A particle of mass 12 kg is stationary on a rough plane inclined at an angle of 25° to the horizontal. A pulling force of magnitude P N acts at an angle of 8° above a line of greatest slope of the plane. This force is used to keep the particle in equilibrium. The coefficient of friction between the particle and the plane is 0.3.

Mark scheme

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

1. [M1] For resolving either parallel to or perpendicular to the plane Three relevant terms in either equation.
2. [A1] Pcos8=F+12g sin 25
3. [A1] 12g cos 25 = R + P sin 8
4. [M1] F=0.3R Use F = 0.3R, where R must involve components of both 12g and P.
5. [M1] Pcos 8 = 0.3(12g cos 25 – Psin8)+12g sin 25 For attempting to solve for P, using equations with the correct number of relevant terms in both.
6. [A1] P=80.8 From P=80.755... Allow P≤ 80.8 If more than one case is considered for direction of friction then a choice must be made for final answer.