Mathematics 9709 · AS & A Level · Forces and equilibrium
Forces and equilibrium — practice question
In the diagram, particles $A$ and $B$, having masses $2\ \text{kg}$ and $3\ \text{kg}$ respectively, are joined by the ends of a light inextensible string. This string passes over a small fixed smooth pulley attached to the top of two inclined planes. Particle $A$ is placed on plane $P$, which makes an angle of $10^\circ$ with the horizontal. Particle $B$ is placed on plane $Q$, which makes an angle of $20^\circ$ with the horizontal. The string is taut, and each section of it is parallel to the line of greatest slope of the plane on which it lies.
(a)[5]
Plane $P$ is smooth, plane $Q$ is rough, and the particles are in limiting equilibrium. Determine the coefficient of friction between particle $B$ and plane $Q$.
(b)[6]
Now both planes are smooth, and the particles are released from rest at the same horizontal level. Find the time taken until the difference in the vertical height of the particles is $1\,\text{m}$. (You should assume that this occurs before $A$ reaches the pulley or $B$ reaches the bottom of plane $Q$.)
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Resolve the forces parallel to the planes to form equations, for example $T=2g\sin10$ or $3g\sin20=F+T$” …