Mathematics 9709 · AS & A Level · Forces and equilibrium

Forces and equilibrium — practice question

Three blocks $P$, $Q$ and $R$, with masses $25\,\text{kg}$, $20\,\text{kg}$ and $m\,\text{kg}$ respectively, are held in equilibrium by three light inextensible strings $OP$, $OQ$ and $OR$. The strings $OP$ and $OR$ each pass over a small fixed smooth pulley, $A$ and $B$ respectively, and $P$ and $R$ hang vertically beneath the pulleys. Block $Q$ hangs vertically below point $O$. The angle between $OA$ and the vertical is $30^\circ$ and the angle $BOQ$ is $\alpha^\circ$ (see diagram).
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Determine the value of $m$ and the value of $\alpha$.

Worked solution & mark scheme

This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: By resolving the forces, obtain equations in $m$ and $\alpha$, for example $25g\cos30-20g-mg\cos\alpha=0$ and $25g\sin30-mg\sin\alpha=0$

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