An 9.0 m, 210 N uniform ladder rests against a smooth wall. The coefficient of static friction between the ladder and the ground is 0.75, and the ladder makes a 50.0° angle with the ground. How far up the ladder can an 890 N person climb before the ladder begins to slip?

Answer 1

All of the weight of ladder and person are balanced by the normal force F at the lower contact point, since the upper contact point is frictionless.

F = 1100 N

At the slipping condition, the friction force at the bottom is the maximum allowed by static friction, which would be 1100*0.75 = 825 N. It would be horizontal and pointed to the wall.

Now apply a moment balance using the three forces F, ladder weight and person weight. For simplicity, apply it at the upper (wall) contact point so you won't have to solve for the force there. You should be able to solve for the unknown position of the man.

Answer 2

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Answer 3

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