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Find $P$ and $\theta$.
Mathematics 9709 · AS & A Level · Forces and equilibrium
Forces and equilibrium — practice question
Four coplanar forces with magnitudes $50\,\text{N}$, $48\,\text{N}$, $14\,\text{N}$ and $P\,\text{N}$ act at a point in the directions shown in the diagram. The system is in equilibrium. Given that $\tan\alpha = \frac{7}{24}$, determine the values of $P$ and $\theta$.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Resolve the forces horizontally or vertically, for example $P\cos\theta = 48\cos\alpha - 14\sin\alpha$ or $P\sin\theta = 50 - 48\sin\alpha - 14\cos\alpha$.” …
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