Two billiard balls, each of mass 0.05 kg, moving in opposite directions with speed 6 ms-1collide and rebound with the same speed. What is the impulse imparted to each ball due to the other?
Initial momentum of each ball before collision
= 0.05 x 6 kg ms-1 = 0.3 kg ms-1
Final momentum of each ball after collision
= – 0.05 x 6 kg ms-1 = – 0.3 kg ms-1 Impulse imparted to each ball due to the other
= final momentum – initial momentum = 0.3 kg m s-1 – 0.3 kg ms-1
= – 0.6 kg ms-1 = 0.6 kg ms-1 (in magnitude)
The two impulses are opposite in direction.
Mass of each ball = 0.05 kg
Initial velocity of each ball = 6 m/s
Magnitude of the initial momentum of each ball, pi = 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, pf = –0.3 kg m/s
Impulse imparted to each ball = Change in the momentum of the system
= pf – pi
= –0.3 – 0.3 = –0.6 kg m/s
The negative sign indicates that the impulses imparted to the balls are opposite in direction.