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AS Daily A Level Physics question

2026-06-21 OCR A Dynamics: terminal velocity & drag (M3.2) OCR-A Module 3.2 Forces in action: drag and terminal speed (qualitative) OCR-A Module 3.1/3.2 Newton’s laws: zero resultant at terminal velocity

In a lab, a single paper coffee filter dropped from rest quickly reaches a steady falling speed of 1.5 m/s. Stacking two identical filters together keeps the cross-sectional area essentially the same but doubles the weight. Over this speed range, measurements show the air resistance on the filters increases with the square of speed. Neglect buoyancy. Which estimate for the steady speed of the two-filter stack is most appropriate?

  1. A About 2.1 m/s, because the speed must increase by a factor of the square root of 2 to balance the larger weight with larger drag. (correct)
  2. B About 3.0 m/s, because doubling the weight requires doubling the terminal speed.
  3. C Still about 1.5 m/s, because terminal speed depends only on shape and area.
  4. D About 2.25 m/s, because doubling the weight increases the speed by 50%.

Answer

The correct answer is A.

Correct: A — About 2.1 m/s, because the speed must increase by a factor of the square root of 2 to balance the larger weight with larger drag. A is correct because at terminal speed the upward resistive force equals the weight; with drag ∝ v^2, doubling weight makes terminal speed increase by √2, so 1.5 × 1.41 ≈ 2.1 m/s. B assumes a linear relation between drag and speed; if v doubled, drag would quadruple, which would overbalance the weight. C ignores Newton’s laws: terminal speed depends on balancing forces, so increasing weight while keeping area the same must change the terminal speed. D misapplies percentages and the square-root scaling; doubling weight does not give a 50% speed increase—√2 is about a 41% increase, not 50%.

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