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) - 0.273 kg m /s

(B) - 0.546 kg m /s

Step-by-step explanation:

mass of paintball, m = 0.0032 kg

initial velocity, u = 85.3 m/s

(A) Momentum is defined as the product of mass of body and the velocity of body.

initial momentum, pi = mass x initial velocity

pi = 0.0032 x 85.3 = 0.273 kg m /s

Finally the ball stops, so final velocity, v = 0 m/s

final momentum, pf = mass x final velocity = 0.0032 x 0 = 0 m/s

change in momentum = pf - pi = 0 - 0.273 = - 0.273 kg m /s

(B) initial velocity, u = + 85.3 m/s

final velocity, v = - 85.3 m/s

initial momentum, pi = mass x initial velocity

pi = 0.0032 x 85.3 = 0.273 kg m /s

final momentum, pf = mass x final velocity = - 0.0032 x 85.3 = - 0.273 kgm/s

change in momentum = pf - pi = - 0.273 - 0.273 = - 0.546 kg m /s

(C) According to the Newton's second law, the rate of change of momentum is directly proportional to the force exerted.

As the change in momentum in case (B) is more than the change in momentum in case (A), so the force exerted on the skin is more in case (B).