2
\includegraphics[max width=\textwidth, alt={}, center]{a8c1e5b3-4d8b-4795-9e9f-4c0db374112e-2_691_767_529_689} Two uniform rods \(A B\) and \(B C\) are of equal length and each has weight 100 N . The rods are freely jointed to each other at \(B\), and \(A\) is freely jointed to a fixed point. The rods are in equilibrium in a vertical plane with \(A B\) horizontal and \(C\) resting on a rough horizontal surface. \(C\) is vertically below the mid-point of \(A B\) (see diagram).

1. By taking moments about \(A\) for \(A B\), find the vertical component of the force on \(A B\) at \(B\). Hence find the vertical component of the contact force on \(B C\) at \(C\).
2. Calculate the magnitude of the frictional force on \(B C\) at \(C\) and state its direction. \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{a8c1e5b3-4d8b-4795-9e9f-4c0db374112e-3_452_345_264_900} \captionsetup{labelformat=empty} \caption{Fig. 1}
   \end{figure} A uniform smooth sphere \(A\) moves on a smooth horizontal surface towards a smooth vertical wall. Immediately before the sphere hits the wall it has components of velocity parallel and perpendicular to the wall each of magnitude \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Immediately after hitting the wall the components have magnitudes \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), respectively (see Fig. 1).