A-LevelMathematicsMechanics9709/42 · Feb/Mar 2024 · Q35 Marks

A crate of mass 600 kg is being pulled up a line of greatest slope of a rough plane at a constant speed of 2 m s⁻¹ by a rope attached to a winch. The plane is inclined at an angle of 30° to the horizontal and the rope is parallel to the plane. The winch is working at a constant rate of 8 kW.

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2024). The mark or mark type is shown in brackets.

[B1] Driving force = 8000/2 or 4000. Use of F = P/v, oe. E.g. DF×2=8000.
[B1] R = 600g cos30[=3000√3=5196.152423]
[*M1] their Driving force – 600g sin 30-F=0. For attempt to resolve parallel to the plane; 3 terms; allow sign errors; allow sin/cos mix; allow g missing; F not resolved. Allow with just DF.
[DM1] Use of F = µR. To form an equation in u only where R is a component of weight or mass.
[A1] µ = 0.192 or √3/9. Awrt 0.192 [0.1924500897]. Oe, e.g. 1/(3√3). Allow 2sf.

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Topic: Mechanics, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source: A-Level Mathematics, Feb/Mar 2024 Paper 4 Variant 2, question 3.

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