A-LevelMathematicsMechanics9709/42 · Oct/Nov 2019 · Q711 Marks

Two particles P and Q, of masses 0.3 kg and 0.2 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 smooth plane. The plane is inclined at an angle θ to the horizontal, where sin θ = 3/5. P lies on the plane and Q hangs vertically below the pulley at a height of 0.8 m above the floor (see diagram). P is released from rest and Q moves vertically downwards. [Figure 7.1]

(i)Find the tension in the string and the magnitude of the acceleration of the particles.[5]
(ii)Find the time, from the instant at which P is released, for Q to reach the floor.[2]
(iii)When Q hits the floor the string becomes slack. Find the time, from the instant at which P is released, for the string to become taut again.[4]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

[M1] Use of Newton's second law for P or Q or the system
[A1] Two correct equations Allow use of θ = 36.9
[M1] For solving either the system for a or for solving a pair of simultaneous equations for a or T
[A1] a = 0.4 ms⁻²
[A1] T = 1.92 N
[M1] For use of the constant acceleration equations with their a from 7(i) and a ≠ ± g for a complete method to find t
[A1] t = 2 s
[B1FT] Using v = u + at with u = 0 Allow FT for their unsimplified v = at or v² = 2as with a from (i), t from (ii) and s = 0.8
[M1] Using Newton's second law for P to find a ≠ ± g
[M1] Use of the constant acceleration equation(s) to find the time taken for P to return to the position where the string first became slack.
[A1] Total time = 2 + 0.266... = 2 + 4/15 = 2.27 = 34/15 s

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