Mathematics 9709 · AS & A Level · Newton's laws of motion

Newton's laws of motion — practice question

Particles A, of mass $0.26\,\text{kg}$, and B, of mass $0.52\,\text{kg}$, are fastened to the two ends of a light inextensible string. That string runs over a small smooth pulley $P$, which is fixed at the top of a smooth plane. The plane is tilted at an angle $\alpha$ to the horizontal, where $\sin\alpha = \frac{16}{65}$ and $\cos\alpha = \frac{63}{65}$. A is kept at rest $2.5\,\text{m}$ from $P$, with the section $AP$ of the string parallel to a line of greatest slope of the plane. B is hanging freely below $P$ at a point $0.6\,\text{m}$ above the floor (see diagram). A is released and the particles begin to move.
(i)[5]

Find the magnitude of the acceleration of the particles and the tension in the string.

(ii)[6]

Find the speed with which B reaches the floor and the distance of A from $P$ when A comes to instantaneous rest.

Worked solution & mark scheme

This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: Newton’s second law applied to one of the particles

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