Mathematics 9709 · AS & A Level · Forces and equilibrium

Forces and equilibrium — practice question

A particle $P$ with mass $0.5\text{ kg}$ is at rest on a rough plane inclined at angle $\alpha$ to the horizontal, where $\sin \alpha = 0.28$. A force of magnitude $0.6\text{ N}$, applied upwards to $P$ at angle $\alpha$ to a line of greatest slope of the plane, is just enough to stop $P$ from sliding down the plane.
(i)[2]

Determine the normal component of the contact force acting on $P$.

(ii)[3]

Determine the frictional component of the contact force on $P$.

(iii)[2]

Determine the coefficient of friction between $P$ and the plane.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: For forces resolved perpendicular to the plane: $R + 0.6\sin\alpha = 0.5g\cos\alpha$

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