A-LevelMathematicsMechanics9709/42 · Oct/Nov 2019 · Q611 Marks

A block of mass 3 kg is initially at rest on a rough horizontal plane. A force of magnitude 6N is applied to the block at an angle of θ above the horizontal, where cos θ = 4/25. The force is applied for a period of 5 s, during which time the block moves a distance of 4.5 m.

(i)Find the magnitude of the frictional force on the block.[4]
(ii)Show that the coefficient of friction between the block and the plane is 0.165, correct to 3 significant figures.[3]
(iii)When the block has moved a distance of 4.5 m, the force of magnitude 6 N is removed and the block then decelerates to rest. Find the total time for which the block is in motion.[4]

Mark scheme

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

[M1] For use of s = ut + ½at² to find a
[A1] a = 0.36
[M1] Resolving horizontally. Allow use of θ = 16.3
[A1] F = 4.68 N
[B1] R = 3g - 6sin16.3 = 3g - 6x(7/25) [= 28.32]
[M1] Use of F = μR
[A1] μ = 0.165 (0.165254...) AG. Allow μ = 39/236
[B1FT] For velocity at t = 5 ft on their a from 6(i)
[M1] Using Newton's second law with new frictional force
[M1] Using constant acceleration equations which would lead to a positive value of t
[A1] Total time = 5 + 1.09 = 6.09 s

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