A uniform rod, ABABAB, of length 4 m and mass M M\,M kg, is at rest with A A\,A against a rough vertical wall. The rod supports a sign of mass 4M 4M\,4M at P P\,P where AP=3AP = 3AP=3 m. The rod is held in a horizontal position by a wire attached to B B\,B and to the wall at CCC. The angle between the wire and the rod is α\alphaα, where tanα=815\displaystyle \tan \alpha = \frac{8}{15}tanα=158. The rod is modelled as a uniform rod, the sign is modelled as a particle and the wire is modelled as a light inextensible string.
Find, in terms of MMM, the tension in the wire BCBCBC.
Find the direction of the force exerted on the rod at AAA.