Mathematics 9709 · AS & A Level · Forces and equilibrium
Forces and equilibrium — practice question
Particles $A$ and $B$, with masses $2.4\text{ kg}$ and $3.3\text{ kg}$ respectively, are joined by a light inextensible string that runs over a smooth pulley fixed at the top of a rough plane. The plane is inclined at an angle of $\theta^\circ$ to horizontal ground. Particle $A$ is on the plane and the part of the string from $A$ to the pulley is parallel to a line of greatest slope of the plane. Particle $B$ hangs vertically beneath the pulley and is $1\text{ m}$ above the ground (see diagram). The coefficient of friction between the plane and $A$ is $\mu$.
(a)[5]
Given that $\theta = 30$ and the system is in equilibrium while $A$ is on the point of moving directly up the plane, show that $\mu = 1.01$ correct to $3$ significant figures.
(b)[8]
Instead, take $\theta = 20$ and $\mu = 1.01$. The system is released from rest with the string taut. Find the total distance travelled by A before it comes to instantaneous rest. You may assume that A does not reach the pulley and that B remains at rest after it hits the ground.
Worked solution & mark scheme
This 13-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Resolve the forces on both particles, or on the system, to obtain the equations” …