AS Daily A Level Physics question
A worker (mass 80 kg) runs at 5.0 m/s and jumps onto a stationary trolley on low-friction wheels; they stick together and roll off as one. Assume external horizontal forces are negligible during the short collision. For quick estimates, compare the shared speed immediately after for two cases: Case 1: trolley mass M = 40 kg; Case 2: trolley mass M = 400 kg. Which option is most consistent with these two estimates?
Answer
The correct answer is D.
Correct: D — About 3.3 m/s in Case 1; about 0.8–0.9 m/s in Case 2. With total horizontal momentum unchanged, v ≈ (m v0)/(m+M) = (80×5)/(80+40) ≈ 3.3 m/s for M=40 kg, and (80×5)/(80+400) ≈ 0.83 m/s for M=400 kg. A says the speed is unchanged at 5.0 m/s, but the combined mass is larger so the speed must drop. B underestimates the heavy-trolley case (0.5 m/s) by ignoring the worker’s 80 kg in the total mass. C gives 2.5 m/s for M=40 kg (which would match equal masses, not 80 vs 40) and overestimates the heavy case at 1.0 m/s. D matches the calculated values for both masses.