A and B are fixed points on a vertical line, with $A$ above $B$. A particle $P$ of mass $0.4\,\text{kg}$ is connected to $A$ by a light inextensible string of length $0.5\,\text{m}$. The particle $P$ is also connected to $B$ by a second light inextensible string. $P$ moves at constant speed in a horizontal circle with centre $O$ between $A$ and $B$. Angle $BAP = 30^\circ$ and angle $ABP = 70^\circ$ (see diagram).
(i)[5]
If the two string tensions are the same, determine the speed of $P$.
(ii)[5]
If instead the angular speed of $P$ is $12\,\text{rad s}^{-1}$, determine the tensions in the strings.
(b(ii))[5]
If instead the angular speed of $P$ is $12\,\text{rad s}^{-1}$, determine the tensions in the strings.
Worked solution & mark scheme
This 15-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Find the value of the radius, $r = 0.5\sin 30 = 0.25\,\text{m}$” …