Elastic Collisions - Revision history

Ebarden3 at 04:06, 1 December 2025

2025-12-01T04:06:22Z

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	Inelastic collisions: Momentum is conserved, kinetic energy is not conserved (deltaK does not equal 0), energy is transformed but not lost! Ex= Car crashes, clay balls, ballistic pendulum.		Inelastic collisions: Momentum is conserved, kinetic energy is not conserved (deltaK does not equal 0), energy is transformed but not lost! Ex= Car crashes, clay balls, ballistic pendulum.

	Here is a great video describing ~~simply~~ the difference between elastic and inelastic collisions: https://www.youtube.com/watch?v=M2xnGcaaAi4		Here is a great video describing the difference between elastic and inelastic collisions in simple terms: https://www.youtube.com/watch?v=M2xnGcaaAi4

	====Conditions and Analysis for Elastic Collision====		====Conditions and Analysis for Elastic Collision====
	*Total kinetic energy before and after the collision is the same.		*Total kinetic energy before and after the collision is the same.
	*Kinetic energy temporarily converts to elastic potential energy and back.		*Kinetic energy temporarily converts to elastic potential energy and back.
	*Occurs frequently at the atomic or molecular level.		*Occurs frequently at the atomic or molecular level, not much in our macroscopic world, there are approximations at best.
	*Relative speed of approach equals relative speed of separation.		*Relative speed of approach equals relative speed of separation.

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	===Nuclear Collisions===		===Nuclear Collisions===
	Although elastic collisions are not a common thing you see, on a nuclear scale it is ~~exetremely~~ important and very common especially in the Nuclear field. Nuclear collisions are interactions between atomic nuclei or between a nucleus and a subatomic particle (such as a neutron or alpha particle). These collisions can be elastic, inelastic, or involve absorption. In these events, extremely high energy levels may result in radiation, decay, or even nuclear fission.		Although elastic collisions are not a common thing you see, on a nuclear scale it is extremely important and very common especially in the Nuclear field. Nuclear collisions utilize the subatomic particles that have elastic collisions! Nuclear collisions are interactions between atomic nuclei or between a nucleus and a subatomic particle (such as a neutron or alpha particle). These collisions can be elastic, inelastic, or involve absorption. In these events, extremely high energy levels may result in radiation, decay, or even nuclear fission.

	====Types of Nuclear Collisions====		====Types of Nuclear Collisions====
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	This formula is useful in applications like neutron moderation, radiation shielding, and analysis of nuclear reactions.		This formula is useful in applications like neutron moderation, radiation shielding, and analysis of nuclear reactions.

	===How to solve elastic collision problems in general===		==How to solve elastic collision problems in general==

	Here is a video of a simple problem that shows the main concepts described below: https://www.youtube.com/watch?v=CFbo_nBdBco		Here is a video of a simple problem that shows the main concepts described below: https://www.youtube.com/watch?v=CFbo_nBdBco
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	===Computational Models===		===Computational Models===

			Here are computational models to help visualize perfectly elastic collisions that occur in computational models, but not in real life due to heat loss, etc.
	[[File:Collision carts elastic.gif\|Collision carts elastic\|right]]		[[File:Collision carts elastic.gif\|Collision carts elastic\|right]]
	The trinket model linked demonstrates an elastic collision between two spheres.		The trinket model linked demonstrates an elastic collision between two spheres.
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	'''''Reminders'''''		'''''Reminders'''''

	Be sure to show all steps in your solution and include diagrams whenever possible. For a lot of the complicated problems, starting with a diagram and writing down the given information and plugging that into either the momentum or energy principle can help you move forward in the problem. It would be helpful to also write the main principles at the side to remind yourself of how you found it. If you still get stuck, try finding similar examples to that problem and look at the solutions to get on the right track.		- Be sure to show all steps in your solution and include diagrams whenever possible.
			- For a lot of the complicated problems, starting with a diagram and writing down the given information and plugging that into either the momentum or energy principle can help you move forward in the problem.
			- It is easiest to solve problems symbolically to find the variable the problem is asking for, then to substitute the real values in at the end of the process.
			- It would be helpful to also write the main principles at the side to remind yourself of how you found it. If you still get stuck, try finding similar examples to that problem and look at the solutions to get on the right track.

