A spherical ball of mass 2 kg is released from rest from a height of 10 m above a sand surface. It penetrates 10 cm into the sand and then comes to rest. Taking g = 10 m·s⁻², what is the average resistive force exerted by the sand on the ball during penetration?
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Question

A spherical ball of mass 2 kg is released from rest from a height of 10 m above a sand surface. It penetrates 10 cm into the sand and then comes to rest. Taking g = 10 m·s⁻², what is the average resistive force exerted by the sand on the ball during penetration?

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G1 Physics · Accepted Answer

The ball starts from rest and finally comes to rest, so its total change in kinetic energy from the release point to the final point is zero. During the complete downward displacement, gravity does positive work through 10 m + 0.10 m = 10.10 m. Hence, W(gravity) = mg(10.10) = 2×10×10.10 = 202 J. The sand force acts upward while the ball moves downward through 0.10 m, so W(sand) = -F(0.10). By the work-energy theorem, W(gravity)+W(sand) = 0. Therefore, 202-0.10F = 0. Thus, F = 202 ÷ 0.10 = 2020…