A-LevelMathematicsMechanics9709/43 · May/June 2021 · Q710 Marks

A particle P of mass 0.3 kg rests on a rough plane inclined at an angle θ to the horizontal, where sin θ = 7/25. A horizontal force of magnitude 4 N, acting in the vertical plane containing a line of greatest slope of the plane, is applied to P (see diagram). The particle is on the point of sliding up the plane.

(a)Show that the coefficient of friction between the particle and the plane is 3/4.[4]
(b)The force acting horizontally is replaced by a force of magnitude 4 N acting up the plane parallel to a line of greatest slope. Find the acceleration of P.[3]
(c)Starting with P at rest, the force of 4 N parallel to the plane acts for 3 seconds and is then removed. Find the total distance travelled until P comes to instantaneous rest.[3]

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Mark scheme

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

[M1] Resolving forces perpendicular to the plane or parallel to the plane. Allow use of θ = 16.3°
[A1] Two correct equations
[M1] For use of F = µR
[A1] AG Must be from correct and exact working, not using 16.3
[B1]
[M1] Use of Newton's second law
[A1]
[B1 FT] Distance s₁ in 3s and v after 3s; FT a from (b)
[M1] Apply Newton's 2nd law after 4 N removed, find a and use v² = u² + 2as to find extra distance s₂
[A1]

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