A student observes a rubber ball hitting a wall and bouncing off. She states: \"

Question

A student observes a rubber ball hitting a wall and bouncing off. She states: "In this situation the wall will exert a larger force on tha ball than the ball exerts on the wall, because the ball undergoes acceleration but the wall doesn't move. That is, the ball goes from an intial speed to zero, and then from zero to rebound speed, but the wall does not accelerate since it is stationary the whole time."

What, if anything, is wrong with this statement? If something is wrong, identify it, and explain how to correct it. If this statement is correct, explain why.

Explanation / Answer

The statement that the wall will exert a larger force on the ball than the ball exerts on the wall is wrong.

According to Newton's third law, if a body A exerts force on body B, then body B also exerts force on body A which will be equal in magnitude and opposite in direction.

So, even in the situation described in the question, wall is exerting force on the ball, therefore, according to Newton's third law, the ball will also exert force on the wall which will be equal in magnitude.

The mistake in the argument above is, the wall is in contact with earth, so effectively the force exerted by the ball is on earth. This force can easily change the velocity of the ball because its mass will be less. But the same force which is acting on the wall ( or earth) will try to accelerate earth, this acceleration will be negligible because the mass of the earth is very large.

So, the force exerted by the wall(or earth) on the ball is same in magnitude to force exerted by the ball on the wall( or earth). But the accelerations are different because their masses are different. In fact, earth's acceleration due to this force will be almost zero.

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