Could anyone explain the case of a ladder leaning on a smooth floor and against a rough wall? It's not clear how there is a vertical frictional force at the wall despite having zero normal reaction there

• If the ladder is leaning against a rough wall, there will be a normal reaction at that point.
– Sam
Feb 19, 2020 at 6:04
• but how is the horizontal equilibrium satisfied for the ladder then since there are no other horizontal forces(because the floor is smooth) Feb 19, 2020 at 6:15
• Floor friction is required for equilibrium Feb 19, 2020 at 8:17
• @BobD but since there must be floor friction, doesn't this contradict that the floor is smooth (which we are assuming)? So either I'm missing something, or one must conclude that it is not possible for a ladder to be in equilibrium propped up against rough wall on a smooth floor... Jul 19, 2021 at 22:46
• @JoelBrennan It is not possible for the ladder to be in equilibrium with wall friction only. Wall friction requires a normal force on the wall, i.e., a horizontal force. In order to have equilibrium in the horizontal direction, the floor needs to exert and equal and opposite horizontal force. The only available horizontal force is static friction. Jul 19, 2021 at 23:09