5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{80dceee7-2eea-4082-ad20-7b3fe4e8bb25-12_597_502_210_721}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
A pole \(A B\) has length 2.5 m and weight 70 N .
The pole rests with end \(B\) against a rough vertical wall. One end of a cable of length 4 m is attached to the pole at \(A\). The other end of the cable is attached to the wall at the point \(C\). The point \(C\) is vertically above \(B\) and \(B C = 2.5 \mathrm {~m}\).
The angle between the cable and the wall is \(\alpha\), as shown in Figure 2.
The pole is in a vertical plane perpendicular to the wall.
The cable is modelled as a light inextensible string and the pole is modelled as a uniform rod.
Given that \(\tan \alpha = \frac { 3 } { 4 }\)
- show that the tension in the cable is 56 N .
Given also that the pole is in limiting equilibrium,
- find the coefficient of friction between the pole and the wall.
\includegraphics[max width=\textwidth, alt={}, center]{80dceee7-2eea-4082-ad20-7b3fe4e8bb25-15_90_61_2613_1886}