Forces Acting on a Ladder

A man of weight (blue arrow) climbs a ladder of length and weight placed against a wall at an angle . Vary the height of the ladder to see the forces acting on this system.
The weight of the ladder is taken to be at its geometrical center (red arrow), the ground exerts a reaction force (brown arrow) on the ladder, and a frictional horizontal force (yellow arrow) stops the ladder from slipping along the ground. Additionally, there is a force at the top of the ladder normal to the wall (orange arrow, between the arms of the man).

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DETAILS

Since the ladder is in static equilibrium, the condition for equilibrium on the forces is , and for torques is
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The minimum coefficient of friction required is
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