3 Fig. 3 shows a smooth ball resting in a rack. The angle in the middle of the rack is \(90 ^ { \circ }\). The rack has one edge at angle \(\alpha\) to the horizontal.
The weight of the ball is \(W \mathrm {~N}\). The reaction forces of the rack on the ball at the points of contact are \(R \mathrm {~N}\) and \(S \mathrm {~N}\).
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\caption{Fig. 3}
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- Draw a fully labelled triangle of forces to show the forces acting on the ball. Your diagram must indicate which angle is \(\alpha\).
- Find the values of \(R\) and \(S\) in terms of \(W\) and \(\alpha\).
- On the same axes draw sketches of \(R\) against \(\alpha\) and \(S\) against \(\alpha\) for \(0 ^ { \circ } \leqslant \alpha \leqslant 90 ^ { \circ }\).
For what values of \(\alpha\) is \(R < S\) ?