# Ladder against wall - reason for movement orthogonal source force?

Intro:

I am under the impression movement is caused by a force, in particular without any boundaries a force causes an acceleration into the direction of the force. With boundaries, "the component" of the force in direction of the possible travel is the source for the acceleration.

An orthogonal component does not exist, hence a source force does not create a movement orthogonal to its direction. (A)

A force can result in a movement orthogonal to it over time by means of "deflection".

From experience a ladder against a wall is pulled down to be flat on the ground for "too low angles".

But, even with neither friction of wall nor ground, why is this? The source for the movement is gravity and the direction of travel is orthogonal to it + rotation.

I like to know the reason by means of a "fundamental law" and a deduction from it (even if it is "there's a path between a higher-energy state and a lower-energy state and hence it will be taken").

What I have pondered is:

1). Without a wall, the base of the leaning ladder cannot move on ground due to (A), but the ladder can rotate around its base because gravity "has" a component in the direction of every tangent along the circular path of travel of the tip of the ladder.

2). With a wall, the tangential component from 1). can be taken as a source for a force and this has a component in direction against the wall (and the wall resisting being moved by that force due a "force" of the same value in the opposite direction). (B)

3). The "resisting force" of the wall from 2). causes the ladder to be pushed away (and then rotate flat to the ground).

The crucial step is (B): the only source force is gravity and from it has been constructed a force orthogonal to it as the cause for the start of any movement at all. Is this a "correct" deduction?

• Yes, leaning on the wall means that the wall pushes horizontally, and that causes the horizontal motion when the floor friction is unable to resist the motion. Commented May 31, 2023 at 0:59

I am under the impression movement is caused by a force

This is not quite correct. Acceleration is caused by a net force.

Usually when we say “movement” we mean “velocity”. So a net force doesn’t cause movement, it causes a change in movement. And it is important to pay attention to the net force, not just one force.

The source for the movement is gravity

In the case of the ladder against the wall without friction, there is a force from the wall pushing horizontally on the top of the ladder, and there is a force from the floor pushing vertically on the bottom of the ladder.

Without a wall, the base of the leaning ladder cannot move on ground

Without the wall and without friction there is no horizontal force. There is gravity pointing vertically down and the force from the floor at the bottom of the ladder pointing vertically up. If the ladder is initially at rest then the center of mass will accelerate in the vertical direction only. This will cause the bottom of the ladder to slide to the right enough to allow the center of mass to fall straight down.

the only source force is gravity

Gravity is not the only force acting on the ladder. The contact forces from the wall also exist. It is incorrect to ignore them based on this concept of a “source” force.

• I'm intrigued, where do these "contact forces" come from? Are they postulated as written "physical laws"? (where?) (or are they actio = reactio?) Commented Jun 3, 2023 at 11:43
• @user5588495 they are not merely postulated, they are observed. Have you never stood on a floor or pushed on a wall? They are the forces that kept you from sinking into the floor or moving into the wall. They come from very small elastic deformations of the floor or wall.
– Dale
Commented Jun 3, 2023 at 17:24
• using a "spring model" for a solid body needs a force to push the spring, it can be an arm pushing a button but an anvil above a head would not exert a pressure if there is no force pushing it down (or if the force is parallel the ground), the force on the ladder is parallel the wall which makes the wall not receive a force in the first place. This is the step I'm struggling with. Commented Jun 3, 2023 at 17:44
• @user5588495 it doesn’t matter why that force is there. Once it is there you cannot ignore it. You cannot say, the anvil force wouldn’t be there without gravity therefore I can ignore the anvil force. The “source” force has no place in the laws of physics. I am not saying that they don’t exist, just that their existence doesn’t justify ignoring the other forces. Btw, in space an anvil may move without a force. If it contacts your head then there will be a contact force without any source force. So there may not be a “source”force, even for contact forces, but it doesn’t matter if there is
– Dale
Commented Jun 3, 2023 at 18:02