Question 6 — A crane lifts a mass - Questions at the end of the chapter - Chapter 7 - Work, Energy, and Simple Machines (Exploration)

Last updated at July 16, 2026 by

A crane lifts a mass m to the 10th floor of a building in a certain time. It then raises the same mass to the 20th floor of the same building in double the time. How much more energy and power are required? Assume that the height of all floors is equal.

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Let the height to the 10th floor be h (so the 20th floor is 2h ) and the first time be t .

Energy: E 1 = mgh ; E 2 = mg(2h) = 2mgh — so twice the energy (an extra mgh ).

Power: P 1 = mgh t ; P 2
= 2mgh 2t
= mgh t — the power is the same .

Energy and power for the crane
First lift — to the 10th floor
height h , time t → energy E = mgh , power P = mgh/t
↓
Second lift — to the 20th floor
height is 2h , so energy = mg(2h) = 2E — twice the energy
↓
But it takes double the time
P'
= 2mgh 2t
= mgh t
↓
Twice the energy, but the same power
← Back to: 7.5 Power
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