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) If the paintball stops completely the magnitude of the change in the paintball’s momentum is
`p=0.273kg*m/s`

B) If the paintball bounces off its target and afterward moves in the opposite direction with the same speed, the change in the paintball’s momentum is
`p=0.546kg*m/s`

C) A paintball bouncing off your skin in the opposite direction with the same speed hurts more than a paintball exploding upon your skin because of the strength exerted is twice than if it explodes.

Step-by-step explanation:

Hi

A) We use the formula of momentum
`p=mv`, so we have
`p=0.0032kg*85.3m/s=0.273kg*m/s`

B) We use the same formula above, then due we have a change of direction at the same speed, therefore the change in the momentum is the double so

`p=2*0.0032kg*85.3m/s=0.546kg*m/s`.

C) The average strength of the force an object exerts during impact is determined by the amount the object’s momentum changes. therefore

`F=(\Delta p)/(\Delta t)`, as we don't have any data about the impact time but we know momentum is twice, time does no matter and strength is twice too.