# Elastic Collision Between Two Balls

• susan_khan
In summary, the conversation discusses a homework question about an elastic collision between two balls of different masses. The question asks for the velocity of the smaller ball immediately after impact. Some possible answers are given, but the correct answer is not specified. The conversation also includes a discussion about the application of Newton's third law and the need for calculations to determine the correct answer. Finally, it is clarified that the velocity of the smaller ball increases from zero to a final value during the short period of time after the masses have exchanged momentum and energy.
susan_khan
Homework Statement
Ball A travelling with velocity, , collides head-on with stationary ball B in an elastic collision. If the mass of ball A is much greater than the mass of ball B, what is the velocity of ball B immediately after impact?
0 (It remains stationary.)
v (the initial velocity of ball A)
2 v (twice the initial velocity of ball A)
0.5 v (half the initial velocity of ball A)
Relevant Equations
N/A
I'm a little confused as to what the answer could be. This was one of my homework questions that I got wrong as I chose 0.5 v as the answer. Would someone be able to tell me what the correct answer would be?

susan_khan said:
Homework Statement:: Ball A travelling with velocity, , collides head-on with stationary ball B in an elastic collision. If the mass of ball A is much greater than the mass of ball B, what is the velocity of ball B immediately after impact?
0 (It remains stationary.)
v (the initial velocity of ball A)
2 v (twice the initial velocity of ball A)
0.5 v (half the initial velocity of ball A)
Relevant Equations:: N/A

I'm a little confused as to what the answer could be. This was one of my homework questions that I got wrong as I chose 0.5 v as the answer. Would someone be able to tell me what the correct answer would be?
The velocity of the traveling ball is not specified in your post.

topsquark
kuruman said:
The velocity of the traveling ball is not specified in your post.
Yes the velocity was not specified in the question, it was more so a scenario to think about. The reason I chose 0.5 as my answer is because I thought that the velocity of the small mass Ball B would change more; in the sense that the smaller mass would lose some energy to the bigger mass. However,now that I think back, won't ball b equal the same velocity as ball a. Because every action has an equal an opposite reaction?

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susan_khan said:
Yes the velocity was not specified in the question, it was more so a scenario to think about. The reason I chose 0.5 as my answer is because I thought that the velocity of the small mass Ball B would change more; in the sense that the smaller mass would lose some energy to the bigger mass. However,now that I think back, won't ball b equal the same velocity as ball a. Because every action has an equal an opposite reaction?
You seem to be guessing wildly. Why do you think Newton’s third law implies what you just said? You should be thinking in terms of conservation of energy and momentum.

What is the energy and momentum before and after the collision?

topsquark
susan_khan said:
Yes the velocity was not specified in the question, it was more so a scenario to think about. The reason I chose 0.5 as my answer is because I thought that the velocity of the small mass Ball B would change more; in the sense that the smaller mass would lose some energy to the bigger mass. However,now that I think back, won't ball b equal the same velocity as ball a. Because every action has an equal an opposite reaction?
Logic may only get you so far. Sometimes you have to do some calculations.

topsquark and nasu
PeroK said:
Sometimes you have to do some calculations.
… but logical ones.

The question wording is weird. If A is much more massive than B then none of the answers is correct. Why not just ask whether it is 0, between 0 and v, v or >v?
Whoops... except that the correct answer is just a good approximation.

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haruspex said:
… but logical ones.

The question wording is weird. If A is much more massive than B then none of the answers is correct.
Yes, there is a correct answer.

haruspex
Orodruin said:
Yes, there is a correct answer.
I agree.

For a perfectly elastic collision, what is the meaning of "immediately after impact"?
After contact?
During contact?
After separation?

The velocity of ball B increases during that short period of time from zero to a final value.

Lnewqban said:
For a perfectly elastic collision, what is the meaning of "immediately after impact"?
After contact?
During contact?
After separation?

The velocity of ball B increases during that short period of time from zero to a final value.
I think of it as "after the masses are done exchanging momentum and energy" otherwise the question cannot be answered.

PeroK and Lnewqban

## 1. What is an elastic collision between two balls?

An elastic collision between two balls is a type of collision in which the total kinetic energy of the two balls is conserved. This means that no energy is lost during the collision and the balls bounce off each other without any deformation.

## 2. How is the momentum conserved in an elastic collision between two balls?

In an elastic collision between two balls, the momentum is conserved because the total momentum before the collision is equal to the total momentum after the collision. This means that the sum of the individual momenta of the two balls remains the same before and after the collision.

## 3. What is the difference between an elastic collision and an inelastic collision?

In an elastic collision, the total kinetic energy is conserved, while in an inelastic collision, some of the kinetic energy is lost in the form of heat or sound. In an inelastic collision, the objects may also deform upon impact, while in an elastic collision, the objects retain their shape.

## 4. What factors affect the outcome of an elastic collision between two balls?

The outcome of an elastic collision between two balls can be affected by factors such as the masses of the balls, their velocities before the collision, and the angle at which they collide. The elasticity of the balls and any external forces acting on them can also impact the outcome of the collision.

## 5. How is the coefficient of restitution related to an elastic collision between two balls?

The coefficient of restitution is a measure of the elasticity of a collision. In an elastic collision between two balls, the coefficient of restitution is equal to 1, indicating a perfectly elastic collision where the kinetic energy is conserved. A lower coefficient of restitution indicates a less elastic collision where some kinetic energy is lost.

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