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I've seen some problems that talk about a ladder leaning against a frictionless wall, with a person standing on it. The ladder doesn't move(net force = 0). The problem is, I don't know what directions the reactions forces(that is, the force of the wall on the ladder, and of the floor on the ladder) should have. I've seen it solved like this:

enter image description here

where the force of the wall on the ladder is horizontal, and the force of the floor on the wall is vertical, and also in this way:

enter image description here

where the normal force of the wall is said to have both y and x components.

EDIT: this is a drawing of the forces acting on the ladder. The original image of the situation is enter image description here

I didn't notice it was leaning against over a corner (and I also wouldn't have thought it would make a difference)

I don't know which interpretation to believe. Is the force of the wall always perpendicular to the wall itself? Or it can it have y and x components?

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  • $\begingroup$ Just to clarify, is the ladder in fact resting against a corner as JMac said. It looks that way but just want to make sure. $\endgroup$ – Bob D Jul 31 '19 at 22:27
  • $\begingroup$ Yes, I'll add an image so that it's clearer $\endgroup$ – Agus Jul 31 '19 at 22:34
  • $\begingroup$ In that case I agree with (upvote) JMac's answer. $\endgroup$ – Bob D Jul 31 '19 at 22:40
  • $\begingroup$ You place friction in any direction and if the solution produces a negative value, then flip it. $\endgroup$ – John Alexiou Jul 31 '19 at 23:57
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Those are different situations.

In the first case, the ladder is leaning against a vertical wall. (it's not shown in your picture, but implied). The wall would then provide a normal force only in the horizontal direction.

In the second case, the ladder is leaning over a corner. In that case, the contact has a normal force based on the angle that the ladder comes into contact with the corner.

Without friction, the reaction force is always perpendicular to the contact surface, which is different in each situation.

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