A ball of mass m falls from height h above the free end of a vertical spring of force constant k, then compresses it by distance d. Find the net work done by gravity and spring during compression/fall.
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Question

A ball of mass m falls from height h above the free end of a vertical spring of force constant k, then compresses it by distance d. Find the net work done by gravity and spring during compression/fall.

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G1 Physics · Accepted Answer

Step 1 — Principle: Elastic spring potential energy is Uₛ = ½kx². Step 2 — Working: Gravity acts over h+d and does +mg(h+d) work. Step 3 — Working: The restoring spring force does −∫₀ᵈkx dx=−½kd². Step 4 — Working: Net work is mg(h+d)−½kd². Correct answer: A — mg(h+d)−½kd².