A uniform beam of length L and mass m is inclined at an angle of ? to the horizo

Question

A uniform beam of length L and mass m is inclined at an angle of ? 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 ?s. Assume the angle ? is such that the static friction force is at its maximum value. (a) Draw a free-body 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 ?. T = (c) Using the condition of translational equilibrium, find a second expression for T in terms of ?s, m, and g. T = (d) Using the results from parts (a) through (c), obtain an expression for ?s involving only the angle ?. ?s = (e) What happens if the beam is lifted upward and its base is placed back on the ground slightly to the left of its position in the figure above? The beam slips. The beam remains stationary. Explain.

Explanation / Answer

a) Use Torque: St = Ia = 0 = r•F1 + r•F2 + r•F3... around different points of rotation. b) Use Newton's Laws: SF = ma = 0 = F1 + F2 + F3... for SFx and SFy. c) Combine the 2 equations for T(tension) in order to solve for ?.

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