Mathematics 9709 · AS & A Level · Forces and equilibrium

Forces and equilibrium — practice question

A block weighing $6.1\,\text{N}$ is stationary on a plane inclined at angle $\alpha$ to the horizontal, with $\tan \alpha = \frac{11}{60}$. The coefficient of friction between the block and the plane is $\mu$. A force of magnitude $5.9\,\text{N}$, applied parallel to the line of greatest slope, acts on the block.
(i)[5]

When the force is directed up the plane (see Fig. 1), the block stays at rest. Show that $\mu \geq \frac{4}{5}$.

(ii)[2]

When the force acts down the plane (see Fig. 2), the block slides downwards. Show that $\mu < \frac{7}{6}$.

(iii)[2]

When the block accelerates at $1.7\,\text{m s}^{-2}$ as the force acts down the plane, determine $\mu$.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: Split the forces into components parallel to the plane.

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