A uniform beam of length L and mass m shown in the figure below is inclined at a

Question

A uniform beam of length L and mass m shown in the figure below is inclined at an angle of 9 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 mu_s. Assume the angle theta is such that the static friction force is at its maximum value. Using the condition of rotational equilibrium, find an expression for the tension Tin the rope in terms of m, g, and theta. Using the condition of translational equilibrium, find a second expression for Tin terms of ns, m, and g. Using the results from parts (a) through (c), obtain an expression for involving only the angle theta. 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 remains stationary. The beam slips.

Explanation / Answer

Try to draw the free diagram yourself. for answer b c and d:

b) Sum the moments about the bottom of the beam
M = 0 = T*L*sin - m*g*L/2*cos
T = mgcos / 2sin = mg / 2tan

c) T = µs*m*g
since the "static friction force is at its maximum value."

d). µs*m*g = mg / 2tan
µs = 1 / 2tan = ½*cot

Hope this helps

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