The uniform prism has cross-section $ABC$ through its centre of mass and is resting with $AB$ on a rough horizontal surface. $AB = 0.4\,\text{m}$ and $C$ stands $0.9\,\text{m}$ above the surface (see diagram). The prism is just on the point of toppling about its edge through $B$.
(i)[3]
Show that $BAC = 48.4^{\circ}$, correct to $3$ significant figures.
(ii)[3]
A force of magnitude $18\,\text{N}$, acting in the plane of the cross-section and perpendicular to $AC$, is now applied at $C$ to the prism. The prism is just about to rotate about its edge through $A$. Calculate the weight of the prism.
(iii)[4]
You are also told that the prism is just about to slip, so calculate the coefficient of friction between the prism and the surface.
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