	===Simple===		===Simple examples===

	'''Question'''		'''Question'''
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	===Mid difficulty===		===Mid difficulty example===

	'''Question'''		'''Question'''
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	<math> v_{2f}=2v_{cm} - v_{2i} = 2(1.57) - (-2) = 5.14m/s </math>		<math> v_{2f}=2v_{cm} - v_{2i} = 2(1.57) - (-2) = 5.14m/s </math>

	===Difficult===		===Difficult example===

	'''Problem'''		'''Problem'''

Ebarden3 at 03:55, 1 December 2025

2025-12-01T03:55:32Z

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	Inelastic collisions: Momentum is conserved, kinetic energy is not conserved (deltaK does not equal 0), energy is transformed but not lost! Ex= Car crashes, clay balls, ballistic pendulum.		Inelastic collisions: Momentum is conserved, kinetic energy is not conserved (deltaK does not equal 0), energy is transformed but not lost! Ex= Car crashes, clay balls, ballistic pendulum.

			Here is a great video describing simply the difference between elastic and inelastic collisions: https://www.youtube.com/watch?v=M2xnGcaaAi4

	====Conditions and Analysis for Elastic Collision====		====Conditions and Analysis for Elastic Collision====
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	====Scattering Efficiency Formula====		====Scattering Efficiency Formula====
	The fraction of energy transferred from an alpha particle (mass m) to a target nucleus (mass M) during an elastic collision is given by: <math> (A-1)^2/(A+1)^2 </math> Where <math> A=M/m </math>. This expression helps quantify energy loss per collision based on the mass ratio.		In elastic collisions on an atomic level: The fraction of energy transferred from an alpha particle (mass m) to a target nucleus (mass M) during an elastic collision is given by: <math> (A-1)^2/(A+1)^2 </math> Where <math> A=M/m </math>. This expression helps quantify energy loss per collision based on the mass ratio.
	This formula is useful in applications like neutron moderation, radiation shielding, and analysis of nuclear reactions.		This formula is useful in applications like neutron moderation, radiation shielding, and analysis of nuclear reactions.

Ebarden3 at 03:46, 1 December 2025

2025-12-01T03:46:57Z

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	So how are collisions connected to the real world? Collisions are all around us!		So how are collisions connected to the real world? Collisions are all around us!

	One main example is cars. Lots of car companies will purposely test and wreck cars to test collisions! Data is then sent to places like the Insurance Institute for Highway Safety where we can learn about car agility and more.		One main example is cars. Lots of car companies will purposely test and wreck cars to test collisions! Data is then sent to places like the Insurance Institute for Highway Safety where we can learn about car agility and more. This is an example of inelastic collisions in the real world.

	[[File:Corvette Crash Tester (3695903512).jpg\|Corvette Crash Tester (3695903512)\|500px]]		[[File:Corvette Crash Tester (3695903512).jpg\|Corvette Crash Tester (3695903512)\|500px]]


	Another example of collisions in real life is billiards. This is one of the most accurate real life examples of elastic collisions. One ball hits another ball at rest, and if done right the first ball stops and transfers nearly all its kinetic energy into kinetic energy in the second ball. We consider this a head on collision of equal masses.		Another example of approximated elastic collisions in real life is billiards. This is one of the most accurate real life examples of elastic collisions. One ball hits another ball at rest, and if done right the first ball stops and transfers nearly all its kinetic energy into kinetic energy in the second ball. We consider this a head on collision of equal masses.

