Mathematics 9709 · AS & A Level · Energy, work and power

Energy, work and power — practice question

Points $A$, $B$ and $C$ are on the line of greatest slope of a plane inclined at $30^\circ$ to the horizontal, with $AB = 1\,\text{m}$ and $BC = 1\,\text{m}$, as shown in the diagram. A particle of mass $0.2\,\text{kg}$ is let go from rest at $A$ and slides down the plane. The section from $A$ to $B$ is smooth, while the section from $B$ to $C$ is rough, with coefficient of friction $\mu$ between the plane and the particle.
(a)[8]

For $\mu = \tfrac{1}{3}\sqrt{3}$, determine the particle’s speed at $C$.

(b)[4]

Instead, if the particle is brought to rest at $C$, determine the exact value of $\mu$.

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: Use PE loss or KE gain from $A$ to $B$, e.g. $0.2 \times 10 \times 0.5 = \tfrac12 \times 0.2 v_B^2$

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