A light inextensible string is threaded through a small smooth bead $B$ of mass $0.4\,\text{kg}$. One end is fastened to a fixed point $A$ $0.4\,\text{m}$ above a fixed point $O$ on a smooth horizontal surface. The other end is fastened to a fixed point $C$, which is vertically below $A$ and $0.3\,\text{m}$ above the surface. The bead moves with constant speed on the surface in a circle centred at $O$ with radius $0.3\,\text{m}$ (see diagram).
(i(a))[3]
Given that the tension in the string is $2\,\text{N}$, Calculate the angular speed of the bead.
(i(b))[2]
Given that the tension in the string is $2\,\text{N}$, 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: “Sets up $2\cos45 + 2\times3/5 = 0.4\omega^2\times0.3$” …