velocity of object 2 is calculated and used in the rest of the simulation. (NOTE: the white sphere visible after the collision represents the origin to add dimension to the model and the delay during the collision is there to emphasis when and where the collision happens. Also use the link below the model for a more detailed explanation of the calculations and concepts.).<br /> <br /> [[File: CollisionsExample.gif]]<br /> <br /> Check out the code used for the simulation at [http://www.glowscript.org/#/user/samsaxlaxman/folder/Private/]. The code is commented pretty heavily (but it does assume some knowledge of python and python animations) in hopes that future students can modify some of the variables to experiment with creating different results.<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> Example 1)<br /> A 0.5 kg soccer ball is moving with a speed of 5 m/s directly toward to 0.7 kg basket ball which is at rest.<br /> When two balls collide and stick together what will their final velocity be?<br /> <br /> ___<br /> <br /> m1 = 0.5 kg<br /> v1,init = 5 m/s<br /> m2 = 0.7 kg<br /> v2,init = 0 m/s<br /> <br /> So m1 * v1 + m2 * + v2 = (m1 + m2) * vfinal<br /> <br /> LHS = 0.5 * 5 + 0.7 * 0 = 2.5 kg*m/s<br /> RHS = (0.5 + 0.7) * vfinal = 1.2 * vfinal<br /> <br /> LHS = RHS in inelastic collision <br /> <br /> 2.5 = 1.2 * vfinal<br /> <br /> vfinal = 2.5 / 1.2 = 2.08333<br /> <br /> Thus, the final velocity is 2.08 m/s. Since the two balls stick together, this is an example of a [[Maximally Inelastic Collision]]<br /> <br /> ===Middling===<br /> Example 2)<br /> A bullet of 50 caliber machine gun is 42 grams. It strikes a wooden target block of mass 10 kg stationed on a friction-less surface. The wooden block gains velocity of 1.8 m/s after being embedded with the bullet.<br /> What was the velocity of the bullet before it collided with the target?<br /> <br /> <br /> ----<br /> <br /> m1 = 42/1000 = 0.042 kg<br /> v1,init = ?<br /> m2 = 10 kg<br /> v2,init = 0<br /> m1,2 = 0.042kg + 10kg<br /> vfinal = 1.8 m/s<br /> <br /> m1 * v1,init + m2 * v2,init = (m1 + m2) * vfinal<br /> <br /> 0.042 kg * v1,init = (0.042 + 10) * 1.8 m/s<br /> v1,init = 18.0756 / 0.042 = 430.37 m/s<br /> <br /> Final Answer: The bullet's speed is 430.37 m/s.<br /> <br /> ===Difficult===<br /> Example 3) Two rocks in space are approaching a third stationary rock. Rock 1 has mass 30kg moves with velocity (13,-10,-2)m/s. Rock 2 has mass 60kg and moves with velocity (-3,23,3)m/s. Rock 3 has mass 35kg and is stationary. The rocks collide at rock 3's location. After the collision it is observed that Rock 1 has embedded into Rock 3, but a chunk of mass 15kg has broken off of the combined rock, Rock 3'. It is also noticed that Rock 2 is now moving with velocity (-2,12,2)m/s. (NOTE: due to the difficulty and use of three dimensions it is suggested to use a computer to solve this problem. Therefore the sample solution will involve code, but conceptually everything remains the same.)<br /> <br /> First determine the momentum of Rock 3' plus the momentum of the 15kg chunk. <br /> <br /> <br /> <br /> Later Rock 3' is observed moving with velocity (x,y,z), what is the velocity of the 15kg chunk?<br /> <br /> <br /> With the information you know, determine the combined change in internal energy for all of the rocks.<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Collisions&diff=22486 Collisions 2016-04-17T21:10:30Z

<p>Swebster9: /* Difficult */</p> <hr /> <div>SECOND EDIT BY SUNGJAE HYUN IN 2016-04-16 ADDITIONS MADE BY (currently in progress, adding computational model and difficult problem) Sam Webster 4-17-16<br /> <br /> This topic covers Collisions, a comprehensive way to combine the Momentum and Energy Principles.<br /> <br /> ==The Main Idea==<br /> <br /> Collisions are special types of contact interactions between objects. From a physics standpoint, collisions are a way to combine the Momentum and Energy Principles. In the case of collisions, if we choose a system of the two objects interacting, the change in momentum of the system and the change in energy of the system are both zero. With this in mind, calculations with collisions become very simple. We are able to choose a system of only the two objects (excluding external forces such as the Earth's gravity) because the collision takes place during such a short time that the external forces have a negligible effect. <br /> There are two types of collisions, [[Elastic Collisions]] and [[Inelastic Collisions]]. <br /> <br /> ===A Mathematical Model===<br /> <math>{E}_{f} = {E}_{i}</math> where <math>{E}_{f}</math> is the total final energy of the system and <math>{E}_{i}</math> is the total initial energy of the system.<br /> <br /> <math>{p}_{f} = {p}_{i}</math> where <math>{p}_{f}</math> is the total final momentum of the system and <math>{p}_{i}</math> is the total initial momentum of the system.<br /> <br /> ===A Computational Model===<br /> The following situation was used for this model created using python:<br /> <br /> Two objects are initially moving towards a third stationary object. Object 1 (in red) at position (-10,0,-2)m has a mass of 2kg and velocity (10,0,2)m/s. Object 2 (in blue) at position (0,6,3)m has a mass of 4kg and velocity (0,-6,3)m/s. Object 3 (in orange) at the origin has a mass of 5kg. The objects collide at the origin and after the collision it is observed that object 1 has embedded in object 3 (hence it is no longer visible in the model) and the combined object moves with velocity (5,-6,0)m/s (This is an example of a [[Maximally Inelastic Collision]]). The final velocity of object 2 is calculated and used in the rest of the simulation. (NOTE: the white sphere visible after the collision represents the origin to add dimension to the model and the delay during the collision is there to emphasis when and where the collision happens. Also use the link below the model for a more detailed explanation of the calculations and concepts.).<br /> <br /> [[File: CollisionsExample.gif]]<br /> <br /> Check out the code used for the simulation at [http://www.glowscript.org/#/user/samsaxlaxman/folder/Private/]. The code is commented pretty heavily (but it does assume some knowledge of python and python animations) in hopes that future students can modify some of the variables to experiment with creating different results.<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> Example 1)<br /> A 0.5 kg soccer ball is moving with a speed of 5 m/s directly toward to 0.7 kg basket ball which is at rest.<br /> When two balls collide and stick together what will their final velocity be?<br /> <br /> ___<br /> <br /> m1 = 0.5 kg<br /> v1,init = 5 m/s<br /> m2 = 0.7 kg<br /> v2,init = 0 m/s<br /> <br /> So m1 * v1 + m2 * + v2 = (m1 + m2) * vfinal<br /> <br /> LHS = 0.5 * 5 + 0.7 * 0 = 2.5 kg*m/s<br /> RHS = (0.5 + 0.7) * vfinal = 1.2 * vfinal<br /> <br /> LHS = RHS in inelastic collision <br /> <br /> 2.5 = 1.2 * vfinal<br /> <br /> vfinal = 2.5 / 1.2 = 2.08333<br /> <br /> Thus, the final velocity is 2.08 m/s.<br /> <br /> ===Middling===<br /> Example 2)<br /> A bullet of 50 caliber machine gun is 42 grams. It strikes a wooden target block of mass 10 kg stationed on a friction-less surface. The wooden block gains velocity of 1.8 m/s after being embedded with the bullet.<br /> What was the velocity of the bullet before it collided with the target?<br /> <br /> <br /> ----<br /> <br /> m1 = 42/1000 = 0.042 kg<br /> v1,init = ?<br /> m2 = 10 kg<br /> v2,init = 0<br /> m1,2 = 0.042kg + 10kg<br /> vfinal = 1.8 m/s<br /> <br /> m1 * v1,init + m2 * v2,init = (m1 + m2) * vfinal<br /> <br /> 0.042 kg * v1,init = (0.042 + 10) * 1.8 m/s<br /> v1,init = 18.0756 / 0.042 = 430.37 m/s<br /> <br /> Final Answer: The bullet's speed is 430.37 m/s.<br /> <br /> ===Difficult===<br /> Example 3) Two rocks in space are approaching a third stationary rock. Rock 1 has mass 30kg moves with velocity (13,-10,-2)m/s. Rock 2 has mass 60kg and moves with velocity (-3,23,3)m/s. Rock 3 has mass 35kg and is stationary. The rocks collide at rock 3's location. After the collision it is observed that Rock 1 has embedded into Rock 3, but a chunk of mass 15kg has broken off of the combined rock, Rock 3'. It is also noticed that Rock 2 is now moving with velocity (-2,12,2)m/s. <br /> (NOTE: due to the difficulty and use of three dimensions it is suggested to use a computer to solve this problem. Therefore the sample solution will involve code, but conceptually everything remains the same.)<br /> First determine the momentum of Rock 3' plus the momentum of the 15kg chunk. <br /> <br /> <br /> <br /> Later Rock 3' is observed moving with velocity (x,y,z), what is the velocity of the 15kg chunk?<br /> <br /> <br /> With the information you know, determine the combined change in internal energy for all of the rocks.<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Collisions&diff=22468 Collisions 2016-04-17T21:00:01Z

<p>Swebster9: </p> <hr /> <div>SECOND EDIT BY SUNGJAE HYUN IN 2016-04-16 ADDITIONS MADE BY (currently in progress, adding computational model and difficult problem) Sam Webster 4-17-16<br /> <br /> This topic covers Collisions, a comprehensive way to combine the Momentum and Energy Principles.<br /> <br /> ==The Main Idea==<br /> <br /> Collisions are special types of contact interactions between objects. From a physics standpoint, collisions are a way to combine the Momentum and Energy Principles. In the case of collisions, if we choose a system of the two objects interacting, the change in momentum of the system and the change in energy of the system are both zero. With this in mind, calculations with collisions become very simple. We are able to choose a system of only the two objects (excluding external forces such as the Earth's gravity) because the collision takes place during such a short time that the external forces have a negligible effect. <br /> There are two types of collisions, [[Elastic Collisions]] and [[Inelastic Collisions]]. <br /> <br /> ===A Mathematical Model===<br /> <br /> What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br /> <math>{E}_{f} = {E}_{i}<math><br /> <br /> ===A Computational Model===<br /> The following situation was used for this model created using python:<br /> <br /> Two objects are initially moving towards a third stationary object. Object 1 (in red) at position (-10,0,-2)m has a mass of 2kg and velocity (10,0,2)m/s. Object 2 (in blue) at position (0,6,3)m has a mass of 4kg and velocity (0,-6,3)m/s. Object 3 (in orange) at the origin has a mass of 5kg. The objects collide at the origin and after the collision it is observed that object 1 has embedded in object 3 (hence it is no longer visible in the model) and the combined object moves with velocity (5,-6,0)m/s. The final velocity of object 2 is calculated and used in the rest of the simulation. (NOTE: the white sphere visible after the collision represents the origin to add dimension to the model and the delay during the collision is to emphasis when and where the collision happens. Also use the link below the model for a more detailed explanation of the calculations and concepts.).<br /> <br /> [[File: CollisionsExample.gif]]<br /> <br /> Check out the code used for the simulation at [http://www.glowscript.org/#/user/samsaxlaxman/folder/Private/]. The code is commented pretty heavily (but it does assume some knowledge of python and python animations) in hopes that future students can modify some of the variables to experiment with creating different results.<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> Example 1)<br /> A 0.5 kg soccer ball is moving with a speed of 5 m/s directly toward to 0.7 kg basket ball which is at rest.<br /> When two balls collide and stick together what will their final velocity be?<br /> <br /> ___<br /> <br /> m1 = 0.5 kg<br /> v1,init = 5 m/s<br /> m2 = 0.7 kg<br /> v2,init = 0 m/s<br /> <br /> So m1 * v1 + m2 * + v2 = (m1 + m2) * vfinal<br /> <br /> LHS = 0.5 * 5 + 0.7 * 0 = 2.5 kg*m/s<br /> RHS = (0.5 + 0.7) * vfinal = 1.2 * vfinal<br /> <br /> LHS = RHS in inelastic collision <br /> <br /> 2.5 = 1.2 * vfinal<br /> <br /> vfinal = 2.5 / 1.2 = 2.08333<br /> <br /> Thus, the final velocity is 2.08 m/s.<br /> <br /> ===Middling===<br /> Example 2)<br /> A bullet of 50 caliber machine gun is 42 grams. It strikes a wooden target block of mass 10 kg stationed on a friction-less surface. The wooden block gains velocity of 1.8 m/s after being embedded with the bullet.<br /> What was the velocity of the bullet before it collided with the target?<br /> <br /> <br /> ----<br /> <br /> m1 = 42/1000 = 0.042 kg<br /> v1,init = ?<br /> m2 = 10 kg<br /> v2,init = 0<br /> m1,2 = 0.042kg + 10kg<br /> vfinal = 1.8 m/s<br /> <br /> m1 * v1,init + m2 * v2,init = (m1 + m2) * vfinal<br /> <br /> 0.042 kg * v1,init = (0.042 + 10) * 1.8 m/s<br /> v1,init = 18.0756 / 0.042 = 430.37 m/s<br /> <br /> Final Answer: The bullet's speed is 430.37 m/s.<br /> <br /> ===Difficult===<br /> Example 3) Two rocks in space are approaching a third stationary rock. Rock 1 has mass 30kg moves with velocity (13,-10,-2)m/s. Rock 2 has mass 60kg and moves with velocity (-3,23,3)m/s. Rock 3 has mass 35kg and is stationary. The rocks collide at rock 3's location. After the collision it is observed that Rock 1 has embedded into Rock 3, but a chunk of mass 15kg has broken off of the combined rock, Rock 3'. It is also noticed that Rock 2 is now moving with velocity (-2,12,2)m/s. <br /> <br /> First determine the momentum of Rock 3' plus the momentum of the 15kg chunk. <br /> <br /> <br /> <br /> Later Rock 3' is observed moving with velocity (x,y,z), what is the velocity of the 15kg chunk?<br /> <br /> <br /> With the information you know, determine the combined change in internal energy for all of the rocks.<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Collisions&diff=22466 Collisions 2016-04-17T20:57:47Z

