A light inextensible string is threaded through a small smooth bead $B$ of mass $0.4\text{ kg}$. One end of the string is fastened to a fixed point $A$ $0.4\text{ m}$ above a fixed point $O$ on a smooth horizontal surface, and the other end is fastened to a fixed point $C$ which lies vertically below $A$ and $0.3\text{ m}$ above the surface. The bead moves at constant speed on the surface in a circle of centre $O$ and radius $0.3\text{ m}$ (see diagram).
(i(a))[3]
With the tension in the string equal to $2\text{ N}$, calculate the angular speed of the bead.
(i(b))[2]
With the tension in the string equal to $2\text{ N}$, calculate the magnitude of the contact force exerted on the bead by the surface.
(ii)[4]
Given instead that the bead is just about to lose contact with the surface, calculate the speed of the bead.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use N2L: $2\cos45 + 2 \times \tfrac{3}{5} = 0.4\omega^2 \times 0.3$” …