	[[File:Billiards_and_snookers.jpg\|500px]]		[[File:Billiards_and_snookers.jpg\|500px]]

Ebarden3 at 03:24, 1 December 2025

2025-12-01T03:24:11Z

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	==The Main Idea==		==The Main Idea==

	While the term "elastic" may evoke rubber bands or bubble gum, in physics it specifically refers to collisions that conserve internal energy and kinetic energy. Elastic collisions are interactions between two or more objects where no kinetic energy is lost during the collision.		While the term "elastic" may evoke rubber bands or bubble gum, in physics it specifically refers to collisions that conserve momentum, internal energy, and kinetic energy. Elastic collisions are interactions between two or more objects where no kinetic energy is lost during the collision, so kinetic energy=0!

	[[File:Elastic collision.svg\|Elastic collision\|right]]		[[File:Elastic collision.svg\|Elastic collision\|right]]
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	Overall in elastic collisions-> Energy (kinetic energy and momentum) is conserved. The change in kinetic energy (deltaK)=0. The system doesn't change its shape, temperature, etc! This never really happens in real life for macroscopic objects, it only happens perfectly on atomic levels, but pool balls colliding is a good approximation of what happens!		Overall in elastic collisions-> Energy (kinetic energy and momentum) is conserved. The change in kinetic energy (deltaK)=0. The system doesn't change its shape, temperature, etc! This never really happens in real life for macroscopic objects, it only happens perfectly on atomic levels, but pool balls colliding is a good approximation of what happens!

	These idealized interactions ~~often~~ occur in microscopic systems, such as between gas molecules, atoms, or subatomic particles. On a macroscopic level, real-world collisions (such as between billiard balls or on air tracks) can approximate elastic collisions if friction and deformation are minimized. Elastic collisions are particularly important in thermodynamics and statistical mechanics, where they help explain gas pressure and temperature as emergent properties from molecular motion.		These idealized interactions occur perfectly only in microscopic systems, such as between gas molecules, atoms, or subatomic particles. On a macroscopic level, real-world collisions (such as between billiard balls or on air tracks) can approximate elastic collisions if friction and deformation are minimized. Elastic collisions are particularly important in thermodynamics and statistical mechanics, where they help explain gas pressure and temperature as emergent properties from molecular motion.

	Although perfect elastic collisions don't exist on a macroscopic scale due to inevitable energy loss (e.g., heat), they can occur in atomic or subatomic interactions where quantized energy levels are involved, provided the collision energy isn't high enough to cause excitation. on a macroscopic scale due to inevitable energy loss (e.g., heat), they can occur in atomic or subatomic interactions where quantized energy levels are involved, provided the collision energy isn't high enough to cause excitation.		Although perfect elastic collisions don't exist on a macroscopic scale due to inevitable energy loss (e.g., heat), they can occur in atomic or subatomic interactions where quantized energy levels are involved, provided the collision energy isn't high enough to cause excitation. on a macroscopic scale due to inevitable energy loss (e.g., heat), they can occur in atomic or subatomic interactions where quantized energy levels are involved, provided the collision energy isn't high enough to cause excitation.
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	*Occurs frequently at the atomic or molecular level.		*Occurs frequently at the atomic or molecular level.
	*Relative speed of approach equals relative speed of separation.		*Relative speed of approach equals relative speed of separation.

			Utilizes the conservation of momentum equation, very important for this sector of physics: m1vi1 + m2vi2 = m1vf1 + m2vf2