<p>Swebster9: /* A Computational Model */</p> <hr /> <div>SECOND EDIT BY SUNGJAE HYUN IN 2016-04-16 ADDITIONS MADE BY (currently in progress, adding computational model and difficult problem) Sam Webster 4-17-16<br /> <br /> This topic covers Collisions, a comprehensive way to combine the Momentum and Energy Principles.<br /> <br /> ==The Main Idea==<br /> <br /> Collisions are special types of contact interactions between objects. From a physics standpoint, collisions are a way to combine the Momentum and Energy Principles. In the case of collisions, if we choose a system of the two objects interacting, the change in momentum of the system and the change in energy of the system are both zero. With this in mind, calculations with collisions become very simple. We are able to choose a system of only the two objects (excluding external forces such as the Earth's gravity) because the collision takes place during such a short time that the external forces have a negligible effect. <br /> There are two types of collisions, [[Elastic Collisions]] and [[Inelastic Collisions]]. <br /> <br /> ===A Mathematical Model===<br /> <br /> What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br /> <math>{E}_{f} = {E}_{i}<br /> <br /> ===A Computational Model===<br /> The following situation was used for this model created using python:<br /> <br /> Two objects are initially moving towards a third stationary object. Object 1 (in red) at position (-10,0,-2)m has a mass of 2kg and velocity (10,0,2)m/s. Object 2 (in blue) at position (0,6,3)m has a mass of 4kg and velocity (0,-6,3)m/s. Object 3 (in orange) at the origin has a mass of 5kg. The objects collide at the origin and after the collision it is observed that object 1 has embedded in object 3 (hence it is no longer visible in the model) and the combined object moves with velocity (5,-6,0)m/s. The final velocity of object 2 is calculated and used in the rest of the simulation. (NOTE: the white sphere visible after the collision represents the origin to add dimension to the model and the delay during the collision is to emphasis when and where the collision happens. Also use the link below the model for a more detailed explanation of the calculations and concepts.).<br /> <br /> [[File: CollisionsExample.gif]]<br /> <br /> Check out the code used for the simulation at [http://www.glowscript.org/#/user/samsaxlaxman/folder/Private/]. The code is commented pretty heavily (but it does assume some knowledge of python and python animations) in hopes that future students can modify some of the variables to experiment with creating different results.<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> Example 1)<br /> A 0.5 kg soccer ball is moving with a speed of 5 m/s directly toward to 0.7 kg basket ball which is at rest.<br /> When two balls collide and stick together what will their final velocity be?<br /> <br /> ___<br /> <br /> m1 = 0.5 kg<br /> v1,init = 5 m/s<br /> m2 = 0.7 kg<br /> v2,init = 0 m/s<br /> <br /> So m1 * v1 + m2 * + v2 = (m1 + m2) * vfinal<br /> <br /> LHS = 0.5 * 5 + 0.7 * 0 = 2.5 kg*m/s<br /> RHS = (0.5 + 0.7) * vfinal = 1.2 * vfinal<br /> <br /> LHS = RHS in inelastic collision <br /> <br /> 2.5 = 1.2 * vfinal<br /> <br /> vfinal = 2.5 / 1.2 = 2.08333<br /> <br /> Thus, the final velocity is 2.08 m/s.<br /> <br /> ===Middling===<br /> Example 2)<br /> A bullet of 50 caliber machine gun is 42 grams. It strikes a wooden target block of mass 10 kg stationed on a friction-less surface. The wooden block gains velocity of 1.8 m/s after being embedded with the bullet.<br /> What was the velocity of the bullet before it collided with the target?<br /> <br /> <br /> ----<br /> <br /> m1 = 42/1000 = 0.042 kg<br /> v1,init = ?<br /> m2 = 10 kg<br /> v2,init = 0<br /> m1,2 = 0.042kg + 10kg<br /> vfinal = 1.8 m/s<br /> <br /> m1 * v1,init + m2 * v2,init = (m1 + m2) * vfinal<br /> <br /> 0.042 kg * v1,init = (0.042 + 10) * 1.8 m/s<br /> v1,init = 18.0756 / 0.042 = 430.37 m/s<br /> <br /> Final Answer: The bullet's speed is 430.37 m/s.<br /> <br /> ===Difficult===<br /> Example 3) Two rocks in space are approaching a third stationary rock. Rock 1 has mass 30kg moves with velocity (13,-10,-2)m/s. Rock 2 has mass 60kg and moves with velocity (-3,23,3)m/s. Rock 3 has mass 35kg and is stationary. The rocks collide at rock 3's location. After the collision it is observed that Rock 1 has embedded into Rock 3, but a chunk of mass 15kg has broken off of the combined rock, Rock 3'. It is also noticed that Rock 2 is now moving with velocity (-2,12,2)m/s. <br /> <br /> First determine the momentum of Rock 3' plus the momentum of the 15kg chunk. <br /> <br /> <br /> <br /> Later Rock 3' is observed moving with velocity (x,y,z), what is the velocity of the 15kg chunk?<br /> <br /> <br /> With the information you know, determine the combined change in internal energy for all of the rocks.<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Collisions&diff=22456 Collisions 2016-04-17T20:51:19Z

<p>Swebster9: /* Simple */</p> <hr /> <div>SECOND EDIT BY SUNGJAE HYUN IN 2016-04-16 ADDITIONS MADE BY (currently in progress, adding computational model and difficult problem) Sam Webster 4-17-16<br /> <br /> This topic covers Collisions, a comprehensive way to combine the Momentum and Energy Principles.<br /> <br /> ==The Main Idea==<br /> <br /> Collisions are special types of contact interactions between objects. From a physics standpoint, collisions are a way to combine the Momentum and Energy Principles. In the case of collisions, if we choose a system of the two objects interacting, the change in momentum of the system and the change in energy of the system are both zero. With this in mind, calculations with collisions become very simple.<br /> There are two types of collisions, [[Elastic Collisions]] and [[Inelastic Collisions]]. <br /> <br /> ===A Mathematical Model===<br /> <br /> What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br /> <br /> ===A Computational Model===<br /> The following situation was used for this model created using python:<br /> <br /> Two objects are initially moving towards a third stationary object. Object 1 (in red) at position (-10,0,-2)m has a mass of 2kg and velocity (10,0,2)m/s. Object 2 (in blue) at position (0,6,3)m has a mass of 4kg and velocity (0,-6,3)m/s. Object 3 (in orange) at the origin has a mass of 5kg. The objects collide at the origin and after the collision it is observed that object 1 has embedded in object 3 (hence it is no longer visible in the model) and the combined object moves with velocity (5,-6,0)m/s. The final velocity of object 2 is calculated and used in the rest of the simulation. (NOTE: the white sphere visible after the collision represents the origin to add dimension to the model. Also use the link below the model for a more detailed explanation of the calculations and concepts).<br /> <br /> [[File: CollisionsExample.gif]]<br /> <br /> Check out the code used for the simulation at [http://www.glowscript.org/#/user/samsaxlaxman/folder/Private/]. The code is commented pretty heavily (but it does assume some knowledge of python and python animations) in hopes that future students can modify some of the variables to experiment with creating different results.<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> Example 1)<br /> A 0.5 kg soccer ball is moving with a speed of 5 m/s directly toward to 0.7 kg basket ball which is at rest.<br /> When two balls collide and stick together what will their final velocity be?<br /> <br /> ___<br /> <br /> m1 = 0.5 kg<br /> v1,init = 5 m/s<br /> m2 = 0.7 kg<br /> v2,init = 0 m/s<br /> <br /> So m1 * v1 + m2 * + v2 = (m1 + m2) * vfinal<br /> <br /> LHS = 0.5 * 5 + 0.7 * 0 = 2.5 kg*m/s<br /> RHS = (0.5 + 0.7) * vfinal = 1.2 * vfinal<br /> <br /> LHS = RHS in inelastic collision <br /> <br /> 2.5 = 1.2 * vfinal<br /> <br /> vfinal = 2.5 / 1.2 = 2.08333<br /> <br /> Thus, the final velocity is 2.08 m/s.<br /> <br /> ===Middling===<br /> Example 2)<br /> A bullet of 50 caliber machine gun is 42 grams. It strikes a wooden target block of mass 10 kg stationed on a friction-less surface. The wooden block gains velocity of 1.8 m/s after being embedded with the bullet.<br /> What was the velocity of the bullet before it collided with the target?<br /> <br /> <br /> ----<br /> <br /> m1 = 42/1000 = 0.042 kg<br /> v1,init = ?<br /> m2 = 10 kg<br /> v2,init = 0<br /> m1,2 = 0.042kg + 10kg<br /> vfinal = 1.8 m/s<br /> <br /> m1 * v1,init + m2 * v2,init = (m1 + m2) * vfinal<br /> <br /> 0.042 kg * v1,init = (0.042 + 10) * 1.8 m/s<br /> v1,init = 18.0756 / 0.042 = 430.37 m/s<br /> <br /> Final Answer: The bullet's speed is 430.37 m/s.<br /> <br /> ===Difficult===<br /> Example 3) Two rocks in space are approaching a third stationary rock. Rock 1 has mass 30kg moves with velocity (13,-10,-2)m/s. Rock 2 has mass 60kg and moves with velocity (-3,23,3)m/s. Rock 3 has mass 35kg and is stationary. The rocks collide at rock 3's location. After the collision it is observed that Rock 1 has embedded into Rock 3, but a chunk of mass 15kg has broken off of the combined rock, Rock 3'. It is also noticed that Rock 2 is now moving with velocity (-2,12,2)m/s. <br /> <br /> First determine the momentum of Rock 3' plus the momentum of the 15kg chunk. <br /> <br /> <br /> <br /> Later Rock 3' is observed moving with velocity (x,y,z), what is the velocity of the 15kg chunk?<br /> <br /> <br /> With the information you know, determine the combined change in internal energy for all of the rocks.<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Collisions&diff=22455 Collisions 2016-04-17T20:50:51Z

