A uniform beam of length L and mass m shown below is inclined at an angle theta

Question

A uniform beam of length L and mass m shown below is inclined at an angle theta to the horizontal. It's 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 theta is such that the static friction force is at its maximum value. Draw a force diagram for the beam. Using the conditions of rotational equilibrium find an expression for the tension t in the rope in terms of m, g, and theta. Using the condition of translational equilibrium find a second expression for t in terms of ms, m and g. Using the results from parts a through c obtain an expression for ms involving only the angle theta. What happens if the ladder is lifted upward and it's base is placed back on the ground slightly to the left of its position ? Explain .

Explanation / Answer

the forces acting on the uniform beam are

Fx = mg x cosA

and Fy = mg x sinA

where m is mass,g = 9.8 m/s^2 and A is the angle inclined

the net force acting on the beam is

F = (Fx^2 + Fy^2)^1/2

the torque acting on the beam is

T = F x L

where L is length of beam

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