# Is friction really always related to the normal force?

• bolzano95
In summary, the conversation discusses the relationship between the force of friction and the normal force, as well as how this relationship applies in different scenarios such as a block between two walls. The equation ##F_t= μ\cdot N## is derived from experiments and shows that the friction force is proportional to the normal force. Additionally, the conversation delves into the difference between static and dynamic friction and how this affects the behavior of objects in contact with each other. Finally, there is a discussion about the existence of friction and how it is justified through empirical evidence.

#### bolzano95

Homework Statement
Does friction exist?
Relevant Equations
More in the solution
What I know is that the force of friction and the normal force are the components of a contact force. So force of friction is related to the contact force. Friction is also related to the normal force by equation ##F_t= μ\cdot N##.

In this case (because the block is not moving) N=0 and therefore ##F_t=0## and there is no friction.

What bothers me is the fact that the wall and the block are in contact so there must be a force acting on the block? Am I even thinking right? So what would be this force?

Also: Does anybody knows how did we get this equation ##F_t= μ\cdot N##?
I know that the experiments showed that on the horizontal surface the force of friction is proportional to the mass of the object we observe and the ##F_t= μ\cdot N## is true.
But how do we get the same conclusion in a vertical case like this?
In other words: were there experiments also in this case or we just took a concept and put it in a vertical direction?
If so - what happens if we side a block vertically between two walls and we have been given a static coefficient? Does the friction acts on the body or not?

bolzano95 said:
What I know is that the force of friction and the normal force are the components of a contact force. So force of friction is related to the contact force. Friction is also related to the normal force by equation ##F_t= μ\cdot N##.

In this case (because the block is not moving) N=0 and therefore ##F_t=0## and there is no friction.

What bothers me is the fact that the wall and the block are in contact so there must be a force acting on the block? Am I even thinking right? So what would be this force?
At an atomic scale, there is a repulsion (and attraction) between the atoms of the wall and the block but this force gets canceled out. hence the Block remains in horizontal equilibrium. as long as the wall is not accelerated in the horizontal direction no normal reaction force will exist and hence there won't be any frictional force.
bolzano95 said:
Also: Does anybody knows how did we get this equation ##F_t= μ\cdot N##
This equation tells us that the frictional force between two surfaces is proportional to the normal reaction on the body (and does not depend on the surface area) the proportionality is removed by adding a constant ##\mu## which depends on the material of the surface.
bolzano95 said:
If so - what happens if we side a block vertically between two walls and we have been given a static coefficient? Does the friction acts on the body or not?
friction does not act on the body here as the Normal reaction with the two walls is zero. Hence the body accelerates down with ##g##.

Lnewqban
bolzano95 said:
What I know is that the force of friction and the normal force are the components of a contact force. So force of friction is related to the contact force. Friction is also related to the normal force by equation ##F_t= μ\cdot N##.

Careful now! In the static case, the magnitude of the friction force is related to the magnitude of the normal force by the inequality ##F_s \leq \mu_s N##. Up to this threshold, the static friction force will just be whatever it needs to be to provide static equilibrium (zero net force). Only if the friction is limiting, i.e. the body is on the point of moving, will ##F_s = \mu_s N##.

On the other hand, dynamic friction is defined by ##F = \mu_d N##.

The origins of these equations are probably empirical, however theoretical justification (or at least models) can probably be found within a tribology textbook.

Lnewqban and Hamiltonian
bolzano95 said:
If so - what happens if we side a block vertically between two walls and we have been given a static coefficient? Does the friction acts on the body or not?

Hamiltonian299792458 said:
friction does not act on the body here as the Normal reaction with the two walls is zero. Hence the body accelerates down with g.

I'm not sure if this is the correct conclusion, as if the block is in contact with two walls, both walls can exert a contact force on the block (friction force + normal force).

Of course if the space between the walls is wide enough for the block to fall without touching the walls, there'll be no contact force on the block due to either of the walls!

Lnewqban
bolzano95 said:
Homework Statement:: Does friction exist?

But how do we get the same conclusion in a vertical case like this?
In other words: were there experiments also in this case or we just took a concept and put it in a vertical direction?
View attachment 271513
If we consider friction force as the resistance to relative movement between two surfaces in contact, the principle of proportionality applies the same to horizontal, inclined or vertical surfaces.

Static μ is a proportionality coeficient between normal and resistive forces that is found experimentally for each couple of different materials.
The value is more or less equal to the tangent of the maximum angle of a slope over which a block is resting without sliding.

Your diagram shows an ideal situation in which the horizontal distances between pulley, rope point of attachment and center of mass of block respect to the vertical wall are exactly the same; therefore, there is no force pressing the block against the wall and vice-verse.
Basically, it is like the two surfaces were not in contact at all.

For any deviation of that ideal situation, you could have some perpendicular force between those two surfaces.
Hence, the block will not move vertically at all until the resultant vertical force becomes greater than certain percentage (static μ) of the magnitude of that perpendicular force (N).
After the relative movement is stablished, there will be a resistive force, of slightly smaller magnitude (dynamic μ * N) than the one previous to the movement.

Ok. Thank you all for your help. I have better understanding of friction now

Lnewqban