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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.
Show Answer
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: \(P_1 = \dfrac{mgh}{t}\); \(P_2 = \dfrac{2mgh}{2t} = \dfrac{mgh}{t}\) — the power is the same .
