4 Fig. 4 shows a thin rigid non-uniform rod PQ of length 0.5 m . End P rests on a rough circular peg. A force of \(T \mathrm {~N}\) acts at the end Q at \(60 ^ { \circ }\) to QP . The weight of the rod is 40 N and its centre of mass is 0.3 m from P .
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{be1851d6-af11-40e1-8a36-5938ee7864d4-4_506_960_977_605}
\captionsetup{labelformat=empty}
\caption{Fig. 4}
\end{figure}
The rod does not slip on the peg and is in equilibrium with PQ horizontal.
- Show that the vertical component of \(T\) is 24 N .
- \(F\) is the contact force at P between the rod and the peg.
Find
- the vertical component of \(F\),
- the horizontal component of \(F\).
- Given that the rod is about to slip on the peg, find the coefficient of friction between the rod and the peg.