6. \begin{figure}[h] \end{figure} A uniform rod, \(A B\), of weight \(W\) and length \(8 a\), rests in equilibrium with the end \(A\) on rough horizontal ground. The rod rests on a smooth cylinder. The cylinder is fixed to the ground with its axis horizontal. The point of contact between the rod and the cylinder is \(C\), where \(A C = 7 a\), as shown in Figure 4. The rod is resting in a vertical plane that is perpendicular to the axis of the cylinder. The rod makes an angle \(\alpha\) with the horizontal .

1. Show that the normal reaction of the ground on the rod at \(A\) has $$\text { magnitude } W \left( 1 - \frac { 4 } { 7 } \cos ^ { 2 } \alpha \right)$$ Given that the coefficient of friction between the rod and the ground is \(\mu\) and that \(\cos \alpha = \frac { 3 } { \sqrt { 10 } }\)
2. find the range of possible values of \(\mu\).
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