Mathematics 9709 · AS & A Level · Forces and equilibrium
Forces and equilibrium — practice question
As the diagram shows, particle $A$ has mass $0.8\text{ kg}$ and rests on a plane inclined at $30^\circ$ to the horizontal, while particle $B$ has mass $1.2\text{ kg}$ and rests on a plane inclined at $60^\circ$ to the horizontal. The particles are linked by a light inextensible string that passes over a small smooth pulley $P$ fixed at the top of the planes. The segments $AP$ and $BP$ of the string are parallel to the lines of greatest slope of the two planes. Both particles are released from rest, with the string taut in both sections.
(i)[6]
Since both planes are smooth, determine the acceleration of $A$ and the tension in the string.
(ii)[6]
Now suppose instead that both planes are rough, with the same coefficient of friction, $\mu$, for each particle. Determine the value of $\mu$ for which the system is in limiting equilibrium.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Set up equations for the system by resolving forces along the plane” …