Serway & Jewett — Static Equilibrium and Elasticity: Problem 35

A uniform beam of mass \( m \) is inclined at an angle \( \theta \) to the horizontal. Its upper end (point \( P \)) produces a \( 90^{\circ} \) bend in a very rough rope tied to a wall, and its lower end rests on a rough floor (Fig. P12.35). Let \( \mu_s \) represent the coefficient of static friction between beam and floor. Assume \( \mu_s \) is less than the cotangent of \( \theta \). (a) Find an expression for the maximum mass \( M \) that can be suspended from the top before the beam slips. Determine (b) the magnitude of the reaction force at the floor and (c) the magnitude of the force exerted by the beam on the rope at \( P \) in terms of \( m, M, \) and \( \mu_s \).