Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
Particles $P$ and $Q$ have masses $0.3\,\text{kg}$ and $0.6\,\text{kg}$ respectively, and are connected to the two ends of a light inextensible string. The string runs over a smooth pulley at the point $B$, where the inclined planes $AB$ and $BC$ meet. $P$ is on the smooth plane $AB$, which is inclined at an angle $\theta$ to the horizontal and has $\sin \theta = 0.4$. $Q$ is on plane $BC$, which is inclined at $30^\circ$ to the horizontal. The string is taut, and the particles can move along the lines of greatest slope of the planes (see diagram). The particles are released from rest.
(a)[5]
Since the plane $BC$ is smooth, Find the tension in the string and the acceleration of $Q$.
(b)[4]
Instead, the plane $BC$ is rough. The work done against the frictional force when $Q$ moves $2\,\text{m}$ down the plane is $1.8\,\text{J}$. Assume that $P$ does not reach the pulley and that $Q$ does not reach $C$. Use an energy method to find the speed of $Q$ when it has moved $2\,\text{m}$ down the plane.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Uses Newton’s second law for $P$, $Q$ or the system.” …