Mathematics 9709 · AS & A Level · Forces and equilibrium

Forces and equilibrium — practice question

A block with mass $11\,\text{kg}$ is initially stationary on a rough plane that is inclined at $30^\circ$ to the horizontal. A force is applied to the block up the plane, along a line of greatest slope. When the force has magnitude $2X\,\text{N}$, the block is just about to move down the plane, and when the force has magnitude $9X\,\text{N}$, the block is just about to move up the plane.
(i)[3]

Find the value of $X$.

(ii)[4]

Find the coefficient of friction between the block and the plane.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: Resolve the forces parallel to the plane in order to obtain two equations

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