Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
$P$ and $Q$ are two fixed points lying on the line of greatest slope of an inclined plane. The point $Q$ is $0.45\,\text{m}$ higher than the level of $P$. A particle with mass $0.3\,\text{kg}$ travels upwards along $PQ$.
(a(i))[3]
Since the plane is smooth and the particle just reaches $Q$, determine the speed at which it passes through $P$.
(a(ii))[4]
Now suppose instead that the plane is rough. The particle goes through $P$ with the same speed as in part (i), and it just reaches a point $R$ situated between $P$ and $Q$. The work done against the frictional force in travelling from $P$ to $R$ is $0.39\,\text{J}$. Determine the potential energy gained by the particle as it moves from $P$ to $R$ and therefore calculate 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: “From KE loss = PE gain or $0^2=u^2-2(g\sin\alpha)(0.45/\sin\alpha)$” …