A-LevelMathematicsMechanics9709/41 · Oct/Nov 2017 · Q710 Marks

Two particles A and B of masses 0.9 kg and 0.4 kg respectively are attached to the ends of a light inextensible string. The string passes over a fixed smooth pulley which is attached to the top of two inclined planes. The particles are initially at rest with A on a smooth plane inclined at angle θ° to the horizontal and B on a plane inclined at angle 25° to the horizontal. The string is taut and the particles can move on lines of greatest slope of the two planes. A force of magnitude 2.5 N is applied to B acting down the plane (see diagram). [Figure 7.1]

(i)For the case where θ = 15 and the plane on which B rests is smooth, find the acceleration of B.[5]
(ii)For a different value of θ, the plane on which B rests is rough with coefficient of friction between the plane and B of 0.8. The system is in limiting equilibrium with B on the point of moving in the direction of the 2.5 N force. Find the value of θ.[5]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

[M1] For applying Newton's 2nd law to either particle (correct number of terms)
[A1] T - 0.9 g sin 15 = 0.9a
[A1] 2.5 + 0.4 g sin 25 – T = 0.4a
[M1] 1.3a = 1.86... Solving simultaneously for a
[A1] a = 1.43 m s⁻²
[B1] F = 0.8 × 0.4g cos 25
[M1] 2.5 + 0.4 g sin 25 – T – F = 0 For using equilibrium of forces acting on particle B with 4 terms
[M1] T - 0.9 g sin θ = 0 For using equilibrium of forces acting on particle A with 2 terms
[M1] For solving for θ
[A1] θ = 8.2°

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