Mathematics 9709 · AS & A Level · Forces and equilibrium

Forces and equilibrium — practice question

The diagram depicts a block of mass $10\,\text{kg}$ hanging under a horizontal ceiling from two strings, $AC$ and $BC$, whose lengths are $0.8\,\text{m}$ and $0.6\,\text{m}$ respectively; these strings are fixed to points on the ceiling. The angle $ACB = 90^\circ$. A horizontal force of magnitude $F\,\text{N}$ acts on the block, and the block is in equilibrium.
(a)[5]

When $F = 20$, find the tensions in both strings.

(b)[3]

Find the greatest value of $F$ for which the block stays in equilibrium in the position shown.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: Resolves forces into horizontal or vertical components, e.g. $0.8T_A-0.6T_B-20=0$ or $0.6T_A+0.8T_B-10g=0$

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