<p>Swebster9: /* Difficult */</p> <hr /> <div>SECOND EDIT BY SUNGJAE HYUN IN 2016-04-16 ADDITIONS MADE BY (currently in progress, adding computational model and difficult problem) Sam Webster 4-17-16<br /> <br /> This topic covers Collisions, a comprehensive way to combine the Momentum and Energy Principles.<br /> <br /> ==The Main Idea==<br /> <br /> Collisions are special types of contact interactions between objects. From a physics standpoint, collisions are a way to combine the Momentum and Energy Principles. In the case of collisions, if we choose a system of the two objects interacting, the change in momentum of the system and the change in energy of the system are both zero. With this in mind, calculations with collisions become very simple.<br /> There are two types of collisions, [[Elastic Collisions]] and [[Inelastic Collisions]]. <br /> <br /> ===A Mathematical Model===<br /> <br /> What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br /> <br /> ===A Computational Model===<br /> The following situation was used for this model created using python:<br /> <br /> Two objects are initially moving towards a third stationary object. Object 1 (in red) at position (-10,0,-2)m has a mass of 2kg and velocity (10,0,2)m/s. Object 2 (in blue) at position (0,6,3)m has a mass of 4kg and velocity (0,-6,3)m/s. Object 3 (in orange) at the origin has a mass of 5kg. The objects collide at the origin and after the collision it is observed that object 1 has embedded in object 3 (hence it is no longer visible in the model) and the combined object moves with velocity (5,-6,0)m/s. The final velocity of object 2 is calculated and used in the rest of the simulation. (NOTE: the white sphere visible after the collision represents the origin to add dimension to the model. Also use the link below the model for a more detailed explanation of the calculations and concepts).<br /> <br /> [[File: CollisionsExample.gif]]<br /> <br /> Check out the code used for the simulation at [http://www.glowscript.org/#/user/samsaxlaxman/folder/Private/]. The code is commented pretty heavily (but it does assume some knowledge of python and python animations) in hopes that future students can modify some of the variables to experiment with creating different results.<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> Example 1)<br /> A 0.5 kg soccer ball is moving with a speed of 5 m/s directly toward to 0.7 kg basket ball which is at rest.<br /> When two balls collide and sticks together what will their final velocity be?<br /> <br /> ___<br /> <br /> m1 = 0.5 kg<br /> v1,init = 5 m/s<br /> m2 = 0.7 kg<br /> v2,init = 0 m/s<br /> <br /> So m1 * v1 + m2 * + v2 = (m1 + m2) * vfinal<br /> <br /> LHS = 0.5 * 5 + 0.7 * 0 = 2.5 kg*m/s<br /> RHS = (0.5 + 0.7) * vfinal = 1.2 * vfinal<br /> <br /> LHS = RHS in inelastic collision <br /> <br /> 2.5 = 1.2 * vfinal<br /> <br /> vfinal = 2.5 / 1.2 = 2.08333<br /> <br /> Thus, the final velocity is 2.08 m/s.<br /> <br /> ===Middling===<br /> Example 2)<br /> A bullet of 50 caliber machine gun is 42 grams. It strikes a wooden target block of mass 10 kg stationed on a friction-less surface. The wooden block gains velocity of 1.8 m/s after being embedded with the bullet.<br /> What was the velocity of the bullet before it collided with the target?<br /> <br /> <br /> ----<br /> <br /> m1 = 42/1000 = 0.042 kg<br /> v1,init = ?<br /> m2 = 10 kg<br /> v2,init = 0<br /> m1,2 = 0.042kg + 10kg<br /> vfinal = 1.8 m/s<br /> <br /> m1 * v1,init + m2 * v2,init = (m1 + m2) * vfinal<br /> <br /> 0.042 kg * v1,init = (0.042 + 10) * 1.8 m/s<br /> v1,init = 18.0756 / 0.042 = 430.37 m/s<br /> <br /> Final Answer: The bullet's speed is 430.37 m/s.<br /> <br /> ===Difficult===<br /> Example 3) Two rocks in space are approaching a third stationary rock. Rock 1 has mass 30kg moves with velocity (13,-10,-2)m/s. Rock 2 has mass 60kg and moves with velocity (-3,23,3)m/s. Rock 3 has mass 35kg and is stationary. The rocks collide at rock 3's location. After the collision it is observed that Rock 1 has embedded into Rock 3, but a chunk of mass 15kg has broken off of the combined rock, Rock 3'. It is also noticed that Rock 2 is now moving with velocity (-2,12,2)m/s. <br /> <br /> First determine the momentum of Rock 3' plus the momentum of the 15kg chunk. <br /> <br /> <br /> <br /> Later Rock 3' is observed moving with velocity (x,y,z), what is the velocity of the 15kg chunk?<br /> <br /> <br /> With the information you know, determine the combined change in internal energy for all of the rocks.<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Collisions&diff=22447 Collisions 2016-04-17T20:34:11Z

<p>Swebster9: /* Difficult */</p> <hr /> <div>SECOND EDIT BY SUNGJAE HYUN IN 2016-04-16 ADDITIONS MADE BY (currently in progress, adding computational model and difficult problem) Sam Webster 4-17-16<br /> <br /> This topic covers Collisions, a comprehensive way to combine the Momentum and Energy Principles.<br /> <br /> ==The Main Idea==<br /> <br /> Collisions are special types of contact interactions between objects. From a physics standpoint, collisions are a way to combine the Momentum and Energy Principles. In the case of collisions, if we choose a system of the two objects interacting, the change in momentum of the system and the change in energy of the system are both zero. With this in mind, calculations with collisions become very simple.<br /> There are two types of collisions, [[Elastic Collisions]] and [[Inelastic Collisions]]. <br /> <br /> ===A Mathematical Model===<br /> <br /> What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br /> <br /> ===A Computational Model===<br /> The following situation was used for this model created using python:<br /> <br /> Two objects are initially moving towards a third stationary object. Object 1 (in red) at position (-10,0,-2)m has a mass of 2kg and velocity (10,0,2)m/s. Object 2 (in blue) at position (0,6,3)m has a mass of 4kg and velocity (0,-6,3)m/s. Object 3 (in orange) at the origin has a mass of 5kg. The objects collide at the origin and after the collision it is observed that object 1 has embedded in object 3 (hence it is no longer visible in the model) and the combined object moves with velocity (5,-6,0)m/s. The final velocity of object 2 is calculated and used in the rest of the simulation. (NOTE: the white sphere visible after the collision represents the origin to add dimension to the model. Also use the link below the model for a more detailed explanation of the calculations and concepts).<br /> <br /> [[File: CollisionsExample.gif]]<br /> <br /> Check out the code used for the simulation at [http://www.glowscript.org/#/user/samsaxlaxman/folder/Private/]. The code is commented pretty heavily (but it does assume some knowledge of python and python animations) in hopes that future students can modify some of the variables to experiment with creating different results.<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> Example 1)<br /> A 0.5 kg soccer ball is moving with a speed of 5 m/s directly toward to 0.7 kg basket ball which is at rest.<br /> When two balls collide and sticks together what will their final velocity be?<br /> <br /> ___<br /> <br /> m1 = 0.5 kg<br /> v1,init = 5 m/s<br /> m2 = 0.7 kg<br /> v2,init = 0 m/s<br /> <br /> So m1 * v1 + m2 * + v2 = (m1 + m2) * vfinal<br /> <br /> LHS = 0.5 * 5 + 0.7 * 0 = 2.5 kg*m/s<br /> RHS = (0.5 + 0.7) * vfinal = 1.2 * vfinal<br /> <br /> LHS = RHS in inelastic collision <br /> <br /> 2.5 = 1.2 * vfinal<br /> <br /> vfinal = 2.5 / 1.2 = 2.08333<br /> <br /> Thus, the final velocity is 2.08 m/s.<br /> <br /> ===Middling===<br /> Example 2)<br /> A bullet of 50 caliber machine gun is 42 grams. It strikes a wooden target block of mass 10 kg stationed on a friction-less surface. The wooden block gains velocity of 1.8 m/s after being embedded with the bullet.<br /> What was the velocity of the bullet before it collided with the target?<br /> <br /> <br /> ----<br /> <br /> m1 = 42/1000 = 0.042 kg<br /> v1,init = ?<br /> m2 = 10 kg<br /> v2,init = 0<br /> m1,2 = 0.042kg + 10kg<br /> vfinal = 1.8 m/s<br /> <br /> m1 * v1,init + m2 * v2,init = (m1 + m2) * vfinal<br /> <br /> 0.042 kg * v1,init = (0.042 + 10) * 1.8 m/s<br /> v1,init = 18.0756 / 0.042 = 430.37 m/s<br /> <br /> Final Answer: The bullet's speed is 430.37 m/s.<br /> <br /> ===Difficult===<br /> Example 3)<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Collisions&diff=22443 Collisions 2016-04-17T20:20:35Z

<p>Swebster9: /* A Computational Model */</p> <hr /> <div>SECOND EDIT BY SUNGJAE HYUN IN 2016-04-16 ADDITIONS MADE BY (currently in progress, adding computational model and difficult problem) Sam Webster 4-17-16<br /> <br /> This topic covers Collisions, a comprehensive way to combine the Momentum and Energy Principles.<br /> <br /> ==The Main Idea==<br /> <br /> Collisions are special types of contact interactions between objects. From a physics standpoint, collisions are a way to combine the Momentum and Energy Principles. In the case of collisions, if we choose a system of the two objects interacting, the change in momentum of the system and the change in energy of the system are both zero. With this in mind, calculations with collisions become very simple.<br /> There are two types of collisions, [[Elastic Collisions]] and [[Inelastic Collisions]]. <br /> <br /> ===A Mathematical Model===<br /> <br /> What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br /> <br /> ===A Computational Model===<br /> The following situation was used for this model created using python:<br /> <br /> Two objects are initially moving towards a third stationary object. Object 1 (in red) at position (-10,0,-2)m has a mass of 2kg and velocity (10,0,2)m/s. Object 2 (in blue) at position (0,6,3)m has a mass of 4kg and velocity (0,-6,3)m/s. Object 3 (in orange) at the origin has a mass of 5kg. The objects collide at the origin and after the collision it is observed that object 1 has embedded in object 3 (hence it is no longer visible in the model) and the combined object moves with velocity (5,-6,0)m/s. The final velocity of object 2 is calculated and used in the rest of the simulation. (NOTE: the white sphere visible after the collision represents the origin to add dimension to the model. Also use the link below the model for a more detailed explanation of the calculations and concepts).<br /> <br /> [[File: CollisionsExample.gif]]<br /> <br /> Check out the code used for the simulation at [http://www.glowscript.org/#/user/samsaxlaxman/folder/Private/]. The code is commented pretty heavily (but it does assume some knowledge of python and python animations) in hopes that future students can modify some of the variables to experiment with creating different results.<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> Example 1)<br /> A 0.5 kg soccer ball is moving with a speed of 5 m/s directly toward to 0.7 kg basket ball which is at rest.<br /> When two balls collide and sticks together what will their final velocity be?<br /> <br /> ___<br /> <br /> m1 = 0.5 kg<br /> v1,init = 5 m/s<br /> m2 = 0.7 kg<br /> v2,init = 0 m/s<br /> <br /> So m1 * v1 + m2 * + v2 = (m1 + m2) * vfinal<br /> <br /> LHS = 0.5 * 5 + 0.7 * 0 = 2.5 kg*m/s<br /> RHS = (0.5 + 0.7) * vfinal = 1.2 * vfinal<br /> <br /> LHS = RHS in inelastic collision <br /> <br /> 2.5 = 1.2 * vfinal<br /> <br /> vfinal = 2.5 / 1.2 = 2.08333<br /> <br /> Thus, the final velocity is 2.08 m/s.<br /> <br /> ===Middling===<br /> Example 2)<br /> A bullet of 50 caliber machine gun is 42 grams. It strikes a wooden target block of mass 10 kg stationed on a friction-less surface. The wooden block gains velocity of 1.8 m/s after being embedded with the bullet.<br /> What was the velocity of the bullet before it collided with the target?<br /> <br /> <br /> ----<br /> <br /> m1 = 42/1000 = 0.042 kg<br /> v1,init = ?<br /> m2 = 10 kg<br /> v2,init = 0<br /> m1,2 = 0.042kg + 10kg<br /> vfinal = 1.8 m/s<br /> <br /> m1 * v1,init + m2 * v2,init = (m1 + m2) * vfinal<br /> <br /> 0.042 kg * v1,init = (0.042 + 10) * 1.8 m/s<br /> v1,init = 18.0756 / 0.042 = 430.37 m/s<br /> <br /> Final Answer: The bullet's speed is 430.37 m/s.<br /> <br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Collisions&diff=22441 Collisions 2016-04-17T20:19:06Z

