(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Both object A and B have mass M and are moving.

An object with mass of m and moving with velocity u collide with the object B elastically. (m < M)

Find the following after m collide with B

1) Velocity of m after bouncing back

2) Velocity of B

Then m collide with A and bounce back

3) The highest value of M/m that velocity of m is lesser than or equal to that of B

(Surface has no friction)

2. Relevant equations

3. The attempt at a solution

Using the Law of Energy Conservation and the Law of Momentum Conservation

##\frac{1}{2} m u^2 = \frac{1}{2} m v_1^2 + \frac{1}{2} M v_2^2##

##m u = -m v_1 + Mv_2##

After solving the equation, I get this

##v_1 = \frac{M - m}{M + m} u## (Answer for (1))

##v_2 = \frac{2 m}{M + m} u## (Answer for (2))

Then object m hit object A. The velocity of m then change into

##(\frac{M - m}{m + M})^2 u##

Velocity of m should be equal to that of B so m cannot reach B

##(\frac{M - m}{m + M})^2 u = \frac{2 m u}{m + M}##

##\frac{M}{m} = 2 + \sqrt{5}## (Answer for (3))

Is that correct?

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# Elastic Collision Problem

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