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

Newton's laws of motion — practice question

Particles $P$ and $Q$, whose masses are $7\,\text{kg}$ and $3\,\text{kg}$ respectively, are secured to the two ends of a light inextensible string. The string goes over two small smooth pulleys fixed at the two ends of a horizontal table. Both particles hang vertically beneath the pulleys. Initially, both particles are at rest, $0.5\,\text{m}$ below table level and $0.4\,\text{m}$ above the horizontal floor (see diagram).
(i)[4]

Find the acceleration of the particles and the speed of $P$ immediately before it reaches the floor.

(ii)[2]

Determine whether $Q$ comes to instantaneous rest before it reaches the pulley directly above it.

Worked solution & mark scheme

This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: Use Newton’s second law, for instance $7g - T = 7a$ and $T - 3g = 3a$ or $7g - 3g = 10a$

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