A uniform beam of length \"L\" and mass \"m\" shown in FIGURE P8.26 is inclined

Question

A uniform beam of length "L" and mass "m" shown in FIGURE P8.26 is inclined at an angle theta 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 "mew s". 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 "theta". (c) Using Newton's second law for equilibrium, find a second expression for "T" in terms of "mew s, m, and g". (d) Using the foregoing results, obtain a relationship involving only "mew s" and the angle "theta". (e) What happens if the angle gets smaller? Is this equation valid for all values of "theta"? Explain.

Explanation / Answer

= 0 with pivot on base of beam

T.L. sin = m.g.L/2. cos

T = m.g.cos / 2.sin

T = ( m.g. cotan ) / 2

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