Mathematics 9709 · AS & A Level · Newton's laws of motion
Newton's laws of motion — practice question
Particles $P$ and $Q$, with masses $0.3\text{ kg}$ and $0.2\text{ kg}$ respectively, are joined by a light inextensible string. The string goes over a fixed smooth pulley at $B$, which is fitted between two inclined planes. $P$ is on the smooth plane $AB$, inclined at $60^\circ$ to the horizontal. $Q$ is on the plane $BC$, inclined at $30^\circ$ to the horizontal. The string is taut, and the particles are able to move along the lines of greatest slope of the two planes (see diagram).
(a)[5]
It is now stated that plane $BC$ is smooth and that the particles are released from rest. Find the tension in the string and the magnitude of the acceleration of the particles.
(b)[5]
It is now given instead that plane $BC$ is rough. A force of magnitude $3\ \text{N}$ is applied to $Q$ directly up the plane along a line of greatest slope of the plane. Find the least value of the coefficient of friction between $Q$ and the plane $BC$ for which the particles remain at rest.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applies Newton’s Second Law” …