Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
The diagram presents the cross-section $OABCDE$ passing through the centre of mass of a uniform prism resting on a rough inclined plane. The section $ADEO$ forms a rectangle with $AD = OE = 0.6\,\text{m}$ and $DE = AO = 0.8\,\text{m}$. The section $BCD$ is an isosceles triangle in which angle $BCD$ is a right angle, and $A$ is the mid-point of $BD$. The plane is at $45^\circ$ to the horizontal, $BC$ is along a line of greatest slope of the plane and $DE$ is horizontal. The prism weighs $21\,\text{N}$, and equilibrium is maintained by a horizontal force of magnitude $P\,\text{N}$ acting along $ED$.
(i)[3]
Calculate the distance of the centre of mass of the prism from $BD$.
(ii(a))[2]
Find the smallest value of $P$ for which the prism does not topple.
(ii(b))[3]
It is stated that the prism is on the point of slipping for this smallest value of $P$. Calculate the coefficient of friction between the prism and the plane.
(iii)[5]
Show that the prism topples before it begins to slide, and state the value of $P$ at which equilibrium is broken.
Worked solution & mark scheme
This 13-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Moments are taken about $BAD$” …