Mathematics 9709 · AS & A Level · Newton's laws of motion
Newton's laws of motion — practice question
Particles $P$ and $Q$ together have a total mass of $1\text{ kg}$. They are connected by a light inextensible string that runs over a smooth fixed pulley. $P$ is kept at rest while $Q$ hangs freely, and both vertical sections of the string are straight. At the start, both particles are at a height of $h\text{ m}$ above the floor (see Fig. 1). $P$ is released from rest and the particles begin to move with the string taut. Fig. 2 gives the velocity-time graphs for the motion of $P$ and for the motion of $Q$, with vertically upwards taken as the positive direction for velocity.
(i)[5]
Calculate the magnitude of the acceleration with which the particles start to move and the mass of each particle.
(ii)[1]
Find the value of $h$.
(iii)[2]
Find the greatest height above the floor reached by particle $P$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Read the acceleration from the gradient of the graph” …