A small ball $B$ with mass $0.5\,\text{kg}$ travels round a horizontal circle of radius $0.4\,\text{m}$ and centre $O$ on the smooth inner face of a hollow cone, which is held with its vertex pointing downwards. The cone's axis is vertical and the semi-vertical angle is $60^\circ$ (see diagram).
(i)[4]
Show that the magnitude of the force from the cone on $B$ is $5.77\,\text{N}$, correct to 3 significant figures, and calculate the angular speed of $B$.
(ii)[6]
A light elastic string of natural length $0.45\,\text{m}$ and modulus of elasticity $36\,\text{N}$ has one end fixed to $B$. Its other end is fixed to the point on the axis $0.3\,\text{m}$ above $O$. The ball $B$ again travels on the cone surface in the same horizontal circle as previously. Calculate the speed of $B$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applies $R\cos30 = 0.5g$” …