Question

A paintball’s mass is 0.0032kg. A typical paintball strikes a target moving at 85.3 m/s.

A) If the paintball stops completely as a result of striking its target, what is the magnitude of the change in the paintball’s momentum?

B) If the paintball bounces off its target and afterward moves in the opposite direction with the same speed, what is the magnitude of the change in the paintball’s momentum?

C) The strength of the force an object exerts during impact is determined by the amount the object’s momentum changes. Use this idea along with your answers to (a) and (b) to explain why a paintball bouncing off your skin hurts more than a paintball exploding upon your skin.

Answer 1

a) The paintball stops after hitting the target i.e., the final velocity (v) is 0 m/s

Hence, change in momentum is

b) The paintball bounces off the target and moves in opposite direction with the same velocity.

If v be the velocity with which it struck then the velocity with which it will bounce off the target is -v

Hence, change in momentum is

c) When a paintball bounces off the skin (case similar to b) the change in momentum is greater than when it explodes( case similar to a). As during explosion the ball came to rest and hence imparted less change in momentum.

Hence, for a unit change in time, force (rate of change of momentum) exerted by a paintball bouncing off the skin will be greater than an exploding paintball.

So, a bouncing paintball hurts more.