<p>Swebster9: /* A Computational Model */</p> <hr /> <div>SECOND EDIT BY SUNGJAE HYUN IN 2016-04-16 ADDITIONS MADE BY (currently in progress, adding computational model and difficult problem) Sam Webster 4-17-16<br /> <br /> This topic covers Collisions, a comprehensive way to combine the Momentum and Energy Principles.<br /> <br /> ==The Main Idea==<br /> <br /> Collisions are special types of contact interactions between objects. From a physics standpoint, collisions are a way to combine the Momentum and Energy Principles. In the case of collisions, if we choose a system of the two objects interacting, the change in momentum of the system and the change in energy of the system are both zero. With this in mind, calculations with collisions become very simple.<br /> There are two types of collisions, [[Elastic Collisions]] and [[Inelastic Collisions]]. <br /> <br /> ===A Mathematical Model===<br /> <br /> What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br /> <br /> ===A Computational Model===<br /> The following situation was used for this model created using python:<br /> <br /> Two objects are initially moving towards a third stationary object. Object 1 (in red) at position (-10,0,-2)m has a mass of 2kg and velocity (10,0,2)m/s. Object 2 (in blue) at position (0,6,3)m has a mass of 4kg and velocity (0,-6,3)m/s. Object 3 (in orange) at the origin has a mass of 5kg. The objects collide at the origin and after the collision it is observed that object 1 has embedded in object 3 (hence it is no longer visible in the model) and the combined object moves with velocity (5,-6,0)m/s. The final velocity of object 2 is calculated and used in the rest of the simulation. (NOTE: the white sphere visible after the collision represents the origin to add dimension to the model.)<br /> <br /> [[File: CollisionsExample.gif]]<br /> <br /> Check out the code used for the simulation at [http://www.glowscript.org/#/user/samsaxlaxman/folder/Private/]. The code is commented pretty heavily (but it does assume some knowledge of python and python animations) in hopes that future students can modify some of the variables to experiment with creating different results.<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> Example 1)<br /> A 0.5 kg soccer ball is moving with a speed of 5 m/s directly toward to 0.7 kg basket ball which is at rest.<br /> When two balls collide and sticks together what will their final velocity be?<br /> <br /> ___<br /> <br /> m1 = 0.5 kg<br /> v1,init = 5 m/s<br /> m2 = 0.7 kg<br /> v2,init = 0 m/s<br /> <br /> So m1 * v1 + m2 * + v2 = (m1 + m2) * vfinal<br /> <br /> LHS = 0.5 * 5 + 0.7 * 0 = 2.5 kg*m/s<br /> RHS = (0.5 + 0.7) * vfinal = 1.2 * vfinal<br /> <br /> LHS = RHS in inelastic collision <br /> <br /> 2.5 = 1.2 * vfinal<br /> <br /> vfinal = 2.5 / 1.2 = 2.08333<br /> <br /> Thus, the final velocity is 2.08 m/s.<br /> <br /> ===Middling===<br /> Example 2)<br /> A bullet of 50 caliber machine gun is 42 grams. It strikes a wooden target block of mass 10 kg stationed on a friction-less surface. The wooden block gains velocity of 1.8 m/s after being embedded with the bullet.<br /> What was the velocity of the bullet before it collided with the target?<br /> <br /> <br /> ----<br /> <br /> m1 = 42/1000 = 0.042 kg<br /> v1,init = ?<br /> m2 = 10 kg<br /> v2,init = 0<br /> m1,2 = 0.042kg + 10kg<br /> vfinal = 1.8 m/s<br /> <br /> m1 * v1,init + m2 * v2,init = (m1 + m2) * vfinal<br /> <br /> 0.042 kg * v1,init = (0.042 + 10) * 1.8 m/s<br /> v1,init = 18.0756 / 0.042 = 430.37 m/s<br /> <br /> Final Answer: The bullet's speed is 430.37 m/s.<br /> <br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Collisions&diff=22439 Collisions 2016-04-17T20:18:13Z

<p>Swebster9: /* A Computational Model */</p> <hr /> <div>SECOND EDIT BY SUNGJAE HYUN IN 2016-04-16 ADDITIONS MADE BY (currently in progress, adding computational model and difficult problem) Sam Webster 4-17-16<br /> <br /> This topic covers Collisions, a comprehensive way to combine the Momentum and Energy Principles.<br /> <br /> ==The Main Idea==<br /> <br /> Collisions are special types of contact interactions between objects. From a physics standpoint, collisions are a way to combine the Momentum and Energy Principles. In the case of collisions, if we choose a system of the two objects interacting, the change in momentum of the system and the change in energy of the system are both zero. With this in mind, calculations with collisions become very simple.<br /> There are two types of collisions, [[Elastic Collisions]] and [[Inelastic Collisions]]. <br /> <br /> ===A Mathematical Model===<br /> <br /> What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br /> <br /> ===A Computational Model===<br /> The following situation was used for this model created using python:<br /> Two objects are initially moving towards a third stationary object. Object 1 (in red) at position (-10,0,-2)m has a mass of 2kg and velocity (10,0,2)m/s. Object 2 (in blue) at position (0,6,3)m has a mass of 4kg and velocity (0,-6,3)m/s. Object 3 (in orange) at the origin has a mass of 5kg. The objects collide at the origin and after the collision it is observed that object 1 has embedded in object 3 (hence it is no longer visible in the model) and the combined object moves with velocity (5,-6,0)m/s. The final velocity of object 2 is calculated and used in the rest of the simulation. (NOTE: the white sphere visible after the collision represents the origin to add dimension to the model.)<br /> <br /> [[File: CollisionsExample.gif]]<br /> <br /> Check out the code used for the simulation at [http://www.glowscript.org/#/user/samsaxlaxman/folder/Private/]. The code is commented pretty heavily (but it does assume some knowledge of python and python animations) in hopes that future students can modify some of the variables to experiment with creating different results.<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> Example 1)<br /> A 0.5 kg soccer ball is moving with a speed of 5 m/s directly toward to 0.7 kg basket ball which is at rest.<br /> When two balls collide and sticks together what will their final velocity be?<br /> <br /> ___<br /> <br /> m1 = 0.5 kg<br /> v1,init = 5 m/s<br /> m2 = 0.7 kg<br /> v2,init = 0 m/s<br /> <br /> So m1 * v1 + m2 * + v2 = (m1 + m2) * vfinal<br /> <br /> LHS = 0.5 * 5 + 0.7 * 0 = 2.5 kg*m/s<br /> RHS = (0.5 + 0.7) * vfinal = 1.2 * vfinal<br /> <br /> LHS = RHS in inelastic collision <br /> <br /> 2.5 = 1.2 * vfinal<br /> <br /> vfinal = 2.5 / 1.2 = 2.08333<br /> <br /> Thus, the final velocity is 2.08 m/s.<br /> <br /> ===Middling===<br /> Example 2)<br /> A bullet of 50 caliber machine gun is 42 grams. It strikes a wooden target block of mass 10 kg stationed on a friction-less surface. The wooden block gains velocity of 1.8 m/s after being embedded with the bullet.<br /> What was the velocity of the bullet before it collided with the target?<br /> <br /> <br /> ----<br /> <br /> m1 = 42/1000 = 0.042 kg<br /> v1,init = ?<br /> m2 = 10 kg<br /> v2,init = 0<br /> m1,2 = 0.042kg + 10kg<br /> vfinal = 1.8 m/s<br /> <br /> m1 * v1,init + m2 * v2,init = (m1 + m2) * vfinal<br /> <br /> 0.042 kg * v1,init = (0.042 + 10) * 1.8 m/s<br /> v1,init = 18.0756 / 0.042 = 430.37 m/s<br /> <br /> Final Answer: The bullet's speed is 430.37 m/s.<br /> <br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Collisions&diff=22438 Collisions 2016-04-17T20:17:50Z

<p>Swebster9: </p> <hr /> <div>SECOND EDIT BY SUNGJAE HYUN IN 2016-04-16 ADDITIONS MADE BY (currently in progress, adding computational model and difficult problem) Sam Webster 4-17-16<br /> <br /> This topic covers Collisions, a comprehensive way to combine the Momentum and Energy Principles.<br /> <br /> ==The Main Idea==<br /> <br /> Collisions are special types of contact interactions between objects. From a physics standpoint, collisions are a way to combine the Momentum and Energy Principles. In the case of collisions, if we choose a system of the two objects interacting, the change in momentum of the system and the change in energy of the system are both zero. With this in mind, calculations with collisions become very simple.<br /> There are two types of collisions, [[Elastic Collisions]] and [[Inelastic Collisions]]. <br /> <br /> ===A Mathematical Model===<br /> <br /> What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br /> <br /> ===A Computational Model===<br /> The following situation was used for this model created using python:<br /> Two objects are initially moving towards a third stationary object. Object 1 (in red) at position (-10,0,-2)m has a mass of 2kg and velocity (10,0,2)m/s. Object 2 (in blue) at position (0,6,3)m has a mass of 4kg and velocity (0,-6,3)m/s. Object 3 (in orange) at the origin has a mass of 5kg. The objects collide at the origin and after the collision it is observed that object 1 has embedded in object 3 (hence it is no longer visible in the model) and the combined object moves with velocity (5,-6,0)m/s. The final velocity of object 2 is calculated and used in the rest of the simulation. (NOTE: the white sphere visible after the collision represents the origin to add dimension to the model.)<br /> [[File: CollisionsExample.gif]]<br /> Check out the code used for the simulation at [http://www.glowscript.org/#/user/samsaxlaxman/folder/Private/]. The code is commented pretty heavily (but it does assume some knowledge of python and python animations) in hopes that future students can modify some of the variables to experiment with creating different results. <br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> Example 1)<br /> A 0.5 kg soccer ball is moving with a speed of 5 m/s directly toward to 0.7 kg basket ball which is at rest.<br /> When two balls collide and sticks together what will their final velocity be?<br /> <br /> ___<br /> <br /> m1 = 0.5 kg<br /> v1,init = 5 m/s<br /> m2 = 0.7 kg<br /> v2,init = 0 m/s<br /> <br /> So m1 * v1 + m2 * + v2 = (m1 + m2) * vfinal<br /> <br /> LHS = 0.5 * 5 + 0.7 * 0 = 2.5 kg*m/s<br /> RHS = (0.5 + 0.7) * vfinal = 1.2 * vfinal<br /> <br /> LHS = RHS in inelastic collision <br /> <br /> 2.5 = 1.2 * vfinal<br /> <br /> vfinal = 2.5 / 1.2 = 2.08333<br /> <br /> Thus, the final velocity is 2.08 m/s.<br /> <br /> ===Middling===<br /> Example 2)<br /> A bullet of 50 caliber machine gun is 42 grams. It strikes a wooden target block of mass 10 kg stationed on a friction-less surface. The wooden block gains velocity of 1.8 m/s after being embedded with the bullet.<br /> What was the velocity of the bullet before it collided with the target?<br /> <br /> <br /> ----<br /> <br /> m1 = 42/1000 = 0.042 kg<br /> v1,init = ?<br /> m2 = 10 kg<br /> v2,init = 0<br /> m1,2 = 0.042kg + 10kg<br /> vfinal = 1.8 m/s<br /> <br /> m1 * v1,init + m2 * v2,init = (m1 + m2) * vfinal<br /> <br /> 0.042 kg * v1,init = (0.042 + 10) * 1.8 m/s<br /> v1,init = 18.0756 / 0.042 = 430.37 m/s<br /> <br /> Final Answer: The bullet's speed is 430.37 m/s.<br /> <br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Collisions&diff=22424 Collisions 2016-04-17T19:56:48Z

