\end{figure}
A box of mass 2 kg is held in equilibrium on a fixed rough inclined plane by a rope. The rope lies in a vertical plane containing a line of greatest slope of the inclined plane. The rope is inclined to the plane at an angle \(\alpha\), where \(\tan \alpha = \frac { 3 } { 4 }\), and the plane is at an angle of \(30 ^ { \circ }\) to the horizontal, as shown in Figure 1. The coefficient of friction between the box and the inclined plane is \(\frac { 1 } { 3 }\) and the box is on the point of slipping up the plane. By modelling the box as a particle and the rope as a light inextensible string, find the tension in the rope.