(i)[2]
Calculate the distance from $AD$ to the centre of mass of the prism.
(ii)[2]
Express the distance of the prism's centre of mass from $AB$ in terms of $a$.
(iii)[3]
Given that the prism is just about to topple, calculate $a$.
Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
The diagram presents cross-section $ABCD$ passing through the centre of mass of a uniform solid prism. $AB = 0.9\,\text{m}$, $BC = 2a\,\text{m}$, $AD = a\,\text{m}$ and angle $ABC = \text{angle } BAD = 90^\circ$. The prism weighs $18\,\text{N}$ and is in equilibrium on a rough horizontal plane, with $AD$ touching the surface. A horizontal force of magnitude $6\,\text{N}$ is applied to the prism. This force passes through the centre of mass in the direction $BC$.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correct moments equation giving $(0.9a+0.9a/2)Y = 0.9a\times0.45 + 0.45a\times0.9\times2/3$” …
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