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, p_i, of each ball is

P_i = m× u= 0.05 kg × 6 m/s

⇒ p_i = 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, p_f of each ball is,

p_f= m× v = 0.05 kg × -6 m/s

⇒ p_f = -0.3 kg m/s

Impulse imparted to each ball, ‘I’ = change in the momentum of the system

⇒ I= p_f - p_i = (-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.