3
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{57f7ca89-f028-447a-9ac9-55f931201e6b-2_561_597_1585_406}
\captionsetup{labelformat=empty}
\caption{Fig. 1}
\end{figure}
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{57f7ca89-f028-447a-9ac9-55f931201e6b-2_447_387_1726_1354}
\captionsetup{labelformat=empty}
\caption{Fig. 2}
\end{figure}
A hollow container consists of a smooth circular cylinder of radius 0.5 m , and a smooth hollow cone of semi-vertical angle \(65 ^ { \circ }\) and radius 0.5 m . The container is fixed with its axis vertical and with the cone below the cylinder. A steel ball of weight 1 N moves with constant speed \(2.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) in a horizontal circle inside the container. The ball is in contact with both the cylinder and the cone (see Fig. 1). Fig. 2 shows the forces acting on the ball, i.e. its weight and the forces of magnitudes \(R \mathrm {~N}\) and \(S \mathrm {~N}\) exerted by the container at the points of contact. Given that the radius of the ball is negligible compared with the radius of the cylinder, find \(R\) and \(S\).