	Here's a video walkthrough of a basic elastic collision: https://www.youtube.com/watch?v=V4vzNk4qppw		Here's a video walkthrough of a basic elastic collision: https://www.youtube.com/watch?v=V4vzNk4qppw
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	The history of collisions originates from the Rutherford Scattering experiment. It consisted of shooting alpha particles through a thin gold foil. As Rutherford studied the scattering of alpha particles through metal foils, he first noticed a collision with a single massive positive particle. Although the alpha particles did not hit the nucleus of the gold atoms, they did interact with each other and therefore can be considered as a collision. Since the interaction did not excite the gold atoms, fortunately enough, it was an elastic collision. This lead to the conclusion that the positive charge of the mass was concentrated in the center, the atomic nucleus! The plum pudding model (where the positive and negative charges were stuck within the atom like plums in a pudding), that had been around was disproved. When further research was done, they measured the angle of the 'scattering' or the particles shot through a tin gold foil. Had the collisions been inelastic, the particles would not have been able to bounce back.		The history of collisions originates from the Rutherford Scattering experiment. It consisted of shooting alpha particles through a thin gold foil. As Rutherford studied the scattering of alpha particles through metal foils, he first noticed a collision with a single massive positive particle. Although the alpha particles did not hit the nucleus of the gold atoms, they did interact with each other and therefore can be considered as a collision. Since the interaction did not excite the gold atoms, fortunately enough, it was an elastic collision. This lead to the conclusion that the positive charge of the mass was concentrated in the center, the atomic nucleus! The plum pudding model (where the positive and negative charges were stuck within the atom like plums in a pudding), that had been around was disproved. When further research was done, they measured the angle of the 'scattering' or the particles shot through a tin gold foil. Had the collisions been inelastic, the particles would not have been able to bounce back.

			The history of specifically elastic collisions started by Isaac Newton formulating the laws of motion and classical mechanics. Later on, James Clerk Maxwell studied gas behavior with kinetic energy and found the molecular interactions participating in elastic collisions with no transformation of energy in a system and kinetic energy=0. In the 20th century, quantum mechanics was developed, which provided a further look into elastic particle interactions! We can now contribute approximations to macroscopic situations, while knowing perfectly elastic collisions only happen in the microscopic world not seen by the human eye, but which can be discovered by physics!

	==Collision Theory==		==Collision Theory==
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	https://www.youtube.com/watch?v=5pZj0u_XMbc		https://www.youtube.com/watch?v=5pZj0u_XMbc

			https://www.ai-futureschool.com/en/physics/understanding-elastic-collisions-in-physics.php

	How to solve elastic problems in general:		How to solve elastic problems in general:

Ebarden3: /* Middling */

2025-12-01T03:14:24Z

Middling

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	===~~Middling~~===		===Mid difficulty===

	'''Question'''		'''Question'''

Ebarden3 at 03:09, 1 December 2025

2025-12-01T03:09:15Z

@@ Line 22: / Line 22: @@
 Although perfect elastic collisions don't exist on a macroscopic scale due to inevitable energy loss (e.g., heat), they can occur in atomic or subatomic interactions where quantized energy levels are involved, provided the collision energy isn't high enough to cause excitation. on a macroscopic scale due to inevitable energy loss (e.g., heat), they can occur in atomic or subatomic interactions where quantized energy levels are involved, provided the collision energy isn't high enough to cause excitation.
-==Inelastic vs. Elastic Collisions==
+===Inelastic vs. Elastic Collisions===
 Elastic collisions: Momentum conserved, kinetic energy conserved (deltaK equals 0), there is no energy transformation, energy is not lost (as always)! Ex= subatomic particles, Billiard balls.
@@ Line 51: / Line 51: @@
 The fraction of energy transferred from an alpha particle (mass m) to a target nucleus (mass M) during an elastic collision is given by: <math> (A-1)^2/(A+1)^2 </math> Where <math> A=M/m </math>. This expression helps quantify energy loss per collision based on the mass ratio.
 This formula is useful in applications like neutron moderation, radiation shielding, and analysis of nuclear reactions.
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 https://www.youtube.com/watch?v=5pZj0u_XMbc
 Newton's Cradle Code:

Ebarden3 at 02:57, 1 December 2025

2025-12-01T02:57:05Z

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	==Inelastic vs. Elastic Collisions==		==Inelastic vs. Elastic Collisions==

	Elastic collisions:		Elastic collisions: Momentum conserved, kinetic energy conserved (deltaK equals 0), there is no energy transformation, energy is not lost (as always)! Ex= subatomic particles, Billiard balls.

