Question

Two billiard balls each of mass 0.05 $\text {kg}$ moving in opposite directions with speed 6 $\text m \,\text s^{-1}$collide and rebound with the same speed. What is the impulse imparted to each ball due to the other ?

Answer 1

Mass of each ball = 0.05 $\text {kg}$
Initial velocity of each ball = 6 $\text m/\text s$
Magnitude of the initial momentum of each ball, $p_i$ $=$ 0.3 $\text {kg}$ $\text m/\text s$
After collision, the balls change their directions of motion without changing the magnitudes of their velocity.
Final momentum of each ball, $p_f$ $=$ –0.3 $\text {kg}$ $\text m/\text s$
Impulse imparted to each ball = Change in the momentum of the system
$=$ $p_f-p_i$
= – 0.3 – 0.3 = –0.6 $\text {kg}$ $\text m/\text s$
The negative sign indicates that the impulses imparted to the balls are opposite in direction.