A-LevelMathematicsMechanics9709/41 · May/June 2021 · Q13 Marks

A winch operates by means of a force applied by a rope. The winch is used to pull a load of mass 50 kg up a line of greatest slope of a plane inclined at 60° to the horizontal. The winch pulls the load a distance of 5 m up the plane at constant speed. There is a constant resistance to motion of 100 N. Find the work done by the winch.

Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

[M1] Force exerted by winch=50g sin60+100[=433.0+100=533.0] For resolving forces along the plane
[M1] Work done =5×(50gsin60+100) Use of WD = Force × distance
[A1] Work done = 2670 J
Alternative method for Question 1
[M1] PE increase = 50g×5sin 60 Correct dimensions
[M1] Work done = 50g×5sin60+100×5 Apply the work-energy equation, 3 terms
[A1] Work done = 2670 J

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Topic: Mechanics, A-Level Mathematics (syllabus 9709). Structured question, 3 marks.
Source: A-Level Mathematics, May/June 2021 Paper 4 Variant 1, question 1.

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