3 Fig. 3.1 shows a rigid, thin, non-uniform 20 cm by 80 cm rectangular panel ABCD of weight 60 N that is in a vertical plane. Its dimensions and the position of its centre of mass, \(G\), are shown in centimetres. The panel is free to rotate about a fixed horizontal axis through A perpendicular to its plane; the panel rests on a small smooth fixed peg at B positioned so that AB is at \(40 ^ { \circ }\) to the horizontal. A horizontal force in the plane of ABCD of magnitude \(P \mathrm {~N}\) acts at D away from the panel.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c8f26b7e-1be1-4abf-8fea-6847185fad81-4_451_737_493_646}
\captionsetup{labelformat=empty}
\caption{Fig. 3.1}
\end{figure}
- Show that the clockwise moment of the weight about A is 9.93 Nm , correct to 3 significant figures.
- Calculate the value of \(P\) for which the panel is on the point of turning about the axis through A .
- In the situation where \(P = 0\), calculate the vertical component of the force exerted on the panel by the axis through A .
The panel is now placed on a line of greatest slope of a rough plane inclined at \(40 ^ { \circ }\) to the horizontal. The panel is at all times in a vertical plane. A horizontal force in the plane ABCD of magnitude 200 N acts at D towards the panel. This situation is shown in Fig. 3.2.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c8f26b7e-1be1-4abf-8fea-6847185fad81-4_497_842_1653_616}
\captionsetup{labelformat=empty}
\caption{Fig. 3.2}
\end{figure} - Given that the panel is moving up the plane with acceleration up the plane of \(1.75 \mathrm {~ms} ^ { - 2 }\), calculate the coefficient of friction between the panel and the plane.