Mathematics 9709 · AS & A Level · Forces and equilibrium

Forces and equilibrium — practice question

A block of mass $2.5\,\text{kg}$ rests on a plane inclined at $30^\circ$ to the horizontal. A light string, which is $20^\circ$ above the line of greatest slope, keeps the block in equilibrium. The tension in the string is $T\,\text{N}$, as shown in the diagram. The coefficient of friction between the block and plane is $\frac{1}{4}$. The block is in limiting equilibrium and is on the point of moving up the plane.
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Determine the value of $T$.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: Resolving forces perpendicular to the plane gives $R+T\sin20=2.5g\cos30$

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