Two billiard balls each of mass 0.05 kg moving in opposite directions with speed 6 m s-1 collide and rebound with the same speed. What is the impulse imparted to each ball due to the other?
The momentum of the ball can be calculated as
p = m× v
Where,
‘m’ is the mass of the ball
‘v’ is the velocity of the ball.
Given,
Mass of each billiard ball, m = 0.05 kg
Initial velocity of each ball, u = 6 m/s
The initial momentum, pi, of each ball is
Pi = m× u= 0.05 kg × 6 m/s
⇒ pi = 0.3 kg m/s
The balls rebound after the collision thus, they change directions but the magnitude of the velocity remains the same,
Now,
Final velocity of each ball, v = -6 m/s
The final momentum, pf of each ball is,
pf= m× v = 0.05 kg × -6 m/s
⇒ pf = -0.3 kg m/s
Impulse imparted to each ball, ‘I’ = change in the momentum of the system
⇒ I= pf - pi = (-0.3 – 0.3) kg m/s
⇒ I= -0.6 kg m/s
The negative sign is because the impulse imparted to each of the balls are in opposite directions.
the impulse imparted to each ball due to the other is 0.6 N in opposite directions.