Edexcel M3 — Question 4

Exam BoardEdexcel
ModuleM3 (Mechanics 3)
TopicCentre of Mass 1

4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{cab238c9-f4e2-4637-a079-f74779548f49-3_447_506_205_657} \captionsetup{labelformat=empty} \caption{Fig. 1}
\end{figure} A stand used to reach high shelves in a storeroom is in the shape of a frustum of a cone. It is modelled as a uniform solid formed by removing a right circular cone of height \(2 h\) from a similar cone of height \(3 h\) and base radius \(3 r\) as shown in Figure 1.
  1. Show that the centre of mass of the stand is a distance of \(\frac { 33 } { 76 } h\) from its larger plane face.
    (7 marks)
    The stand is stored hanging in equilibrium from a point on the circumference of the larger plane face. Given that \(h = 2 r\),
  2. find, correct to the nearest degree, the acute angle which the plane faces of the stand make with the vertical.
    (4 marks)