3 A crate of mass 300 kg is at rest on rough horizontal ground. The coefficient of friction between the crate and the ground is 0.5 . A force of magnitude \(X \mathrm {~N}\), acting at an angle \(\alpha\) above the horizontal, is applied to the crate, where \(\sin \alpha = 0.28\). Find the greatest value of \(X\) for which the crate remains at rest.
\includegraphics[max width=\textwidth, alt={}, center]{213e26a8-3e4e-4dd4-b287-02e5925f3f47-06_849_807_255_669} Three coplanar forces of magnitudes \(20 \mathrm {~N} , 100 \mathrm {~N}\) and \(F \mathrm {~N}\) act at a point. The directions of these forces are shown in the diagram. Given that the three forces are in equilibrium, find \(F\) and \(\alpha\).