A-LevelMathematicsMechanics9709/41 · May/June 2020 · Q57 Marks

A child of mass 35 kg is swinging on a rope. The child is modelled as a particle P and the rope is modelled as a light inextensible string of length 4 m. Initially P is held at an angle of 45° to the vertical (see diagram). [The diagram]

(a)Given that there is no resistance force, find the speed of P when it has travelled half way along the circular arc from its initial position to its lowest point.[4]
(b)It is given instead that there is a resistance force. The work done against the resistance force as P travels from its initial position to its lowest point is X J. The speed of P at its lowest point is 4 m s⁻¹. Find X.[3]

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Mark scheme

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

[M1] Attempt at finding PE lost
[A1] PE lost = 35g (4cos22.5 – 4cos45)
[M1] ½ × 35v² = 35g (4cos22.5 – 4cos45)
[A1] Speed = 4.16 ms⁻¹ (4.1643...)
[M1] Use of the work-energy equation in the form: PE lost = KE gain + WD against resistance
[A1] ½ × 35 × 4² = 35g (4 – 4cos45) – X
[A1] X = 130 (130.05...)

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