A-LevelMathematicsMechanics9709/42 · Feb/Mar 2021 · Q59 Marks

A block of mass 5 kg is being pulled along a rough horizontal floor by a force of magnitude X N acting at 30° above the horizontal (see diagram). The block starts from rest and travels 2 m in the first 5 s of its motion.

(a)Find the acceleration of the block.[2]
(b)Given that the coefficient of friction between the block and the floor is 0.4, find X.[4]
(c)The block is now placed on a part of the floor where the coefficient of friction between the block and the floor has a different value. The value of X is changed to 25, and the block is now in limiting equilibrium. Find the value of the coefficient of friction between the block and this part of the floor.[3]

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Mark scheme

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

[1] Use of s = ut + ½at² OE using u = 0, s = 2 and t = 5.
[1] Allow a = 4/25
[1] R = 5g - X sin 30
[1] Apply Newton's 2nd law to the block, using their a.
[1] Use F = 0.4R to obtain an equation in X only, using their R which must involve 5g and a component of X only.
[1] X = 19.5 (3sf)
[1] R = (5g - 25 sin 30) [R = 37.5]
[1] F = 25 cos 30 [F = 25√3/2]
[1] Allow μ = √3/3 or μ = 1/√3.

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