<p>Swebster9: </p> <hr /> <div>SECOND EDIT BY SUNGJAE HYUN IN 2016-04-16 ADDITIONS MADE BY (currently in progress, adding computational model and difficult problem) Sam Webster 4-17-16<br /> <br /> This topic covers Collisions, a comprehensive way to combine the Momentum and Energy Principles.<br /> <br /> ==The Main Idea==<br /> <br /> Collisions are special types of contact interactions between objects. From a physics standpoint, collisions are a way to combine the Momentum and Energy Principles. In the case of collisions, if we choose a system of the two objects interacting, the change in momentum of the system and the change in energy of the system are both zero. With this in mind, calculations with collisions become very simple.<br /> There are two types of collisions, [[Elastic Collisions]] and [[Inelastic Collisions]]. <br /> <br /> ===A Mathematical Model===<br /> <br /> What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br /> <br /> ===A Computational Model===<br /> <br /> <br /> [[File: CollisionsExample.gif]]<br /> Check out the code used for the simulation at [http://www.glowscript.org/#/user/samsaxlaxman/folder/Private/]. The code is commented pretty heavily (but it does assume some knowledge of python and python animations) in hopes that future students can modify some of the variables to experiment with creating different results. <br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> Example 1)<br /> A 0.5 kg soccer ball is moving with a speed of 5 m/s directly toward to 0.7 kg basket ball which is at rest.<br /> When two balls collide and sticks together what will their final velocity be?<br /> <br /> ___<br /> <br /> m1 = 0.5 kg<br /> v1,init = 5 m/s<br /> m2 = 0.7 kg<br /> v2,init = 0 m/s<br /> <br /> So m1 * v1 + m2 * + v2 = (m1 + m2) * vfinal<br /> <br /> LHS = 0.5 * 5 + 0.7 * 0 = 2.5 kg*m/s<br /> RHS = (0.5 + 0.7) * vfinal = 1.2 * vfinal<br /> <br /> LHS = RHS in inelastic collision <br /> <br /> 2.5 = 1.2 * vfinal<br /> <br /> vfinal = 2.5 / 1.2 = 2.08333<br /> <br /> Thus, the final velocity is 2.08 m/s.<br /> <br /> ===Middling===<br /> Example 2)<br /> A bullet of 50 caliber machine gun is 42 grams. It strikes a wooden target block of mass 10 kg stationed on a friction-less surface. The wooden block gains velocity of 1.8 m/s after being embedded with the bullet.<br /> What was the velocity of the bullet before it collided with the target?<br /> <br /> <br /> ----<br /> <br /> m1 = 42/1000 = 0.042 kg<br /> v1,init = ?<br /> m2 = 10 kg<br /> v2,init = 0<br /> m1,2 = 0.042kg + 10kg<br /> vfinal = 1.8 m/s<br /> <br /> m1 * v1,init + m2 * v2,init = (m1 + m2) * vfinal<br /> <br /> 0.042 kg * v1,init = (0.042 + 10) * 1.8 m/s<br /> v1,init = 18.0756 / 0.042 = 430.37 m/s<br /> <br /> Final Answer: The bullet's speed is 430.37 m/s.<br /> <br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Collisions&diff=22410 Collisions 2016-04-17T19:51:40Z

<p>Swebster9: </p> <hr /> <div>SECOND EDIT BY SUNGJAE HYUN IN 2016-04-16 ADDITIONS MADE BY (currently in progress, adding computational model and difficult problem) Sam Webster 4-17-16<br /> <br /> This topic covers Collisions, a comprehensive way to combine the Momentum and Energy Principles.<br /> <br /> ==The Main Idea==<br /> <br /> Collisions are special types of contact interactions between objects. From a physics standpoint, collisions are a way to combine the Momentum and Energy Principles. In the case of collisions, if we choose a system of the two objects interacting, the change in momentum of the system and the change in energy of the system are both zero. With this in mind, calculations with collisions become very simple.<br /> There are two types of collisions, [[Elastic Collisions]] and [[Inelastic Collisions]]. <br /> <br /> ===A Mathematical Model===<br /> <br /> What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br /> <br /> ===A Computational Model===<br /> <br /> <div id="glowscript" class="glowscript"><br /> <link type="text/css" href="http://www.glowscript.org/css/redmond/2.1/jquery-ui.custom.css" rel="stylesheet" /><br /> <link href="http://fonts.googleapis.com/css?family=Inconsolata" rel="stylesheet" type="text/css"><br /> <link type="text/css" href="http://www.glowscript.org/css/ide.css" rel="stylesheet" /><br /> <script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS_HTML"></script><br /> <script type="text/javascript" src="http://www.glowscript.org/lib/jquery/2.1/jquery.min.js"></script><br /> <script type="text/javascript" src="http://www.glowscript.org/lib/jquery/2.1/jquery-ui.custom.min.js"></script><br /> <script type="text/javascript" src="http://www.glowscript.org/package/glow.2.1.min.js"></script><br /> <script type="text/javascript" src="http://www.glowscript.org/package/RSrun.2.1.min.js"></script><br /> <script type="text/javascript"><br /> ;(function() { var __rt=srequire('streamline/lib/callbacks/runtime').runtime(__filename, false),__func=__rt.__func,__cb=__rt.__cb; function _$rapyd$_print() {<br /> var args, output;<br /> args = [].slice.call(arguments, 0);<br /> output = JSON.stringify(args);<br /> if (("console" in window)) { console.log(output.substr(1, output.length["-"](2))); };};<br /> <br /> function main(wait) { var version, box, sphere, cylinder, pyramid, cone, helix, ellipsoid, ring, arrow, graph, display, vector, _$GS_$END, scene, _$rapyd$_Temp, _$rapyd$_print, arange, dT, m1i, v1i, m2i, v2i, m3i, v3i, o1, o2, o3, origin, totalP, totalPX, totalPY, totalPZ, m, m1f, v1f, m2f, m3f, v3f, pOf1and3, t; var __frame = { name: "main", line: 7 }; return __func(wait, this, arguments, main, 0, __frame, function __$main() {<br /> <br /> version = ["2.1","glowscript",];<br /> Array.prototype["+"] = function(r) { return this.concat(r); };<br /> window.__GSlang = "vpython";<br /> box = vp_box;<br /> sphere = vp_sphere;<br /> cylinder = vp_cylinder;<br /> pyramid = vp_pyramid;<br /> cone = vp_cone;<br /> helix = vp_helix;<br /> ellipsoid = vp_ellipsoid;<br /> ring = vp_ring;<br /> arrow = vp_arrow;<br /> graph = vp_graph;<br /> display = canvas;<br /> vector = vec;<br /> _$GS_$END = 0;<br /> scene = canvas();<br /> _$rapyd$_Temp = 0;<br /> _$rapyd$_print = GSprint;<br /> arange = range;<br /> "6";<br /> scene.width = 1024;<br /> "7";<br /> scene.height = 760;<br /> "8";<br /> scene.background = color.black;<br /> "12";<br /> dT = 0.1;<br /> "13";<br /> m1i = 2;<br /> "14";<br /> v1i = vector(10, 0, 2);<br /> "15";<br /> m2i = 4;<br /> "16";<br /> v2i = vector(0, 6["-u"](), 3);<br /> "17";<br /> m3i = 5;<br /> "18";<br /> v3i = vector(0, 0, 0);<br /> "22";<br /> o1 = sphere({ pos: vector(10["-u"](), 0, 2["-u"]()), radius: 0.5, color: color.red });<br /> "23";<br /> o1.v = v1i;<br /> "24";<br /> o1.m = m1i;<br /> "25";<br /> o1.p = o1.v["*"](o1.m);<br /> "26";<br /> o2 = sphere({ pos: vector(0, 6, 3), radius: 0.5, color: color.blue });<br /> "27";<br /> o2.v = v2i;<br /> "28";<br /> o2.m = m2i;<br /> "29";<br /> o2.p = o2.v["*"](o2.m);<br /> "30";<br /> o3 = sphere({ pos: vector(0, 0, 0), radius: 0.5, color: color.orange });<br /> "31";<br /> o3.v = v3i;<br /> "32";<br /> o3.m = m3i;<br /> "33";<br /> o3.p = o3.m["*"](o3.v);<br /> "35";<br /> origin = sphere({ pos: vector(0, 0, 0), radius: 0.1, color: color.white });<br /> "39";<br /> totalP = o1.p["+"](o2.p)["+"](o3.p);<br /> "40";<br /> totalPX = totalP.x;<br /> "41";<br /> totalPY = totalP.y;<br /> "42";<br /> totalPZ = totalP.z;<br /> "43";<br /> _$rapyd$_print("The total momentum vector is initially,", totalP);<br /> "44";<br /> _$rapyd$_print("This is calculated by adding the x, y, and z components of each");<br /> "45";<br /> _$rapyd$_print("objects individual momentum, calculated using P = M*V");<br /> "46";<br /> _$rapyd$_print("Take note of the x, y, and z values of this total for later");<br /> "48";<br /> m = 0;<br /> "49"; return (function ___(__break) { var __more; var __loop = __cb(wait, __frame, 0, 0, function __$main() { __more = false;<br /> var __1 = (m < 15.9); if (__1) {<br /> "50";<br /> return rate(10, __cb(wait, __frame, 89, 8, function __$main() {<br /> "51";<br /> m = m["+"](0.1); while (__more) { __loop(); }; __more = true; }, true)); } else { __break(); } ; }); do { __loop(); } while (__more); __more = true; })(function __$main() {<br /> <br /> "53";<br /> t = 0;<br /> "55"; return (function ___(__break) { var __more; var __loop = __cb(wait, __frame, 0, 0, function __$main() { __more = false;<br /> var __3 = (t < 0.9); if (__3) {<br /> "56";<br /> return rate(10, __cb(wait, __frame, 98, 8, function __$main() {<br /> "57";<br /> o1.pos = o1.pos["+"](o1.v["*"](dT));<br /> "58";<br /> o2.pos = o2.pos["+"](o2.v["*"](dT));<br /> "59";<br /> o3.pos = o3.pos["+"](o3.v["*"](dT));<br /> "60";<br /> t = t["+"](dT); while (__more) { __loop(); }; __more = true; }, true)); } else { __break(); } ; }); do { __loop(); } while (__more); __more = true; })(function __$main() {<br /> <br /> "61";<br /> _$rapyd$_print("The Collision Happens");<br /> "63";<br /> m = 0;<br /> "64"; return (function ___(__break) { var __more; var __loop = __cb(wait, __frame, 0, 0, function __$main() { __more = false;<br /> var __5 = (m < 1.9); if (__5) {<br /> "65";<br /> return rate(10, __cb(wait, __frame, 115, 8, function __$main() {<br /> "66";<br /> m = m["+"](0.1); while (__more) { __loop(); }; __more = true; }, true)); } else { __break(); } ; }); do { __loop(); } while (__more); __more = true; })(function __$main() {<br /> <br /> "71";<br /> m1f = 2;<br /> "72";<br /> v1f = vector(5, 6["-u"](), 0);<br /> "73";<br /> m2f = 4;<br /> "75";<br /> m3f = 5;<br /> "76";<br /> v3f = v1f;<br /> "79";<br /> o1.v = v1f;<br /> "80";<br /> o3.v = v3f;<br /> "85";<br /> pOf1and3 = v1f["*"](m1f["+"](m2f));<br /> "92";<br /> o2.p = totalP["-"](pOf1and3);<br /> "95";<br /> o2.v = o2.p["/"](m2f);<br /> "98"; return (function ___(__break) { var __more; var __loop = __cb(wait, __frame, 0, 0, function __$main() { __more = false;<br /> var __7 = (t < 4); if (__7) {<br /> "99";<br /> return rate(10, __cb(wait, __frame, 142, 8, function __$main() {<br /> "100";<br /> o1.pos = o1.pos["+"](o1.v["*"](dT));<br /> "101";<br /> o2.pos = o2.pos["+"](o2.v["*"](dT));<br /> "102";<br /> o3.pos = o3.pos["+"](o3.v["*"](dT));<br /> "103";<br /> t = t["+"](dT); while (__more) { __loop(); }; __more = true; }, true)); } else { __break(); } ; }); do { __loop(); } while (__more); __more = true; })(function __$main() {<br /> <br /> "105";<br /> _$rapyd$_print("It is observed that object 1 embeds in in object 3, therefore");<br /> "106";<br /> _$rapyd$_print("they move together after the collision. They both move with a");<br /> "107";<br /> _$rapyd$_print("velocity of ", o1.v, " and their momentum can be calculated as one");<br /> "108";<br /> _$rapyd$_print("object with m = m1 + m2. Knowing this we can calculating the velocity");<br /> "109";<br /> _$rapyd$_print("of object 2 to be,", o2.v, " using the momentum principle because");<br /> "110";<br /> _$rapyd$_print("the final total momentum of the system equals the initial total");<br /> "111";<br /> _$rapyd$_print("momentum", totalP, ". Notice that this is the same in every demension");<br /> "112";<br /> _$rapyd$_print("x, y, and z. This is different than having the same magnitude of final");<br /> "113";<br /> _$rapyd$_print("momentum with different x, y and z components.");<br /> "114";<br /> _$rapyd$_print("Feel free to try changing the initial and final values in the code to");<br /> "115";<br /> _$rapyd$_print("produce different results using the momentum principle"); wait(); }); }); }); }); });};<br /> <br /> main;<br /> <br /> ;$(function(){ window.__context = { glowscript_container: $("#glowscript").removeAttr("id") }; main(__func) })})()<br /> </script><br /> </div><br /> [[File: CollisionsExample.gif]]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> Example 1)<br /> A 0.5 kg soccer ball is moving with a speed of 5 m/s directly toward to 0.7 kg basket ball which is at rest.<br /> When two balls collide and sticks together what will their final velocity be?<br /> <br /> ___<br /> <br /> m1 = 0.5 kg<br /> v1,init = 5 m/s<br /> m2 = 0.7 kg<br /> v2,init = 0 m/s<br /> <br /> So m1 * v1 + m2 * + v2 = (m1 + m2) * vfinal<br /> <br /> LHS = 0.5 * 5 + 0.7 * 0 = 2.5 kg*m/s<br /> RHS = (0.5 + 0.7) * vfinal = 1.2 * vfinal<br /> <br /> LHS = RHS in inelastic collision <br /> <br /> 2.5 = 1.2 * vfinal<br /> <br /> vfinal = 2.5 / 1.2 = 2.08333<br /> <br /> Thus, the final velocity is 2.08 m/s.<br /> <br /> ===Middling===<br /> Example 2)<br /> A bullet of 50 caliber machine gun is 42 grams. It strikes a wooden target block of mass 10 kg stationed on a friction-less surface. The wooden block gains velocity of 1.8 m/s after being embedded with the bullet.<br /> What was the velocity of the bullet before it collided with the target?<br /> <br /> <br /> ----<br /> <br /> m1 = 42/1000 = 0.042 kg<br /> v1,init = ?<br /> m2 = 10 kg<br /> v2,init = 0<br /> m1,2 = 0.042kg + 10kg<br /> vfinal = 1.8 m/s<br /> <br /> m1 * v1,init + m2 * v2,init = (m1 + m2) * vfinal<br /> <br /> 0.042 kg * v1,init = (0.042 + 10) * 1.8 m/s<br /> v1,init = 18.0756 / 0.042 = 430.37 m/s<br /> <br /> Final Answer: The bullet's speed is 430.37 m/s.<br /> <br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Collisions&diff=22406 Collisions 2016-04-17T19:49:40Z

