AS Daily A Level Physics question
Two identical coffee-filter cones are dropped in still air. A single filter reaches a steady terminal speed of 1.5 m/s. In a wind-tunnel test on this shape, the drag force is 0.05 N at 1.5 m/s and 0.20 N at 3.0 m/s. If two filters are nested together (mass doubles but shape and area are unchanged), what is the best estimate of their terminal speed?
Answer
The correct answer is C.
Correct: C — 2.1 m/s. A assumes terminal speed depends only on shape; but with the same area the drag at a given speed is unchanged, and doubling mass doubles weight, so a higher speed is needed. B assumes drag is proportional to speed so you’d need double the speed, but the data show doubling speed quadruples drag, so less than 3.0 m/s is required. C uses that at 1.5 m/s the single filter’s drag equals its weight (0.05 N), so the nested pair needs 0.10 N; since the drag quadruples when speed doubles, drag ∝ speed^2 here, so speed must rise by √2: 1.5 × √2 ≈ 2.1 m/s. D comes from treating drag roughly linear with speed or linearly interpolating; at 2.0 m/s the drag would be about (2.0/1.5)^2 × 0.05 ≈ 0.089 N, still below the required 0.10 N.