Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
A particle $P$ of mass $0.2\,\text{kg}$ is at rest on a rough plane tilted at $30^\circ$ to the horizontal. The coefficient of friction between $P$ and the plane is $0.3$. A force of magnitude $T\,\text{N}$ acts on $P$ upwards at $15^\circ$ above a line of greatest slope of the plane (see diagram).
(i)[6]
Find the smallest value of $T$ for which the particle stays at rest.
(ii)[5]
The force of magnitude $T\ \text{N}$ is now taken away. Another force, of magnitude $0.25\ \text{N}$, acts on $P$ up the plane and is parallel to a line of greatest slope of the plane. From rest, $P$ slides down the plane. Once it has moved a distance of $3\ \text{m}$, $P$ passes through the point $A$. Use an energy method to determine the speed of $P$ at $A$.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “$R = 0.2g\cos 30 - T\sin 15$” …