Solved: A uniform beam of length L and mass m shown in

Chapter , Problem 26

(choose chapter or problem)

A uniform beam of length L and mass m shown in Figure P8.26 is inclined at an angle u to the horizontal. Its upper end is connected to a wall by a rope, and its lower end rests on a rough horizontal surface. The coefficient of static friction between the beam and surface is ms. Assume the angle is such that the static friction force is at its maximum value. (a) Draw a force diagram for the beam. (b) Using the condition of rotational equilibrium, find an expression for the tension T in the rope in terms of m, g, and u. (c) Using Newtons second law for equilibrium, find a second expression for T in terms of ms, m, and g. (d) Using the foregoing results, obtain a relationship involving only ms and the angle u. (e) What happens if the angle gets smaller? Is this equation valid for all values of u? Explain.