Question

Ball 1 collides with an another identical ball 2 at rest For what values of coefficient of restitution e the velocity of 2nd ball becomes two times of ball 1 after collision?

Answer 1

Let the velocities of ball 1 and ball 2 be v1 and v2 after collision.

Conserving momentum

mv + m(0) = mv1+ mv2

It is given that we want the condition,
v2 = 2v1

mv = 3mv1. => v = 3v1
So,
e = velocity of Separation/velocity of approach
= v2-v1 / v = v1/3v1 = 1/3

Therefore, the value of Coefficient of restitution should be 1/3 to meet the required conditions.

Answer 2

Answer:

$e = \frac{1}{3}$

Explanation:

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