Mathematics 9709 · AS & A Level · Newton's laws of motion
Newton's laws of motion — practice question
Particles $P$ and $Q$, with masses $0.3\,\text{kg}$ and $0.2\,\text{kg}$ respectively, are fastened to the two ends of a light inextensible string. The string runs over a fixed smooth pulley attached to the edge of a smooth plane. The plane is set at an angle $\theta$ to the horizontal, with $\sin\theta = \frac{3}{5}$. $P$ is on the plane, while $Q$ hangs vertically beneath the pulley at a height of $0.8\,\text{m}$ above the floor. The section of string between $P$ and the pulley lies parallel to a line of greatest slope of the plane. $P$ is let go from rest and $Q$ moves vertically downwards.
(i)[5]
Determine the tension in the string and the size of the acceleration of the particles.
(ii)[2]
$Q$ reaches the floor and does not rebound. It is given that $P$ does not arrive at the pulley in the later motion. Determine the time, measured from the instant $P$ is released, taken for $Q$ to reach the floor.
(iii)[4]
After $Q$ strikes the floor, the string is slack. Determine the time, measured from the instant $P$ is released, for the string to become taut again.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply Newton’s second law to $P$ or $Q$ to set up equations” …