<p>Swebster9: </p> <hr /> <div>SECOND EDIT BY SUNGJAE HYUN IN 2016-04-16 ADDITIONS MADE BY (currently in progress, adding computational model and difficult problem) Sam Webster 4-17-16<br /> <br /> This topic covers Collisions, a comprehensive way to combine the Momentum and Energy Principles.<br /> <br /> ==The Main Idea==<br /> <br /> Collisions are special types of contact interactions between objects. From a physics standpoint, collisions are a way to combine the Momentum and Energy Principles. In the case of collisions, if we choose a system of the two objects interacting, the change in momentum of the system and the change in energy of the system are both zero. With this in mind, calculations with collisions become very simple.<br /> There are two types of collisions, [[Elastic Collisions]] and [[Inelastic Collisions]]. <br /> <br /> ===A Mathematical Model===<br /> <br /> What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<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 /> [[File: CollisionsExample.gif]]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> Example 1)<br /> A 0.5 kg soccer ball is moving with a speed of 5 m/s directly toward to 0.7 kg basket ball which is at rest.<br /> When two balls collide and sticks together what will their final velocity be?<br /> <br /> ___<br /> <br /> m1 = 0.5 kg<br /> v1,init = 5 m/s<br /> m2 = 0.7 kg<br /> v2,init = 0 m/s<br /> <br /> So m1 * v1 + m2 * + v2 = (m1 + m2) * vfinal<br /> <br /> LHS = 0.5 * 5 + 0.7 * 0 = 2.5 kg*m/s<br /> RHS = (0.5 + 0.7) * vfinal = 1.2 * vfinal<br /> <br /> LHS = RHS in inelastic collision <br /> <br /> 2.5 = 1.2 * vfinal<br /> <br /> vfinal = 2.5 / 1.2 = 2.08333<br /> <br /> Thus, the final velocity is 2.08 m/s.<br /> <br /> ===Middling===<br /> Example 2)<br /> A bullet of 50 caliber machine gun is 42 grams. It strikes a wooden target block of mass 10 kg stationed on a friction-less surface. The wooden block gains velocity of 1.8 m/s after being embedded with the bullet.<br /> What was the velocity of the bullet before it collided with the target?<br /> <br /> <br /> ----<br /> <br /> m1 = 42/1000 = 0.042 kg<br /> v1,init = ?<br /> m2 = 10 kg<br /> v2,init = 0<br /> m1,2 = 0.042kg + 10kg<br /> vfinal = 1.8 m/s<br /> <br /> m1 * v1,init + m2 * v2,init = (m1 + m2) * vfinal<br /> <br /> 0.042 kg * v1,init = (0.042 + 10) * 1.8 m/s<br /> v1,init = 18.0756 / 0.042 = 430.37 m/s<br /> <br /> Final Answer: The bullet's speed is 430.37 m/s.<br /> <br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=File:CollisionsExample.gif&diff=22404 File:CollisionsExample.gif 2016-04-17T19:48:16Z

<p>Swebster9: </p> <hr /> <div></div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Collisions&diff=22401 Collisions 2016-04-17T19:47:35Z

<p>Swebster9: </p> <hr /> <div>SECOND EDIT BY SUNGJAE HYUN IN 2016-04-16 ADDITIONS MADE BY (currently in progress, adding computational model and difficult problem) Sam Webster 4-17-16<br /> <br /> This topic covers Collisions, a comprehensive way to combine the Momentum and Energy Principles.<br /> <br /> ==The Main Idea==<br /> <br /> Collisions are special types of contact interactions between objects. From a physics standpoint, collisions are a way to combine the Momentum and Energy Principles. In the case of collisions, if we choose a system of the two objects interacting, the change in momentum of the system and the change in energy of the system are both zero. With this in mind, calculations with collisions become very simple.<br /> There are two types of collisions, [[Elastic Collisions]] and [[Inelastic Collisions]]. <br /> <br /> ===A Mathematical Model===<br /> <br /> What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<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 /> [[File: CollisionsExample]]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> Example 1)<br /> A 0.5 kg soccer ball is moving with a speed of 5 m/s directly toward to 0.7 kg basket ball which is at rest.<br /> When two balls collide and sticks together what will their final velocity be?<br /> <br /> ___<br /> <br /> m1 = 0.5 kg<br /> v1,init = 5 m/s<br /> m2 = 0.7 kg<br /> v2,init = 0 m/s<br /> <br /> So m1 * v1 + m2 * + v2 = (m1 + m2) * vfinal<br /> <br /> LHS = 0.5 * 5 + 0.7 * 0 = 2.5 kg*m/s<br /> RHS = (0.5 + 0.7) * vfinal = 1.2 * vfinal<br /> <br /> LHS = RHS in inelastic collision <br /> <br /> 2.5 = 1.2 * vfinal<br /> <br /> vfinal = 2.5 / 1.2 = 2.08333<br /> <br /> Thus, the final velocity is 2.08 m/s.<br /> <br /> ===Middling===<br /> Example 2)<br /> A bullet of 50 caliber machine gun is 42 grams. It strikes a wooden target block of mass 10 kg stationed on a friction-less surface. The wooden block gains velocity of 1.8 m/s after being embedded with the bullet.<br /> What was the velocity of the bullet before it collided with the target?<br /> <br /> <br /> ----<br /> <br /> m1 = 42/1000 = 0.042 kg<br /> v1,init = ?<br /> m2 = 10 kg<br /> v2,init = 0<br /> m1,2 = 0.042kg + 10kg<br /> vfinal = 1.8 m/s<br /> <br /> m1 * v1,init + m2 * v2,init = (m1 + m2) * vfinal<br /> <br /> 0.042 kg * v1,init = (0.042 + 10) * 1.8 m/s<br /> v1,init = 18.0756 / 0.042 = 430.37 m/s<br /> <br /> Final Answer: The bullet's speed is 430.37 m/s.<br /> <br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Collisions&diff=22385 Collisions 2016-04-17T19:33:52Z

<p>Swebster9: </p> <hr /> <div>SECOND EDIT BY SUNGJAE HYUN IN 2016-04-16 ADDITIONS MADE BY (currently in progress, adding computational model and difficult problem) Sam Webster 4-17-16<br /> <br /> This topic covers Collisions, a comprehensive way to combine the Momentum and Energy Principles.<br /> <br /> ==The Main Idea==<br /> <br /> Collisions are special types of contact interactions between objects. From a physics standpoint, collisions are a way to combine the Momentum and Energy Principles. In the case of collisions, if we choose a system of the two objects interacting, the change in momentum of the system and the change in energy of the system are both zero. With this in mind, calculations with collisions become very simple.<br /> There are two types of collisions, [[Elastic Collisions]] and [[Inelastic Collisions]]. <br /> <br /> ===A Mathematical Model===<br /> <br /> What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<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 /> [[File: CollisionsExample.py]]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> Example 1)<br /> A 0.5 kg soccer ball is moving with a speed of 5 m/s directly toward to 0.7 kg basket ball which is at rest.<br /> When two balls collide and sticks together what will their final velocity be?<br /> <br /> ___<br /> <br /> m1 = 0.5 kg<br /> v1,init = 5 m/s<br /> m2 = 0.7 kg<br /> v2,init = 0 m/s<br /> <br /> So m1 * v1 + m2 * + v2 = (m1 + m2) * vfinal<br /> <br /> LHS = 0.5 * 5 + 0.7 * 0 = 2.5 kg*m/s<br /> RHS = (0.5 + 0.7) * vfinal = 1.2 * vfinal<br /> <br /> LHS = RHS in inelastic collision <br /> <br /> 2.5 = 1.2 * vfinal<br /> <br /> vfinal = 2.5 / 1.2 = 2.08333<br /> <br /> Thus, the final velocity is 2.08 m/s.<br /> <br /> ===Middling===<br /> Example 2)<br /> A bullet of 50 caliber machine gun is 42 grams. It strikes a wooden target block of mass 10 kg stationed on a friction-less surface. The wooden block gains velocity of 1.8 m/s after being embedded with the bullet.<br /> What was the velocity of the bullet before it collided with the target?<br /> <br /> <br /> ----<br /> <br /> m1 = 42/1000 = 0.042 kg<br /> v1,init = ?<br /> m2 = 10 kg<br /> v2,init = 0<br /> m1,2 = 0.042kg + 10kg<br /> vfinal = 1.8 m/s<br /> <br /> m1 * v1,init + m2 * v2,init = (m1 + m2) * vfinal<br /> <br /> 0.042 kg * v1,init = (0.042 + 10) * 1.8 m/s<br /> v1,init = 18.0756 / 0.042 = 430.37 m/s<br /> <br /> Final Answer: The bullet's speed is 430.37 m/s.<br /> <br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Collisions&diff=22382 Collisions 2016-04-17T19:32:31Z

