Mathematics 9709 · AS & A Level · Forces and equilibrium

Forces and equilibrium — practice question

In Fig. 6.1, particles $A$ and $B$, with masses $4\,\text{kg}$ and $3\,\text{kg}$ respectively, are fixed to the ends of a light inextensible string that runs over a small smooth pulley. The pulley is attached at the top of a plane inclined at $30^\circ$ to the horizontal. $A$ hangs freely beneath the pulley, while $B$ rests on the inclined plane. The string is taut, and the part of the string from $B$ to the pulley is parallel to a line of greatest slope of the plane.
(a)[6]

The plane is rough and the particles are in limiting equilibrium. Determine the coefficient of friction between $B$ and the plane.

(b)[6]

Use an energy method to determine the speed of the particles at the instant when the particles are at the same horizontal level.

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: The tension is $T = 4g$

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