Edexcel M2 — Question 3

Exam BoardEdexcel
ModuleM2 (Mechanics 2)
TopicCentre of Mass 1

3. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{9126ebb1-eaa7-4a40-953f-5dc819c9f479-4_698_1271_296_488} \captionsetup{labelformat=empty} \caption{Fig. 2}
\end{figure} A uniform plane lamina is in the shape of an isosceles triangle \(A B C\), where \(A B = A C\). The mid-point of \(B C\) is \(M , A M = 30 \mathrm {~cm}\) and \(B M = 40 \mathrm {~cm}\). The mid-points of \(A C\) and \(A B\) are \(D\) and \(E\) respectively. The triangular portion \(A D E\) is removed leaving a uniform plane lamina \(B C D E\) as shown in Fig. 2.
  1. Show that the centre of mass of the lamina \(B C D E\) is \(6 \frac { 2 } { 3 } \mathrm {~cm}\) from \(B C\).
    (6 marks)
    The lamina \(B C D E\) is freely suspended from \(D\) and hangs in equilibrium.
  2. Find, in degrees to one decimal place, the angle which \(D E\) makes with the vertical.
    (3 marks)