A vertical spring with force constant k is fixed on a table. A ball of mass m at a height h above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance d. The net work done in the process is

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(1) mg(h+d)-1/2kd². Given: the ball falls a height h onto the spring and then compresses it by d. Idea: net work is the sum of the work done by each force acting on the ball. Gravity acts downwards over the whole descent h+d, so W_gravity=mg(h+d), positive. The spring pushes upwards while the ball moves down, so its work is negative: W_spring=-1/2kd². Wₙₑₜ=mg(h+d)-1/2kd². Note that if d were the maximum compression the ball would be at rest there and this expression would come out as zero, which is the usual way the equation is used.

A vertical spring with force constant k is fixed on a table. A ball of mass m at a height h above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance d. The net work done in the process is

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