3
\includegraphics[max width=\textwidth, alt={}, center]{f334f6e4-2a60-4647-8b37-e48937c85747-2_465_757_1146_694} Two identical uniform rods, \(A B\) and \(B C\), are freely jointed to each other at \(B\), and \(A\) is freely jointed to a fixed point. The rods are in limiting equilibrium in a vertical plane, with \(C\) resting on a rough horizontal surface. \(A B\) is horizontal, and \(B C\) is inclined at \(60 ^ { \circ }\) to the horizontal. The weight of each rod is 160 N (see diagram).

1. By taking moments for \(A B\) about \(A\), find the vertical component of the force on \(A B\) at \(B\). Hence or otherwise find the magnitude of the vertical component of the contact force on \(B C\) at \(C\). [3]
2. Calculate the magnitude of the frictional force on \(B C\) at \(C\) and state its direction.
3. Calculate the value of the coefficient of friction at \(C\).