A-LevelMathematicsMechanics9709/52 · Oct/Nov 2018 · Q710 Marks
A rough horizontal rod AB of length 0.45 m rotates with constant angular velocity 6 rad s⁻¹ about a vertical axis through A. A small ring R of mass 0.2 kg can slide on the rod. A particle P of mass 0.1 kg is attached to the mid-point of a light inextensible string of length 0.6 m. One end of the string is attached to R and the other end of the string is attached to B, with angle RPB = 60° (see diagram). R and P move in horizontal circles as the system rotates. R is in limiting equilibrium. [Figure 7.1]
- (i)Show that the tension in the portion PR of the string is 1.66 N, correct to 3 significant figures.[5]
- (ii)Find the coefficient of friction between the ring and the rod.[5]
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 2018). The mark or mark type is shown in brackets.
- [B1] Tcos30 + Ucos30 = 0.1g (= 1)
- [M1A1] Tcos60 – Ucos60 = 0.1 × 6² × 0.3 ( = 1.08)
- [M1] Attempt to eliminate U
- [AG] T ( = 1.65735) = 1.66 N
- [M1] F – Tcos60 = 0.2 × 6² × 0.15 or R = 0.2g + Tcos30
- [A1] F (= 1.9086) = 1.91 N
- [A1] R ( = 3.4353) = 3.44 N
- [M1] μ = 1.9086/3.4353
- [A1] μ = 0.556
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