A-LevelMathematicsMechanics9709/41 · May/June 2019 · Q614 Marks

Two particles A and B, of masses 0.4 kg and 0.2 kg respectively, are connected by a light inextensible string. Particle A is held on a smooth plane inclined at an angle of θ° to the horizontal. The string passes over a small smooth pulley P fixed at the top of the plane, and B hangs freely 0.5 m above horizontal ground (see diagram). The particles are released from rest with both sections of the string taut. [Figure 6.1]

(i)Given that the system is in equilibrium, find θ.[3]
(ii)(a)It is given instead that θ = 20. In the subsequent motion particle A does not reach P and B remains at rest after reaching the ground. Find the tension in the string and the acceleration of the system.[4]
(ii)(b)Find the speed of A at the instant B reaches the ground.[2]
(ii)(c)Use an energy method to find the total distance A moves up the plane before coming to instantaneous rest.[5]

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 (May/June 2019). The mark or mark type is shown in brackets.

[M1] Resolve forces for A and for B
[M1] Eliminate T and solve for θ
[A1] θ = 30
[M1] Apply Newton's second law to A or to B or to the system
[A1] Two correct equations
[M1] Solve for a or T
[A1] Both correct
[M1] Attempt to find v using their a ≠ g
[A1] v = 1.03 ms⁻¹
[M1] Attempt KE loss or PE gain for particle A only after particle B hits the ground.
[A1ft] Both correct, d is distance moved up the plane after B hits ground
[M1] Apply KE loss = PE gain
[A1ft] Correct energy equation
[A1] Total dist A moves up plane = 0.5 + d = 0.654 m

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