Mathematics 9709 · AS & A Level · Newton's laws of motion
Newton's laws of motion — practice question
Particles $P$ and $Q$ have masses $m\,\text{kg}$ and $(1-m)\,\text{kg}$ respectively. They are connected to the ends of a light inextensible string that passes over a smooth fixed pulley. At the start, $P$ is kept at rest with the string taut and the two straight sections of string vertical. Each particle is at a height of $h\,\text{m}$ above horizontal ground. When $P$ is released, $Q$ moves downwards. After that, $Q$ reaches the ground and stops. Fig. 2 gives the velocity-time graph for $P$ during the time that $Q$ is moving downwards.
(i)[2]
Determine the value of $h$.
(ii)[6]
Find the value of $m$, and also determine the tension in the string while $Q$ is moving.
(iii)[3]
While $Q$ is at rest on the ground, the string is slack. Determine the total time from the moment $P$ is released until the string becomes taut again.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Area under the velocity-time graph or a constant-acceleration formula is used” …