Mathematics 9709 · AS & A Level · Newton's laws of motion
Newton's laws of motion — practice question
Particles $P$ and $Q$, with masses $0.2\,\text{kg}$ and $0.1\,\text{kg}$ respectively, are connected to the two ends of a light inextensible string. This string goes over a fixed smooth pulley $B$ that is attached to two inclined planes. Particle $P$ is situated on a smooth plane $AB$ inclined at $60^{\circ}$ to the horizontal. Particle $Q$ is situated on a plane $BC$ inclined at an angle of $\theta^{\circ}$ to the horizontal. The string is taut, and the particles can travel along the lines of greatest slope of the planes (see diagram).
(a)[4]
Given that $\theta = 60$, plane $BC$ is rough and the coefficient of friction between $Q$ and plane $BC$ is $0.7$, the particles are released from rest. Determine whether the particles move.
(b)[4]
It is given instead that plane $BC$ is smooth. The particles are released from rest, and during the resulting motion the tension in the string is $(\sqrt{3}-1)\,\text{N}$. Find the magnitude of the acceleration of $P$ as it moves on the plane, and find the value of $\theta$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Resolve forces correctly perpendicular to the plane so that $R=0.1g\cos60$.” …