Two billiard balls each of mass $0.05\; kg$ moving in opposite directions with speed $6\; m/s$ collide and rebound with the same speed. What is the impulse imparted to each ball due to the other?
Two billiard balls each of mass $0.05\; kg$ moving in opposite directions with speed $6\; m/s$ collide and rebound with the same speed. What is the impulse imparted to each ball due to the other?
Mass of each ball $=0.05\, kg$
Initial velocity of each ball $=6\, m / s$
Magnitude of the initial momentum of each ball, $p_{i}=0.3 \,kg\, m / s$
After collision, the balls change their directions of motion without changing the magnitudes of their velocity.
Final momentum of each ball, $p_{f}=-0.3 \,kg \,m / s$
Impulse imparted to each ball $=$ Change in the momentum of the system
$=p_{f}-p_{i}$
$=-0.3-0.3=-0.6\, kg \,m / s$
The negative sign indicates that the impulses imparted to the balls are opposite in direction.
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- [KVPY 2010]