AS Daily A Level Physics question
A lab hoist lifts a 50 kg crate vertically at steady speed. In Test 1, the speed is 0.40 m s^-1 and the hoist draws 400 W from the mains. In Test 2, the speed is increased to 0.60 m s^-1 and the input power rises to 520 W. Neglect air resistance. Which statement best describes how the hoist’s efficiency changes from Test 1 to Test 2?
Answer
The correct answer is A.
Correct: A — The efficiency increases by about 15%. A is correct because the useful output power is the rate of gain of GPE, m g v, so it scales with speed: from 50×9.81×0.40 ≈ 196 W to 50×9.81×0.60 ≈ 294 W; dividing by input powers gives efficiencies ≈ 196/400 = 0.490 and ≈ 294/520 = 0.566, so the relative increase is about (0.566/0.490 − 1) ≈ 15%. B is wrong because although input power rose, the useful output rose by a larger fraction (about +50% vs +30%), so efficiency cannot decrease. C is wrong because a ~40% rise would require the efficiency ratio to be ≈1.4; the correct ratio is ≈1.15. D is wrong because output increased much more than input; the efficiency change is not negligible.