6 Fig. 6.1 shows a solid uniform prism OABCDEFG . The \(\mathrm { Ox } , \mathrm { Oy }\) and Oz axes are also shown. The cross-section of the prism is a trapezium.
Fig. 6.2 shows the face OABC .
The dimensions shown in the figures are in centimetres.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b20e2254-955e-466c-8161-9614d8ccdba0-6_528_672_571_274}
\captionsetup{labelformat=empty}
\caption{Fig. 6.1}
\end{figure}
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b20e2254-955e-466c-8161-9614d8ccdba0-6_524_538_571_1242}
\captionsetup{labelformat=empty}
\caption{Fig. 6.2}
\end{figure}
The centre of mass of the prism has coordinates \(( \bar { x } , \bar { y } , \bar { z } )\).
- Determine the values of \(\bar { x } , \bar { y }\) and \(\bar { z }\).
- By considering triangle PBA, where P has coordinates ( \(\bar { x } , 0 , \bar { z }\) ), determine whether it is possible for the prism to rest with the face ABEF in contact with a horizontal plane without toppling.