A uniform shelf, ABABAB, of length 4 m and mass 2M 2M\,2M kg, is at rest with A A\,A against a rough vertical wall. The shelf is held in a horizontal position by a steel cable attached to B B\,B and to the vertical wall at the point CCC. A heavy vase of mass 4M 4M\,4M is placed on the shelf at P P\,P where AP=3AP = 3AP=3 m. The angle between the cable and the shelf is α\alphaα, where tanα=43\displaystyle \tan \alpha = \frac{4}{3}tanα=34. The shelf is modelled as a uniform rod, the vase is modelled as a particle and the cable is modelled as a light inextensible string.
Find, in terms of MMM, the tension in the cable BCBCBC.
Find the direction of the force exerted on the shelf at AAA.