Two particles P and Q, of masses 0.4 kg and 0.7 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 edge of a rough plane. The coefficient of friction between P and the plane is 0.5. The plane is inclined at an angle α to the horizontal, where tan α = 3/4. Particle P lies on the plane and particle Q hangs vertically. The string between P and the pulley is parallel to a line of greatest slope of the plane [Figure X.X]. A force of magnitude XN, acting directly down the plane, is applied to P.

Q: What topic does this question test?

This question tests Mechanics in A-Level Mathematics (syllabus code 9709). It is worth 8 marks.

Q: Which exam paper is this question from?

This question appeared in the Cambridge A-Level Mathematics Oct/Nov 2018 examination, Paper 4 Variant 2 (9709_w18_qp_42.pdf).

Question

Two particles P and Q, of masses 0.4 kg and 0.7 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 edge of a rough plane. The coefficient of friction between P and the plane is 0.5. The plane is inclined at an angle α to the horizontal, where tan α = 3/4. Particle P lies on the plane and particle Q hangs vertically. The string between P and the pulley is parallel to a line of greatest slope of the plane [Figure X.X]. A force of magnitude XN, acting directly down the plane, is applied to P.

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