7 The vertices of a uniform triangular lamina, which is in the \(x - y\) plane, are at the origin and the points \(( 20,60 )\) and \(( 100,0 )\).
- Determine the coordinates of the lamina's centre of mass.
Fig. 7.1 shows a uniform lamina consisting of a triangular section and two identical rectangular sections. The coordinates of some of the vertices of the lamina are given in Fig. 7.1.
The rectangular sections are then folded at right-angles to the triangular section, to give the rigid three-dimensional object illustrated in Fig. 7.2. Two of the edges, \(E _ { 1 }\) and \(E _ { 2 }\), are marked on both figures.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5c1cfe41-d7a2-4f69-ae79-67d9f023c246-7_933_739_799_164}
\captionsetup{labelformat=empty}
\caption{Fig. 7.1}
\end{figure}
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5c1cfe41-d7a2-4f69-ae79-67d9f023c246-7_924_725_808_1133}
\captionsetup{labelformat=empty}
\caption{Fig. 7.2}
\end{figure} - Show that the \(x\)-coordinate of the centre of mass of the folded object is 43.6, and determine the \(y\) - and \(z\)-coordinates.
- Determine whether it is possible for the folded object to rest in equilibrium with edges \(E _ { 1 }\) and \(E _ { 2 }\) in contact with a horizontal surface.