A-LevelMathematicsMechanics9709/41 · May/June 2018 · Q712 Marks

The diagram shows a triangular block with sloping faces inclined to the horizontal at 45° and 30°. Particle A of mass 0.8 kg lies on the face inclined at 45° and particle B of mass 1.2 kg lies on the face inclined at 30°. The particles are connected by a light inextensible string which passes over a small smooth pulley P fixed at the top of the faces. The parts AP and BP of the string are parallel to lines of greatest slope of the respective faces. The particles are released from rest with both parts of the string taut. In the subsequent motion neither particle reaches the pulley and neither particle reaches the bottom of a face. [Figure X.X]

(i)Given that both faces are smooth, find the speed of A after each particle has travelled a distance of 0.4 m.[6]
(ii)It is given instead that both faces are rough. The coefficient of friction between each particle and a face of the block is µ. Find the value of µ for which the system is in limiting equilibrium.[6]

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Mark scheme

Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.

[M1] Apply Newton 2nd law to either A or to B or to the system
[A1] One correct equation
[A1] A second correct equation
[M1] Solve for a
[M1] Use v² = u² + 2as with u = 0
[A1] v = 0.370 so speed of A is 0.370 m s⁻¹
[M1] Attempt KE gain or PE loss
[A1] v is the required speed of A
[M1] 4 term energy equation
[M1] Solving for v
[A1] v = 0.370 so speed of A is 0.370 m s⁻¹
[B1] For either R_A or R_B
[M1] Either F_A or F_B used
[M1] Resolve parallel to the plane either for both particles A and B or for the system equation
[A1] Correct equation(s)
[M1] Eliminate T and solve for µ
[A1] µ = 0.0214

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