			Inelastic collisions: Momentum is conserved, kinetic energy is not conserved (deltaK does not equal 0), energy is transformed but not lost! Ex= Car crashes, clay balls, ballistic pendulum.

	====Conditions and Analysis for Elastic Collision====		====Conditions and Analysis for Elastic Collision====

Ebarden3 at 02:53, 1 December 2025

2025-12-01T02:53:46Z

← Older revision		Revision as of 22:53, 30 November 2025
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	*There is no lasting deformation or generation of heat within the bodies involved.		*There is no lasting deformation or generation of heat within the bodies involved.

			Overall in elastic collisions-> Energy (kinetic energy and momentum) is conserved. The change in kinetic energy (deltaK)=0. The system doesn't change its shape, temperature, etc! This never really happens in real life for macroscopic objects, it only happens perfectly on atomic levels, but pool balls colliding is a good approximation of what happens!

	These idealized interactions often occur in microscopic systems, such as between gas molecules, atoms, or subatomic particles. On a macroscopic level, real-world collisions (such as between billiard balls or on air tracks) can approximate elastic collisions if friction and deformation are minimized. Elastic collisions are particularly important in thermodynamics and statistical mechanics, where they help explain gas pressure and temperature as emergent properties from molecular motion.		These idealized interactions often occur in microscopic systems, such as between gas molecules, atoms, or subatomic particles. On a macroscopic level, real-world collisions (such as between billiard balls or on air tracks) can approximate elastic collisions if friction and deformation are minimized. Elastic collisions are particularly important in thermodynamics and statistical mechanics, where they help explain gas pressure and temperature as emergent properties from molecular motion.
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	==Inelastic vs. Elastic Collisions==		==Inelastic vs. Elastic Collisions==

			Elastic collisions:

	====Conditions and Analysis for Elastic Collision====		====Conditions and Analysis for Elastic Collision====
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	http://blogs.bu.edu/ggarber/archive/bua-physics/collisions-and-conservation-of-momentum/		http://blogs.bu.edu/ggarber/archive/bua-physics/collisions-and-conservation-of-momentum/

			Inelastic vs. Elastic Collisions:

			https://kingofthecurve.org/blog/elastic-vs-inelastic-collisions

Ebarden3 at 02:48, 1 December 2025

2025-12-01T02:48:16Z

← Older revision		Revision as of 22:48, 30 November 2025
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	Although perfect elastic collisions don't exist on a macroscopic scale due to inevitable energy loss (e.g., heat), they can occur in atomic or subatomic interactions where quantized energy levels are involved, provided the collision energy isn't high enough to cause excitation. on a macroscopic scale due to inevitable energy loss (e.g., heat), they can occur in atomic or subatomic interactions where quantized energy levels are involved, provided the collision energy isn't high enough to cause excitation.		Although perfect elastic collisions don't exist on a macroscopic scale due to inevitable energy loss (e.g., heat), they can occur in atomic or subatomic interactions where quantized energy levels are involved, provided the collision energy isn't high enough to cause excitation. on a macroscopic scale due to inevitable energy loss (e.g., heat), they can occur in atomic or subatomic interactions where quantized energy levels are involved, provided the collision energy isn't high enough to cause excitation.

			==Inelastic vs. Elastic Collisions==

	====Conditions and Analysis for Elastic Collision====		====Conditions and Analysis for Elastic Collision====

Ebarden3 at 02:47, 1 December 2025

2025-12-01T02:47:07Z

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	Edit by ~~Aidan Looman Summer~~ 2025		Edit by Ella Barden Fall 2025
	==The Main Idea==		==The Main Idea==