(i)[4]
Determine the work done by the friction force as the particle moves from $P$ to $Q$.
(ii)[4]
Hence determine the speed of the particle at $Q$.
(iii)[3]
Determine the value of $h$.
Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
The figure gives the vertical cross-section $PQR$ of a slide. Segment $PQ$ is a straight section of length $8\,\text{m}$, making an angle $\alpha$ with the horizontal, where $\sin\alpha = 0.8$. The straight section $PQ$ is tangent to the curved section $QR$, and $R$ is $h\,\text{m}$ above the level of $P$. The straight section $PQ$ is rough, whereas the curved section $QR$ is smooth. A particle of mass $0.25\,\text{kg}$ is projected from $P$ towards $Q$ with speed $15\,\text{m s}^{-1}$ and comes to rest at $R$. The coefficient of friction between the particle and $PQ$ is $0.5$.