Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
Particles $P$ and $Q$, with masses $2\,\text{kg}$ and $0.25\,\text{kg}$ respectively, are joined by a light inextensible string passing over a fixed smooth pulley. Particle $P$ rests on an inclined plane set at an angle of $30^\circ$ to the horizontal. Particle $Q$ is suspended beneath the pulley. Points $A$, $B$ and $C$ are on the line of greatest slope of the plane, with $AB = 0.8\,\text{m}$ and $BC = 1.2\,\text{m}$ (see diagram).
Particle $P$ is let go from rest at $A$ with the string taut and moves down the plane. While $P$ travels from $A$ to $C$, $Q$ does not get to the pulley. The section of the plane from $A$ to $B$ is rough, and the coefficient of friction between the plane and $P$ is $0.3$. The section from $B$ to $C$ is smooth.
(a(i))[4]
Calculate the acceleration of $P$ between $A$ and $B$.
(a(ii))[5]
Hence, determine the speed of $P$ at $C$.
(b)[4]
Calculate the time taken for $P$ to move from $A$ to $C$.
Worked solution & mark scheme
This 13-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply Newton’s second law to the particle or system using the correct force terms” …