# Elastic Collision - Symbolic Question

1. Homework Statement

Suppose you hold a small ball of mass m1 in contact with, and directly over, the center of mass of a large ball of mass m2. If you then drop the small ball a short time after dropping the large ball, the small ball rebounds with surprising speed. If we ignore air resistance and assume the large ball makes an elastic collision with the floor and then makes an elastic collision with the still descending small ball and that large ball has much larger mass than the small ball then:

a) If the velocity of the small ball immediately before the collision is v, what is the velocity of the large ball? (in terms of v)

b) What is the velocity of the small ball immediately after its collision with the large ball? (in terms of v)

c) What is the ratio of the small ball's rebound distance to the distance it fell before the collision? (a number)

2. Homework Equations

1/2mv^2 + mgh = 1/2mv^2 + mgh
Elastic collision: V1 = -V2

3. The Attempt at a Solution

a. -V
b. ?
c. ?

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Doc Al
Mentor
Hint: Analyze the problem in the center of mass frame, then transform back to the lab frame. (Assume m2 >> m1.)

That...doesn't make a bit of sense to me. Pardon my lack of knowledge, but I'm not really familiar with the terms you were using, Doc Al.

Doc Al
Mentor
That...doesn't make a bit of sense to me. Pardon my lack of knowledge, but I'm not really familiar with the terms you were using, Doc Al.
No problem. Sometimes problems are easier to solve in certain frames of reference--but let's forget that for the moment.

What do you know about elastic collision?

1/2mv^2 + mgh = 1/2mv^2 + mgh
You'll need this for part c.

Elastic collision: V1 = -V2
What does this mean? If you mean the relative velocity reverses: Great! Use it.

3. The Attempt at a Solution

a. -V
Assuming you meant -v (the same v as the small ball): Good!

Here's a hint for part b: If a ping pong ball hits a bowling ball, what happens to the velocity of the bowling ball? (To a good approximation.)