Mathematics 9709 · AS & A Level · Forces and equilibrium
Forces and equilibrium — practice question
Particles $A$ and $B$, with masses $0.9\,\text{kg}$ and $0.4\,\text{kg}$ respectively, are fixed to the two ends of a light inextensible string. The string passes over a fixed smooth pulley attached to the top of two inclined planes. Initially the particles are at rest, with $A$ on a smooth plane inclined at angle $\theta^\circ$ to the horizontal and $B$ on a plane inclined at $25^\circ$ to the horizontal. The string is taut, and the particles can move along the lines of greatest slope of the two planes. A force of magnitude $2.5\,\text{N}$ acts on $B$ down the plane (see diagram).
(i)[5]
Find the acceleration of $B$ when $\theta = 15^\circ$ and the plane on which $B$ rests is smooth.
(ii)[5]
For a different value of $\theta$, the plane on which $B$ rests is rough with coefficient of friction between the plane and $B$ of $0.8$. The system is in limiting equilibrium, with $B$ on the point of moving in the direction of the $2.5\,\text{N}$ force. Find the value of $\theta$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply Newton’s second law to either particle with the correct force terms” …