A-LevelMathematicsMechanics9709/41 · Oct/Nov 2020 · Q57 Marks

Two particles of masses 0.8 kg and 0.2 kg are connected by a light inextensible string that passes over a fixed smooth pulley. The system is released from rest with both particles 0.5 m above a horizontal floor (see diagram). In the subsequent motion the 0.2 kg particle does not reach the pulley. [Figure 5.1]

(a)Show that the magnitude of the acceleration of the particles is 6 m s⁻² and find the tension in the string.[4]
(b)When the 0.8 kg particle reaches the floor it comes to rest. Find the greatest height of the 0.2 kg particle above the floor.[3]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.

[M1] Apply Newton's 2nd law to either particle or to the system
[A1] Any 2 correct equations
[M1] Attempt to solve for either a or T
[A1] AG. Both correct
[M1] Attempt to find v or v² as 0.8 kg particle reaches the ground using a from 5(a)
[M1] Attempt to find the extra height reached by 0.2 kg particle using v² from previous M1 mark
[A1] Greatest height = 0.5 + 0.5 + 0.3 = 1.3 m

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