# Leaning ladder problem: minimum angle and frictionless floor

This video shows how to calculate the minimum angle for a leaning ladder considering static friction on the floor and a perfectly frictionless wall.

I have 2 questions:

1. If the wall had friction, would that influence the minimum angle?
2. Could the ladder stay in equilibrium using only the friction on the wall (unlimited friction, for example), if the floor was perfectly frictionless?

## 2 Answers

As to 2: no, this is not possible. The wall would exert a horizontal normal force on the ladder, and there would be no force to counter it. The ladder would be pushed away from the wall and start to slip.

• True. Interesting, although maybe if it was attached to a sort of hinge or horizontal surface at the wall there could be an upwards normal force and this setup could work, right?
– user137288
Commented Jan 24, 2021 at 22:28
• Sure, though for a hinge we wouldn't call it a normal force but a reaction force. And if it was "hooked" over a horizontal surface as you say, you could have a stabilizing friction force in the horizontal direction. Commented Jan 25, 2021 at 8:47

If the wall had friction, would that influence the minimum angle?

Yes, of course. The friction would provide an upward force, counteracting any tendency for the ladder to slip.

Could the ladder stay in equilibrium using only the friction on the wall (unlimited friction, for example), if the floor was perfectly frictionless?

• The attachment example is flawed: no matter how high the coefficient of friction, the normal force must be non-zero for any friction to exist, and any non-zero normal force would prevent the system from being in equilibrium. Commented Jan 24, 2021 at 18:44