<p>Swebster9: </p> <hr /> <div>SECOND EDIT BY SUNGJAE HYUN IN 2016-04-16 ADDITIONS MADE BY (currently in progress, adding computational model and difficult problem) Sam Webster 4-17-16<br /> <br /> This topic covers Collisions, a comprehensive way to combine the Momentum and Energy Principles.<br /> <br /> ==The Main Idea==<br /> <br /> Collisions are special types of contact interactions between objects. From a physics standpoint, collisions are a way to combine the Momentum and Energy Principles. In the case of collisions, if we choose a system of the two objects interacting, the change in momentum of the system and the change in energy of the system are both zero. With this in mind, calculations with collisions become very simple.<br /> There are two types of collisions, [[Elastic Collisions]] and [[Inelastic Collisions]]. <br /> <br /> ===A Mathematical Model===<br /> <br /> What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<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 /> [File: CollisionsExample.py]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> Example 1)<br /> A 0.5 kg soccer ball is moving with a speed of 5 m/s directly toward to 0.7 kg basket ball which is at rest.<br /> When two balls collide and sticks together what will their final velocity be?<br /> <br /> ___<br /> <br /> m1 = 0.5 kg<br /> v1,init = 5 m/s<br /> m2 = 0.7 kg<br /> v2,init = 0 m/s<br /> <br /> So m1 * v1 + m2 * + v2 = (m1 + m2) * vfinal<br /> <br /> LHS = 0.5 * 5 + 0.7 * 0 = 2.5 kg*m/s<br /> RHS = (0.5 + 0.7) * vfinal = 1.2 * vfinal<br /> <br /> LHS = RHS in inelastic collision <br /> <br /> 2.5 = 1.2 * vfinal<br /> <br /> vfinal = 2.5 / 1.2 = 2.08333<br /> <br /> Thus, the final velocity is 2.08 m/s.<br /> <br /> ===Middling===<br /> Example 2)<br /> A bullet of 50 caliber machine gun is 42 grams. It strikes a wooden target block of mass 10 kg stationed on a friction-less surface. The wooden block gains velocity of 1.8 m/s after being embedded with the bullet.<br /> What was the velocity of the bullet before it collided with the target?<br /> <br /> <br /> ----<br /> <br /> m1 = 42/1000 = 0.042 kg<br /> v1,init = ?<br /> m2 = 10 kg<br /> v2,init = 0<br /> m1,2 = 0.042kg + 10kg<br /> vfinal = 1.8 m/s<br /> <br /> m1 * v1,init + m2 * v2,init = (m1 + m2) * vfinal<br /> <br /> 0.042 kg * v1,init = (0.042 + 10) * 1.8 m/s<br /> v1,init = 18.0756 / 0.042 = 430.37 m/s<br /> <br /> Final Answer: The bullet's speed is 430.37 m/s.<br /> <br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Collisions&diff=22223 Collisions 2016-04-17T17:37:24Z

<p>Swebster9: </p> <hr /> <div>'''CLAIMED BY MEGAN STEVENS'''<br /> SECOND EDIT BY SUNGJAE HYUN IN 2016-04-16 ADDITIONS MADE BY (currently in progress, adding computational model and difficult problem) Sam Webster 4-17-16<br /> <br /> This topic covers Collisions, a comprehensive way to combine the Momentum and Energy Principles.<br /> <br /> ==The Main Idea==<br /> <br /> Collisions are special types of contact interactions between objects. From a physics standpoint, collisions are a way to combine the Momentum and Energy Principles. In the case of collisions, if we choose a system of the two objects interacting, the change in momentum of the system and the change in energy of the system are both zero. With this in mind, calculations with collisions become very simple.<br /> There are two types of collisions, [[Elastic Collisions]] and [[Inelastic Collisions]]. <br /> <br /> ===A Mathematical Model===<br /> <br /> What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<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 /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> Example 1)<br /> A 0.5 kg soccer ball is moving with a speed of 5 m/s directly toward to 0.7 kg basket ball which is at rest.<br /> When two balls collide and sticks together what will their final velocity be?<br /> <br /> ___<br /> <br /> m1 = 0.5 kg<br /> v1,init = 5 m/s<br /> m2 = 0.7 kg<br /> v2,init = 0 m/s<br /> <br /> So m1 * v1 + m2 * + v2 = (m1 + m2) * vfinal<br /> <br /> LHS = 0.5 * 5 + 0.7 * 0 = 2.5 kg*m/s<br /> RHS = (0.5 + 0.7) * vfinal = 1.2 * vfinal<br /> <br /> LHS = RHS in inelastic collision <br /> <br /> 2.5 = 1.2 * vfinal<br /> <br /> vfinal = 2.5 / 1.2 = 2.08333<br /> <br /> Thus, the final velocity is 2.08 m/s.<br /> <br /> ===Middling===<br /> Example 2)<br /> A bullet of 50 caliber machine gun is 42 grams. It strikes a wooden target block of mass 10 kg stationed on a friction-less surface. The wooden block gains velocity of 1.8 m/s after being embedded with the bullet.<br /> What was the velocity of the bullet before it collided with the target?<br /> <br /> <br /> ----<br /> <br /> m1 = 42/1000 = 0.042 kg<br /> v1,init = ?<br /> m2 = 10 kg<br /> v2,init = 0<br /> m1,2 = 0.042kg + 10kg<br /> vfinal = 1.8 m/s<br /> <br /> m1 * v1,init + m2 * v2,init = (m1 + m2) * vfinal<br /> <br /> 0.042 kg * v1,init = (0.042 + 10) * 1.8 m/s<br /> v1,init = 18.0756 / 0.042 = 430.37 m/s<br /> <br /> Final Answer: The bullet's speed is 430.37 m/s.<br /> <br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Collisions&diff=22222 Collisions 2016-04-17T17:36:14Z

<p>Swebster9: </p> <hr /> <div>'''CLAIMED BY MEGAN STEVENS'''<br /> SECOND EDIT BY SUNGJAE HYUN IN 2016-04-16 ADDITIONS MADE BY Sam Webster 4-17-16<br /> <br /> This topic covers Collisions, a comprehensive way to combine the Momentum and Energy Principles.<br /> <br /> ==The Main Idea==<br /> <br /> Collisions are special types of contact interactions between objects. From a physics standpoint, collisions are a way to combine the Momentum and Energy Principles. In the case of collisions, if we choose a system of the two objects interacting, the change in momentum of the system and the change in energy of the system are both zero. With this in mind, calculations with collisions become very simple.<br /> There are two types of collisions, [[Elastic Collisions]] and [[Inelastic Collisions]]. <br /> <br /> ===A Mathematical Model===<br /> <br /> What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<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 /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> Example 1)<br /> A 0.5 kg soccer ball is moving with a speed of 5 m/s directly toward to 0.7 kg basket ball which is at rest.<br /> When two balls collide and sticks together what will their final velocity be?<br /> <br /> ___<br /> <br /> m1 = 0.5 kg<br /> v1,init = 5 m/s<br /> m2 = 0.7 kg<br /> v2,init = 0 m/s<br /> <br /> So m1 * v1 + m2 * + v2 = (m1 + m2) * vfinal<br /> <br /> LHS = 0.5 * 5 + 0.7 * 0 = 2.5 kg*m/s<br /> RHS = (0.5 + 0.7) * vfinal = 1.2 * vfinal<br /> <br /> LHS = RHS in inelastic collision <br /> <br /> 2.5 = 1.2 * vfinal<br /> <br /> vfinal = 2.5 / 1.2 = 2.08333<br /> <br /> Thus, the final velocity is 2.08 m/s.<br /> <br /> ===Middling===<br /> Example 2)<br /> A bullet of 50 caliber machine gun is 42 grams. It strikes a wooden target block of mass 10 kg stationed on a friction-less surface. The wooden block gains velocity of 1.8 m/s after being embedded with the bullet.<br /> What was the velocity of the bullet before it collided with the target?<br /> <br /> <br /> ----<br /> <br /> m1 = 42/1000 = 0.042 kg<br /> v1,init = ?<br /> m2 = 10 kg<br /> v2,init = 0<br /> m1,2 = 0.042kg + 10kg<br /> vfinal = 1.8 m/s<br /> <br /> m1 * v1,init + m2 * v2,init = (m1 + m2) * vfinal<br /> <br /> 0.042 kg * v1,init = (0.042 + 10) * 1.8 m/s<br /> v1,init = 18.0756 / 0.042 = 430.37 m/s<br /> <br /> Final Answer: The bullet's speed is 430.37 m/s.<br /> <br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Scattering:_Collisions_in_2D_and_3D&diff=22221 Scattering: Collisions in 2D and 3D 2016-04-17T17:33:44Z

<p>Swebster9: </p> <hr /> <div>Claimed by: Andreas Ward (Fall 2015)<br /> <br /> ==The Main Idea==<br /> <br /> Unlike normal collisions, atomic and nuclear collisions are far too small to observe the curving trajectories of the interacting particles. The only thing that can be noticed is the initial and final states of the interaction. Scattering experiments are incorporated in the world of collisions to be able to study the minute details (structure) of atoms, nuclei, and other tiny particles as the interact with one another. <br /> <br /> ==Impact Parameters==<br /> Definition: The distance between centers perpendicular to the incoming velocity. Impact parameter is often denoted by the variable b. <br /> <br /> A head-on collision has an impact parameter of zero and with equal masses fully transfers the momentum such as with Newton's Cradle. As the impact parameter gets smaller the collision has a larger effect, and an even large deflection angle (scattering).<br /> <br /> Elastic collisions between two billiard balls (Double Click Image)<br /> [[File:ImpactParameter.png]]<br /> <br /> ==Examples==<br /> ===Simple===<br /> The collision of an alpha particle (helium nucleus) with the nucleus of a gold atom<br /> <br /> ==History==<br /> <br /> In 1871 Lord Rayleigh published a paper on scattering. Rayleigh scattering is the dispersion of electromagnetic radiation by particles that have a minute radius less than approximately 1/10 the wavelength. It laid the foundation to research on scattering and information we have today. <br /> <br /> == See also ==<br /> <br /> [[Category:Collisions] (Main page)<br /> <br /> ===Further reading===<br /> <br /> Matter and Interactions, Volume I: Modern Mechanics, 4th Edition. (Chapter 10.6)<br /> <br /> ===External links===<br /> [http://physics-animations.com/Physics/English/par_txt.htm]<br /> [http://www.britannica.com/science/Rayleigh-scattering]<br /> [http://hypernews.slac.stanford.edu/slacsite/aux/HiPPP/scattering/]<br /> <br /> ==References==<br /> <br /> Chabay, Ruth W., Bruce Sherwood. Matter and Interactions, Volume I: Modern Mechanics, 4th Edition. Wiley, 19/2014.<br /> <br /> [[Category:Collisions]]</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Scattering:_Collisions_in_2D_and_3D&diff=22219 Scattering: Collisions in 2D and 3D 2016-04-17T17:27:24Z

<p>Swebster9: /* Impact Parameters */</p> <hr /> <div>Claimed by: Andreas Ward (Fall 2015) and Sam Webster (Spring 2016)<br /> <br /> ==The Main Idea==<br /> <br /> Unlike normal collisions, atomic and nuclear collisions are far too small to observe the curving trajectories of the interacting particles. The only thing that can be noticed is the initial and final states of the interaction. Scattering experiments are incorporated in the world of collisions to be able to study the minute details (structure) of atoms, nuclei, and other tiny particles as the interact with one another. <br /> <br /> ==Impact Parameters==<br /> Definition: The distance between centers perpendicular to the incoming velocity. Impact parameter is often denoted by the variable b. <br /> <br /> A head-on collision has an impact parameter of zero and with equal masses fully transfers the momentum such as with Newton's Cradle. As the impact parameter gets smaller the collision has a larger effect, and an even large deflection angle (scattering).<br /> <br /> Elastic collisions between two billiard balls (Double Click Image)<br /> [[File:ImpactParameter.png]]<br /> <br /> ==Examples==<br /> ===Simple===<br /> The collision of an alpha particle (helium nucleus) with the nucleus of a gold atom<br /> ===Simulation in Python===<br /> Coming Soon<br /> <br /> ==History==<br /> <br /> In 1871 Lord Rayleigh published a paper on scattering. Rayleigh scattering is the dispersion of electromagnetic radiation by particles that have a minute radius less than approximately 1/10 the wavelength. It laid the foundation to research on scattering and information we have today. <br /> <br /> == See also ==<br /> <br /> [[Category:Collisions] (Main page)<br /> <br /> ===Further reading===<br /> <br /> Matter and Interactions, Volume I: Modern Mechanics, 4th Edition. (Chapter 10.6)<br /> <br /> ===External links===<br /> [http://physics-animations.com/Physics/English/par_txt.htm]<br /> [http://www.britannica.com/science/Rayleigh-scattering]<br /> [http://hypernews.slac.stanford.edu/slacsite/aux/HiPPP/scattering/]<br /> <br /> ==References==<br /> <br /> Chabay, Ruth W., Bruce Sherwood. Matter and Interactions, Volume I: Modern Mechanics, 4th Edition. Wiley, 19/2014.<br /> <br /> [[Category:Collisions]]</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Scattering:_Collisions_in_2D_and_3D&diff=22218 Scattering: Collisions in 2D and 3D 2016-04-17T17:26:57Z

