June 2022 Paper 3 Q8

OCR ACurrent spec2 marksResolving Forces

A sledge on horizontal ground with a rope attached to its front, rising at 15° above the horizontal

A child attempts to drag a sledge along horizontal ground by means of a rope attached to the sledge. The rope makes an angle of 15° with the horizontal (see diagram).

Given that the sledge remains at rest and that the frictional force acting on the sledge is 60 N, find the tension in the rope. [2]

Mark scheme

Scheme	Marks	AO
\(T\cos 15 = 60\)	M1	1.1
\(T = 62.1\) (N)	A1	1.1
	[2]

Notes

M1: Resolve horizontally, correct number of terms, allow sin/cos confusion (e.g. \(T\sin 15 = 60\) scores M1 but \(T = 60\cos 15\) scores M0)
Where \(T\) is the tension in the rope

A1: awrt 62.1 – allow the exact answer of \(60(\sqrt{6} - \sqrt{2})\)
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