4 A shovel consists of a blade and handle, as shown in Fig. 4.1 and Fig. 4.2. The dimensions shown in the figures are in metres.
The blade is modelled as a uniform rectangular lamina ABCD lying in the Oxy plane, where O is the mid-point of AB . The handle is modelled as a thin uniform rod EF . The handle lies in the Oyz plane, and makes an angle \(\alpha\) with \(\mathrm { O } y\), where \(\sin \alpha = \frac { 7 } { 25 }\). The rod and lamina are rigidly attached at E, the mid-point of CD.
The blade of the shovel has mass 1.25 kg and the handle of the shovel has mass 0.5 kg .
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{6b27d322-417e-4cea-85cc-65d3728173c8-3_746_671_1217_246}
\captionsetup{labelformat=empty}
\caption{Fig. 4.1}
\end{figure}
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{6b27d322-417e-4cea-85cc-65d3728173c8-3_664_766_1226_1064}
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\caption{Fig. 4.2}
\end{figure}
- Find,
- the \(y\)-coordinate of the centre of mass of the shovel,
- the \(z\)-coordinate of the centre of mass of the shovel.
The shovel is freely suspended from O and hangs in equilibrium.
- Calculate the angle that OE makes with the vertical.