Mathematics 9709 · AS & A Level · Newton's laws of motion
Newton's laws of motion — practice question
The sketch represents particle $P$ with mass $6\text{ kg}$ on a rough plane inclined at $30^\circ$ to the horizontal. Two light inextensible strings are fastened to $P$. Each string passes over a small smooth pulley fixed at an end of the plane. The non-vertical sections of the strings run parallel to a line of greatest slope of the plane. Particles $Q$ and $R$, with masses $5\text{ kg}$ and $2\text{ kg}$ respectively, hang vertically from the free ends of the strings. Both strings are taut, and the system is released from rest. It is stated that the tension in the string attached to $Q$ is twice the tension in the string attached to $R$.
(a)[5]
Find, in terms of $g$, the tension in each string and the magnitude of the particles' acceleration.
(b)[5]
Find the coefficient of friction between $P$ and the plane.
(c)[2]
You are told that, when the system is released from rest, $P$ is at the midpoint of the plane. During the motion that follows, $R$ does not reach the pulley at the top of the plane, and $P$ takes $1.5\text{ s}$ to reach the pulley at the bottom of the plane. Find the total length of the plane.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply N2L to $Q$ and $R$ to set up two equations” …