Mathematics 9709 · AS & A Level · Energy, work and power

Energy, work and power — practice question

Particles $P$ and $Q$, with masses $2.5\text{ kg}$ and $0.5\text{ kg}$ respectively, are joined by a light inextensible string that runs over a small smooth pulley fixed at the top of a plane inclined at an angle of $30^\circ$ to the horizontal. $P$ rests on the plane while $Q$ hangs below the pulley, with $Q$ initially $2\,\text{m}$ lower than $P$ in level (see diagram). $P$ is let go from rest with the string taut and moves down the plane. The plane is rough, and the coefficient of friction between the plane and $P$ is $0.2$.
(a)[5]

Determine the acceleration of $P$.

(b)[5]

Apply an energy method to determine the speed of the particles at the moment when they are at the same vertical height.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Normal reaction correctly found, $R = 2.5g\cos30$

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