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A paintball gun shoots a small hollow sphere filled with paint, which usually bursts on impact to splash paint on whoever is hits. Consider the two scenarios: (a) a paintball hits you and bursts and (b) a paintball hits you and bounces off. Assuming both paintballs have the same mass and velocity, which will hurt you more? (Which exerts the most force?) Both will hurt exactly the same amount. It is impossible to know without knowing the forces. The paintball that bounces off you. The paintball that burst.

Question

A paintball gun shoots a small hollow sphere filled with paint, which usually bursts on impact to splash paint on whoever is hits. Consider the two scenarios: (a) a paintball hits you and bursts and (b) a paintball hits you and bounces off. Assuming both paintballs have the same mass and velocity, which will hurt you more? (Which exerts the most force?) Both will hurt exactly the same amount. It is impossible to know without knowing the forces. The paintball that bounces off you. The paintball that burst.

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Solution

The paintball that bounces off you will hurt more. This is because of the law of conservation of momentum. When the paintball hits and bounces back, it not only transfers its momentum to you but also takes some momentum back, which results in a greater change in momentum and thus a greater force according to Newton's second law of motion (Force = change in momentum / change in time). On the other hand, when the paintball bursts upon impact, it transfers all its momentum to you but doesn't take any back, resulting in a smaller change in momentum and thus a smaller force.

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