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Question
Two billiard balls each of mass 0.05kg moving in opposite directions with speed 6ms−1collide and rebound with the same speed. What is the impulse imparted to each ball due to the other?
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Solution
Mass of each ball =0.05kg
Initial velocity of each ball =6m/s
Magnitude of the initial momentum of each ball, Pi=mvi=0.05×6=0.3 kg m/s
After collision, the balls change their directions of motion without changing the magnitudes of their velocity.
Final momentum of first ball, P1f=−0.3 kg m/s
Final momentum of second ball, P2f=0.3 kg m/s
Impulse imparted to first ball = P1f−P1i=−0.3−0.3 kg m/s=−0.6 kg m/s
Impulse imparted to second ball = P2f−P2i=0.3−(−0.3)=0.6 kg m/s
The negative sign indicates that the impulses imparted to the balls are opposite in direction.
Initial velocity of each ball =6m/s
Magnitude of the initial momentum of each ball, Pi=mvi=0.05×6=0.3 kg m/s
After collision, the balls change their directions of motion without changing the magnitudes of their velocity.
Final momentum of first ball, P1f=−0.3 kg m/s
Final momentum of second ball, P2f=0.3 kg m/s
Impulse imparted to first ball = P1f−P1i=−0.3−0.3 kg m/s=−0.6 kg m/s
Impulse imparted to second ball = P2f−P2i=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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