Question

Two billiard balls each of mass m moving in opposite directios with speed m collide and rebound with the same speed. What is the impulse imparted to each ball due to the other.

Answer 1

Let the first billiard ball collide with the other with a velocity v but rebounds with -v. Then, since the second billiard ball has the same velocity, it collides with the first with the velocity -v and then rebounds with v.

The impulse imparted to the first ball is its change in momentum, i.e.,

$\displaystyle\longrightarrow\sf {\Delta p_1=-m}\bf{v}-\sf{m}\bf{v}$

$\displaystyle\longrightarrow\underline {\underline {\sf{\Delta p_1=-2m}\bf{v}}}$

Similarly, the impulse imparted to the second ball is,

$\displaystyle\longrightarrow\sf{\Delta p_2=m}\bf{v}-(-\sf{m}\bf{v})$

$\displaystyle\longrightarrow\underline {\underline {\sf{\Delta p_2=2m}\bf{v}}}$