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 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 force diagram for the beam. (Do this on paper. Your instructor may ask you to turn in this work.)

(b) Using the condition of rotational equilibrium, find an expression for the tension T in the rope in terms of m, g, and .

(c) Using Newton's second law for equilibrium, find a second expression for T in terms of s, m, and g.
T =

(d) Using the foregoing results, obtain a relationship involving only s and the angle .
s =

(e) What happens if the angle gets smaller?

The beam will slip. The beam will not slip.    

Is this equation valid for all values of ?

Yes No    

Explain.

Explanation / Answer

(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

(E) the beam will slip if theta value is very small

Hope this helps!

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