A uniform beam of mass $m$ is inclined at an angle $\theta$ to the horizontal. Its upper end produces a $90^{\circ}$ bend in a very rough rope tied to a wall, and its lower end rests on a rough floor (Fig. Pl2.47). (a) Let $\mu_{s}$ represent the coeffcient of static friction between beam and floor. Assume $\mu_{s}$ is less than the cotangent of $\theta .$ Determine an expression for the maximum mass $M$ that can be suspended from the top before the beam slips. (b) Determine the magnitude of the reaction force at the floor and the magnitude of the force exerted by the beam on the rope at $P$ in terms of $m, M,$ and $\mu_{s}$ .