Elastic Collision Between Two Balls

[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?

 

[kuruman]

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.
Also, to receive help youhave to post your attempt at a solution. What was your reasoning for choosing your answer?

 

[susan_khan]

The velocity of the traveling ball is not specified in your post.
Also, to receive help youhave to post your attempt at a solution. What was your reasoning for choosing your answer?

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?

 

[Orodruin]

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?

 

[PeroK]

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.

 

[haruspex]

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.

 

[Orodruin]

… 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.

 

[kuruman]

Yes, there is a correct answer.

I agree.

 

[Lnewqban]

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.

 

[kuruman]

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.