A-LevelMathematicsMechanics9709/51 · Oct/Nov 2017 · Q14 Marks
A hollow cylinder with a rough inner surface has radius 0.5 m. A particle P of mass 0.4kg is in contact with the inner surface of the cylinder. The particle and cylinder rotate together with angular speed 6 rad s⁻¹ about the vertical axis of the cylinder, so that the particle moves in a horizontal circle (see diagram). Given that P is about to slip downwards, find the coefficient of friction between P and the surface of the cylinder.
- A hollow cylinder with a rough inner surface has radius 0.5 m. A particle P of mass 0.4kg is in contact with the inner surface of the cylinder. The particle and cylinder rotate together with angular speed 6 rad s⁻¹ about the vertical axis of the cylinder, so that the particle moves in a horizontal circle (see diagram). Given that P is about to slip downwards, find the coefficient of friction between P and the surface of the cylinder.[4]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.
- [B1] R = 0.4 × 6² × 0.5 ( = 7.2 N) Uses Newton's Second Law horizontally and a = r ω² .
- [B1] F = 0.4 g Resolve vertically.
- [M1] μ = 4/7.2 Use F = μR.
- [A1] μ = 0.556 or 5/9 Accept μ = 0.56.
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