Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
Particles $P$ and $Q$ have masses $0.5\,\text{kg}$ and $m\,\text{kg}$ respectively, and they are connected by a light inextensible string. The string runs over a fixed smooth pulley mounted at the top of two inclined planes. At the start, both particles are at rest, with $P$ on a smooth plane at $30^\circ$ to the horizontal and $Q$ on a plane at $45^\circ$ to the horizontal. The string is taut, and the particles may travel along the lines of greatest slope of the two planes. A force of magnitude $0.8\,\text{N}$ is applied to $P$ down the plane, making $P$ move down the plane (see diagram).
(a)[5]
With $\mu = 0.3$, and with the plane supporting $Q$ smooth, find the tension in the string.
(b)[5]
Now the plane carrying $Q$ is rough, and after each particle has travelled a distance of $1\,\text{m}$, their speed is $0.6\,\text{m s}^{-1}$. The work done against friction during this part of the motion is $0.5\,\text{J}$. Use an energy method to determine the value of $m$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use Newton’s second law for particle or system” …