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Chapter 4: Problem 2

A ball bounces off a wall with the same speed it had before it hit the wall. Has its momentum changed? Has a force acted on the ball? Has a force acted on the wall? Relate your answers to Newton's laws of motion.

Short Answer

Expert verified
Yes, the ball's momentum has changed due to a change in its velocity direction. Yes, a force has acted on the ball - the force exerted by the wall which caused the ball's momentum to change. Yes, a force has acted on the wall due to Newton's third law of motion stating every action (ball hitting the wall) will have an equal and opposite reaction (wall exerting force on the ball). All these are in accordance with Newton's second and third laws of motion.

Step by step solution

01

Understand momentum

Momentum is a vector quantity calculated by multiplying an object's mass by its velocity (\( p = mv \)). Because velocity is a vector quantity and includes a direction, any change in velocity, including a change in direction, implies a change in momentum.
02

Application to the bouncing ball

When the ball hits the wall and bounces back, although its speed remains the same, the direction of its velocity changes (from towards the wall to away from the wall). Therefore, the ball's momentum changes, because momentum depends on both the magnitude and direction of velocity.
03

Apply Newton's Second Law

By Newton's second law, a net force acting on an object will cause its momentum to change. Since the ball's momentum changed, a force must have acted on the ball. This force is exerted by the wall when the ball hits it.
04

Apply Newton's Third Law

Based on Newton's third law, every action has an equal and opposite reaction. When the ball exerts force onto the wall, the wall also exerts an equal and opposite force onto the ball. Therefore, a force has also acted on the wall.

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