4. Fig. 5.1 shows a solid L-shaped ornament, of uniform density. The ornament is 3 cm thick. The \(x , y\) and \(z\) axes are shown, along with the dimensions of the ornament. The measurements are in centimetres.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{2040be6b-3940-4ebb-83e5-8f93c2ea9688-08_518_830_319_283}
\captionsetup{labelformat=empty}
\caption{Fig. 5.1}
\end{figure}
- Determine, with reference to the axes shown, the coordinates of the ornament's centre of mass.
Fig. 5.2 shows the ornament placed so that the shaded face (indicated in Fig. 5.1) is in contact with a plane inclined at \(\theta ^ { \circ }\) to the horizontal, with the 4 cm edge parallel to a line of greatest slope. The surface of the plane is sufficiently rough so that the ornament will not slip down the plane.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{2040be6b-3940-4ebb-83e5-8f93c2ea9688-08_597_780_1281_287}
\captionsetup{labelformat=empty}
\caption{Fig. 5.2}
\end{figure} - Determine the minimum and maximum possible values of \(\theta\) for which the ornament does not topple.