Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
The diagram represents the cross-section $ABCDEF$ through the centre of mass of a uniform prism that stands with $AB$ on rough horizontal ground. $ABCD$ is a rectangle for which $AB = CD = 0.4\,\text{m}$ and $BC = AD = 1.8\,\text{m}$. The remaining part of the cross-section is a semicircle whose diameter is $DF$ and whose radius is $r\,\text{m}$.
(i)[3]
Assuming that the prism is just about to topple, show that $r = 0.6$.
(ii)[4]
A force of magnitude $P\,\text{N}$ acts on the prism at $60^\circ$ to the upwards vertical, along a tangent to the semicircle at a point between $D$ and $E$. The prism weighs $15\,\text{N}$ and is in equilibrium on the point of toppling about $B$. Show that $P = 3.26$, correct to 3 significant figures.
(iii)[2]
Determine the least possible value of the coefficient of friction between the prism and the ground.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Centre of mass of semicircle used: $DF = \frac{4r}{3\pi}$” …