Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
A uniform solid cone with height $1.2\,\text{m}$ and semi-vertical angle $\theta^\circ$ is split into two sections by a cut that is parallel to the circular base and lies $0.4\,\text{m}$ above it. The top conical section, $C$, has weight $16\,\text{N}$, while the bottom section, $L$, has weight $38\,\text{N}$. The solid is then in equilibrium, with the larger plane face of $L$ resting on a horizontal surface and the smaller plane face of $L$ covered by the base of $C$ (see diagram).
(i)[3]
Calculate the distance from the larger plane face of $L$ to its centre of mass.
(ii(a))[1]
By considering the forces on $C$, find the coefficient of friction between $C$ and $L$.
(ii(b))[2]
By considering the forces on $C$, show that $\theta > 14.0^\circ$, correct to $3$ significant figures.
(iii)[3]
$C$ is taken away and $L$ is set on the horizontal surface with its curved surface in contact. Given that $L$ is just about to topple, Calculate $\theta$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Uses the principle of moments” …