Two boxes are connected by a rope that passes over a pulley. On box of $30$kg hangs vertically from the end of the rope. The other box of $50$kg rests on a slope where the angle between the downward vertical and the slope is $70$ degrees. The box on the slope is in equilibrium and not at the stage of

slipping either up nor down on the slope.

$1.$ What are the two forces that act on the vertically hanging $30$Kg box and draw a force diagram to show them. Also $,$ label each vector on the force diagram and define symbols used. The Cartesian unit vectors i and j point horizontally to the right and vertically up$.$Show these vectors on the diagram.

$2.$ Express both forces, acting on the vertically hanging $30$kg box, in component form using unknown magnitude where appropriate. Find both forces in component form in terms of g$.$