AS Daily A Level Physics question
A warehouse hoist lifts the same 80 kg crate vertically at constant speed. When it raises the crate at 0.40 m/s, the electrical input power is 1.6 kW. The load and the machine’s efficiency stay the same. If the lifting speed is increased to 0.80 m/s, what is the new input power?
Answer
The correct answer is C.
Correct: C — It doubles to 3.2 kW. A halves to 0.8 kW — wrong because lifting faster increases the rate of gain of gravitational potential energy, so power cannot decrease. B is unchanged at 1.6 kW — wrong because at constant load, the output power is proportional to lifting speed, so doubling speed doubles required power. C — correct because output power ∝ speed (m g v), and with the same efficiency the input power scales the same way: 1.6 kW × 2 = 3.2 kW. D quadruples to 6.4 kW — wrong because this assumes a square dependence on speed, which does not apply to vertical lifting at constant speed.