A bead $B$ of mass $m\,\text{kg}$ travels at constant speed around a horizontal circle on a fixed smooth wire. The wire is a circle of radius $0.4\,\text{m}$ with centre $O$. One end of a light elastic string, whose natural length is $0.4\,\text{m}$ and modulus of elasticity is $42m\,\text{N}$, is fixed to $B$. The other end is fastened to a fixed point $A$ that lies $0.3\,\text{m}$ vertically above $O$ (see diagram).
(i)[3]
Show that the vertical component of the force from the wire on the bead is $3.7m\,\text{N}$ upwards.
(ii)[2]
Assuming the contact force has no horizontal component, determine the angular speed of $B$.
(iii)[3]
If the horizontal component of the contact force is instead of magnitude $2m\,\text{N}$, determine the two possible speeds of $B$.
(iv)[3]
Determine the speed of $B$.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Finding $T = 10.5m$ by taking moments in equilibrium” …