posted by Mandy .
A ladder rests inclined against a wall. Are you safer on the ladder when the floor is frictionless but the wall is rough or when the wall is frictionless and the floor is rough?
As I see it, the only way for the ladder to fall is for the bottom to move away from the wall (that is, the ladder can't fall by pushing the wall away). Therefore, I think you will be more safe with a frictionless wall and a rough floor so that the bottom of the ladder has a tougher time moving away from the wall. But I'm not a physicist. Perhaps DrWLS will give his opinion, also.
If the floor is frictionless, no horizontal force can be applied to the ladder there. Then, considering horizontal force equilbrium, there can be no "normal" force at the wall, either. With no horizontal normal wall force,there can be no friction force at the wall. The wall will be useless for stabilizing the ladder. Friction is absolutely essential at the floor.
The static friction coefficient needed at the floor varies with the cotangent of the ladder tilt angle, measured from vertical. This can be very low if the ladder is close to vertical.