Mathematics 9709 · AS & A Level · Forces and equilibrium

Forces and equilibrium — practice question

Blocks $P$ and $Q$, with masses $m\,\text{kg}$ and $5\,\text{kg}$ respectively, are joined by the ends of a light inextensible string. The string passes over a small smooth pulley fixed at the top of a rough plane inclined at $35^\circ$ to the horizontal. Block $P$ rests on the plane, while block $Q$ hangs vertically below the pulley (see diagram). The coefficient of friction between block $P$ and the plane is $0.2$.
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Determine the values of $m$ for which the two blocks stay at rest.

Worked solution & mark scheme

This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: Take $F = 0.2mg\cos35$ as the maximum possible value of $F$.

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