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Forces Acting on a Ladder

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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.

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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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Contributed by: Enrique Zeleny (September 2008)
Open content licensed under CC BY-NC-SA

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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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