Mathematics 9709 · AS & A Level · Newton's laws of motion
Newton's laws of motion — practice question
Two particles $P$ and $Q$, with masses $0.3\text{ kg}$ and $0.5\text{ kg}$ respectively, are fastened to the two ends of a light inextensible string. The string goes over a fixed smooth pulley, and the particles hang freely beneath it (see diagram). $Q$ is kept stationary with the string taut at a height of $h\text{ m}$ above a horizontal floor (see diagram). $Q$ is then let go, and both particles begin to move. The pulley is high enough for $P$ never to reach it at any stage. The time for $Q$ to reach the floor is $0.6\text{ s}$.
(i)[6]
Determine the acceleration of $Q$ before it reaches the floor, and hence determine the value of $h$.
(ii)[3]
$Q$ stays at rest when it reaches the floor, and $P$ continues upwards. Find the velocity of $P$ at the instant $Q$ reaches the floor and the total time from the instant $Q$ is released until the string becomes taut again.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Newton’s second law gives: $T-0.3g=0.3a$ or $0.5g-T=0.5a$” …