Mathematics 9709 · AS & A Level · Forces and equilibrium

Forces and equilibrium — practice question

A particle with mass $m\text{ kg}$ is at rest on a rough plane that is inclined at $30^\circ$ to the horizontal. A force of magnitude $10\text{ N}$ acting on the particle up a line of greatest slope of the plane is just enough to prevent the particle from sliding down the plane. When a force of $75\text{ N}$ acts on the particle up a line of greatest slope of the plane, the particle is just about to slide up the plane.
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Determine $m$ and the coefficient of friction between the particle and the plane.

Worked solution & mark scheme

This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: Write $F = \mu mg\cos30$

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