3 A uniform plank is 2.8 m long and has weight 200 N . The centre of mass is G.
- Fig. 3.1 shows the plank horizontal and in equilibrium, resting on supports at A and B .
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8d4aeab2-332a-442f-b1e7-0bbf8a945f0f-5_229_1125_434_459}
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\caption{Fig. 3.1}
\end{figure}
Calculate the reactions of the supports on the plank at A and at B . - Fig. 3.2 shows the plank horizontal and in equilibrium between a support at C and a peg at D .
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8d4aeab2-332a-442f-b1e7-0bbf8a945f0f-5_236_1141_993_461}
\captionsetup{labelformat=empty}
\caption{Fig. 3.2}
\end{figure}
Calculate the reactions of the support and the peg on the plank at C and at D , showing the directions of these forces on a diagram.
Fig. 3.3 shows the plank in equilibrium between a support at P and a peg at Q . The plank is inclined at \(\alpha\) to the horizontal, where \(\sin \alpha = 0.28\) and \(\cos \alpha = 0.96\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8d4aeab2-332a-442f-b1e7-0bbf8a945f0f-5_424_1099_1692_475}
\captionsetup{labelformat=empty}
\caption{Fig. 3.3}
\end{figure} - Calculate the normal reactions at P and at Q .
- Just one of the contacts is rough. Determine which one it is if the value of the coefficient of friction is as small as possible. Find this value of the coefficient of friction.