<p>Swebster9: /* Impact Parameters */</p> <hr /> <div>Claimed by: Andreas Ward (Fall 2015) and Sam Webster (Spring 2016)<br /> <br /> ==The Main Idea==<br /> <br /> Unlike normal collisions, atomic and nuclear collisions are far too small to observe the curving trajectories of the interacting particles. The only thing that can be noticed is the initial and final states of the interaction. Scattering experiments are incorporated in the world of collisions to be able to study the minute details (structure) of atoms, nuclei, and other tiny particles as the interact with one another. <br /> <br /> ==Impact Parameters==<br /> Definition: The distance between centers perpendicular to the incoming velocity. Impact parameter is often denoted by the variable b. <br /> <br /> As the impact parameter A head-on collision has an impact parameter of zero and with equal masses fully transfers the momentum such as with Newton's Cradle. As the impact parameter gets smaller the collision has a larger effect, and an even large deflection angle (scattering).<br /> <br /> Elastic collisions between two billiard balls (Double Click Image)<br /> [[File:ImpactParameter.png]]<br /> <br /> ==Examples==<br /> ===Simple===<br /> The collision of an alpha particle (helium nucleus) with the nucleus of a gold atom<br /> ===Simulation in Python===<br /> Coming Soon<br /> <br /> ==History==<br /> <br /> In 1871 Lord Rayleigh published a paper on scattering. Rayleigh scattering is the dispersion of electromagnetic radiation by particles that have a minute radius less than approximately 1/10 the wavelength. It laid the foundation to research on scattering and information we have today. <br /> <br /> == See also ==<br /> <br /> [[Category:Collisions] (Main page)<br /> <br /> ===Further reading===<br /> <br /> Matter and Interactions, Volume I: Modern Mechanics, 4th Edition. (Chapter 10.6)<br /> <br /> ===External links===<br /> [http://physics-animations.com/Physics/English/par_txt.htm]<br /> [http://www.britannica.com/science/Rayleigh-scattering]<br /> [http://hypernews.slac.stanford.edu/slacsite/aux/HiPPP/scattering/]<br /> <br /> ==References==<br /> <br /> Chabay, Ruth W., Bruce Sherwood. Matter and Interactions, Volume I: Modern Mechanics, 4th Edition. Wiley, 19/2014.<br /> <br /> [[Category:Collisions]]</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Scattering:_Collisions_in_2D_and_3D&diff=22167 Scattering: Collisions in 2D and 3D 2016-04-17T16:58:11Z

<p>Swebster9: /* External links */</p> <hr /> <div>Claimed by: Andreas Ward (Fall 2015) and Sam Webster (Spring 2016)<br /> <br /> ==The Main Idea==<br /> <br /> Unlike normal collisions, atomic and nuclear collisions are far too small to observe the curving trajectories of the interacting particles. The only thing that can be noticed is the initial and final states of the interaction. Scattering experiments are incorporated in the world of collisions to be able to study the minute details (structure) of atoms, nuclei, and other tiny particles as the interact with one another. <br /> <br /> ==Impact Parameters==<br /> Definition: distance between centers perpendicular to the incoming velocity. Impact parameters is often denoted by b. A head-on collision has an impact parameter of zero and with equal masses fully transfers the momentum such as with Newton's Cradle. As the impact parameter gets smaller the collision has a larger effect, and an even large deflection angle (scattering).<br /> <br /> Elastic collisions between two billiard balls (Double Click Image)<br /> [[File:ImpactParameter.png]]<br /> ==Examples==<br /> ===Simple===<br /> The collision of an alpha particle (helium nucleus) with the nucleus of a gold atom<br /> ===Simulation in Python===<br /> Coming Soon<br /> <br /> ==History==<br /> <br /> In 1871 Lord Rayleigh published a paper on scattering. Rayleigh scattering is the dispersion of electromagnetic radiation by particles that have a minute radius less than approximately 1/10 the wavelength. It laid the foundation to research on scattering and information we have today. <br /> <br /> == See also ==<br /> <br /> [[Category:Collisions] (Main page)<br /> <br /> ===Further reading===<br /> <br /> Matter and Interactions, Volume I: Modern Mechanics, 4th Edition. (Chapter 10.6)<br /> <br /> ===External links===<br /> [http://physics-animations.com/Physics/English/par_txt.htm]<br /> [http://www.britannica.com/science/Rayleigh-scattering]<br /> [http://hypernews.slac.stanford.edu/slacsite/aux/HiPPP/scattering/]<br /> <br /> ==References==<br /> <br /> Chabay, Ruth W., Bruce Sherwood. Matter and Interactions, Volume I: Modern Mechanics, 4th Edition. Wiley, 19/2014.<br /> <br /> [[Category:Collisions]]</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Scattering:_Collisions_in_2D_and_3D&diff=22157 Scattering: Collisions in 2D and 3D 2016-04-17T16:53:42Z

<p>Swebster9: /* 3-D Simulation */</p> <hr /> <div>Claimed by: Andreas Ward (Fall 2015) and Sam Webster (Spring 2016)<br /> <br /> ==The Main Idea==<br /> <br /> Unlike normal collisions, atomic and nuclear collisions are far too small to observe the curving trajectories of the interacting particles. The only thing that can be noticed is the initial and final states of the interaction. Scattering experiments are incorporated in the world of collisions to be able to study the minute details (structure) of atoms, nuclei, and other tiny particles as the interact with one another. <br /> <br /> ==Impact Parameters==<br /> Definition: distance between centers perpendicular to the incoming velocity. Impact parameters is often denoted by b. A head-on collision has an impact parameter of zero and with equal masses fully transfers the momentum such as with Newton's Cradle. As the impact parameter gets smaller the collision has a larger effect, and an even large deflection angle (scattering).<br /> <br /> Elastic collisions between two billiard balls (Double Click Image)<br /> [[File:ImpactParameter.png]]<br /> ==Examples==<br /> ===Simple===<br /> The collision of an alpha particle (helium nucleus) with the nucleus of a gold atom<br /> ===Simulation in Python===<br /> Coming Soon<br /> <br /> ==History==<br /> <br /> In 1871 Lord Rayleigh published a paper on scattering. Rayleigh scattering is the dispersion of electromagnetic radiation by particles that have a minute radius less than approximately 1/10 the wavelength. It laid the foundation to research on scattering and information we have today. <br /> <br /> == See also ==<br /> <br /> [[Category:Collisions] (Main page)<br /> <br /> ===Further reading===<br /> <br /> Matter and Interactions, Volume I: Modern Mechanics, 4th Edition. (Chapter 10.6)<br /> <br /> ===External links===<br /> [http://physics-animations.com/Physics/English/par_txt.htm]<br /> [http://www.britannica.com/science/Rayleigh-scattering]<br /> <br /> <br /> ==References==<br /> <br /> Chabay, Ruth W., Bruce Sherwood. Matter and Interactions, Volume I: Modern Mechanics, 4th Edition. Wiley, 19/2014.<br /> <br /> [[Category:Collisions]]</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Scattering:_Collisions_in_2D_and_3D&diff=22138 Scattering: Collisions in 2D and 3D 2016-04-17T16:38:56Z

<p>Swebster9: </p> <hr /> <div>Claimed by: Andreas Ward (Fall 2015) and Sam Webster (Spring 2016)<br /> <br /> ==The Main Idea==<br /> <br /> Unlike normal collisions, atomic and nuclear collisions are far too small to observe the curving trajectories of the interacting particles. The only thing that can be noticed is the initial and final states of the interaction. Scattering experiments are incorporated in the world of collisions to be able to study the minute details (structure) of atoms, nuclei, and other tiny particles as the interact with one another. <br /> <br /> ==Impact Parameters==<br /> Definition: distance between centers perpendicular to the incoming velocity. Impact parameters is often denoted by b. A head-on collision has an impact parameter of zero and with equal masses fully transfers the momentum such as with Newton's Cradle. As the impact parameter gets smaller the collision has a larger effect, and an even large deflection angle (scattering).<br /> <br /> Elastic collisions between two billiard balls (Double Click Image)<br /> [[File:ImpactParameter.png]]<br /> ==Examples==<br /> ===Simple===<br /> The collision of an alpha particle (helium nucleus) with the nucleus of a gold atom<br /> ===3-D Simulation===<br /> Coming Soon<br /> <br /> ==History==<br /> <br /> In 1871 Lord Rayleigh published a paper on scattering. Rayleigh scattering is the dispersion of electromagnetic radiation by particles that have a minute radius less than approximately 1/10 the wavelength. It laid the foundation to research on scattering and information we have today. <br /> <br /> == See also ==<br /> <br /> [[Category:Collisions] (Main page)<br /> <br /> ===Further reading===<br /> <br /> Matter and Interactions, Volume I: Modern Mechanics, 4th Edition. (Chapter 10.6)<br /> <br /> ===External links===<br /> [http://physics-animations.com/Physics/English/par_txt.htm]<br /> [http://www.britannica.com/science/Rayleigh-scattering]<br /> <br /> <br /> ==References==<br /> <br /> Chabay, Ruth W., Bruce Sherwood. Matter and Interactions, Volume I: Modern Mechanics, 4th Edition. Wiley, 19/2014.<br /> <br /> [[Category:Collisions]]</div>

Swebster9 http://www.physicsbook.gatech.edu/index.php?title=Scattering:_Collisions_in_2D_and_3D&diff=22137 Scattering: Collisions in 2D and 3D 2016-04-17T16:37:24Z

<p>Swebster9: </p> <hr /> <div>Claimed by: Andreas Ward (Fall 2015) and Sam Webster (Spring 2016)<br /> <br /> ==The Main Idea==<br /> <br /> Unlike normal collisions, atomic and nuclear collisions are far too small to observe the curving trajectories of the interacting particles. The only thing that can be noticed is the initial and final states of the interaction. Scattering experiments are incorporated in the world of collisions to be able to study the minute details (structure) of atoms, nuclei, and other tiny particles as the interact with one another. <br /> <br /> ==Impact Parameters==<br /> Definition: distance between centers perpendicular to the incoming velocity. Impact parameters is often denoted by b. A head-on collision has an impact parameter of zero and with equal masses fully transfers the momentum such as with Newton's Cradle. As the impact parameter gets smaller the collision has a larger effect, and an even large deflection angle (scattering).<br /> <br /> Elastic collisions between two billiard balls (Double Click Image)<br /> [[File:ImpactParameter.png]]<br /> ==Example==<br /> ===Simple===<br /> The collision of an alpha particle (helium nucleus) with the nucleus of a gold atom<br /> <br /> ==History==<br /> <br /> In 1871 Lord Rayleigh published a paper on scattering. Rayleigh scattering is the dispersion of electromagnetic radiation by particles that have a minute radius less than approximately 1/10 the wavelength. It laid the foundation to research on scattering and information we have today. <br /> <br /> == See also ==<br /> <br /> [[Category:Collisions] (Main page)<br /> <br /> ===Further reading===<br /> <br /> Matter and Interactions, Volume I: Modern Mechanics, 4th Edition. (Chapter 10.6)<br /> <br /> ===External links===<br /> [http://physics-animations.com/Physics/English/par_txt.htm]<br /> [http://www.britannica.com/science/Rayleigh-scattering]<br /> <br /> <br /> ==References==<br /> <br /> Chabay, Ruth W., Bruce Sherwood. Matter and Interactions, Volume I: Modern Mechanics, 4th Edition. Wiley, 19/2014.<br /> <br /> [[Category:Collisions]]</div>

Swebster9