The diagram shows two particles $P$ and $Q$ on the line of greatest slope of plane $ABC$. Each particle has mass $m\,\text{kg}$. The plane is inclined at an angle $\theta$ to the horizontal, with $\sin \theta = 0.6$. $AB$ is $0.75\,\text{m}$ long and $BC$ is $3.25\,\text{m}$ long. Section $AB$ of the plane is smooth, whereas section $BC$ is rough. The coefficient of friction between each particle and section $BC$ is $0.25$. Particle $P$ is released from rest at $A$. At the same moment, particle $Q$ is released from rest at $B$.
(a)[3]
Verify that particle $P$ reaches $B\;0.5\,\text{s}$ after release, with a speed of $3\,\text{m s}^{-1}$.
(b)[4]
Find the time from the instant of release of the two particles until they collide.
(c)[5]
Find the time from the instant of collision until the combined particle reaches $C$.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply Newton’s second law to determine the acceleration, $a=6$” …