A-LevelMathematicsMechanics9709/42 · Oct/Nov 2018 · Q48 Marks
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.
- (i)Show that the greatest value of X for which P remains stationary is 6.2.[4]
- (ii)Given instead that X = 0.8, find the acceleration of P.[4]
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] T = 0.7g
- [B1] R = 0.4g × 4/5 [ = 16/5 = 3.2] Normal reaction on particle P
- [M1] [X+0.4g × 3/5 - F - T = 0] Attempt to resolve forces along the plane
- [A1] X = 6.2 AG
- [M1] [0.7g – T= 0.7a] [T-0.8 – 0.4g × 3/5 – F= 0.4a] For using Newton's 2nd law for both particle P and particle Q or the system equation
- [A1] Both equations correct or system equation correct
- [M1] Solve either the system equation or solve two simultaneous equations to find a
- [A1] a = 2 ms-2
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