A-LevelMathematicsMechanics9709/41 · Oct/Nov 2019 · Q37 Marks

A block of mass 3 kg is at rest on a rough plane inclined at 60° to the horizontal. A force of magnitude 15 N acting up a line of greatest slope of the plane is just sufficient to prevent the block from sliding down the plane.

(i)Find the coefficient of friction between the block and the plane.[5]
(ii)The force of magnitude 15 N is now replaced by a force of magnitude XN acting up the line of greatest slope. Find the greatest value of X for which the block does not move.[2]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

[B1] R = 3 g cos 60
[M1] Use F = µR
[M1] Resolve forces parallel to the plane, 3 terms ([3gsin 60 – µ3gcos60 – 15 = 0])
[A1] Correct equation [3gsin 60 – µ3gcos60 – 15 = 0]
[A1] μ = 0.732 (Allow μ = √3 −1)
[M1] [Maximum force = 3gsin60 + F = 3gsin60 + µ3gcos60]
[A1] X = 37(.0) (Allow X = 15(2√3-1))

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Topic: Mechanics, A-Level Mathematics (syllabus 9709). Structured question, 7 marks.
Source: A-Level Mathematics, Oct/Nov 2019 Paper 4 Variant 1, question 3.

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