At rest on a rough horizontal plane is the end $A$ of a non-uniform rod $AB$ with length $0.6\,\text{m}$ and weight $8\,\text{N}$, where $AB$ is set at $60^\circ$ to the horizontal. The rod is kept in equilibrium by a force of magnitude $3\,\text{N}$ applied at $B$. This force acts $30^\circ$ above the horizontal in the vertical plane containing the rod (see diagram).
(i)[2]
Find how far the centre of mass of the rod is from $A$.
(ii)[2]
The $3\,\text{N}$ force is removed, and the rod is held in equilibrium by a force of magnitude $P\,\text{N}$ applied at $B$, acting in the vertical plane containing the rod, at an angle of $30^\circ$ below the horizontal. Calculate $P$.
(iii)[4]
In one of the two situations described, the rod $AB$ is in limiting equilibrium. Find the coefficient of friction at $A$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Takes moments about A: $3 \times 0.6 = 8\cos60\, \bar{x}$” …