Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
$P$ and $Q$ are two fixed points on the line of greatest slope of an inclined plane. Point $Q$ is $0.45 \text{ m}$ above the level of $P$. A particle with mass $0.3 \text{ kg}$ moves in the upward direction along $PQ$.
(i)[3]
Since the plane is smooth and the particle only just gets to $Q$, determine the speed at which it goes through $P$.
(ii)[4]
Now suppose instead that the plane is rough. The particle passes through $P$ with the same speed as in part (i), and only just reaches a point $R$ located between $P$ and $Q$. The work done against the frictional force while moving from $P$ to $R$ is $0.39 \text{ J}$. Determine the potential energy gained by the particle in travelling from $P$ to $R$ and hence determine the height of $R$ above the level of $P$.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applies KE lost = PE gained or $v^2 = u^2 - 2g\sin\alpha \times \frac{0.45}{\sin\alpha}$” …