# Coefficient of Friction and Normal Force

1. Jul 5, 2008

### Abraham

I know that the force of friction is the (coefficient of friction) x (normal force). My question is, why isn't area involved? That is, why wouldn't a larger surface have more friction than a smaller surface, if the normal force is the same?

PS: Sorry, just in case this is in the wrong section

2. Jul 5, 2008

### nicksauce

There is no reason why the coefficient of friction can't implicitly depend on area.

3. Jul 5, 2008

### tiny-tim

erm … I've no idea what that means.
Hi Abraham!

Because the larger the surface, the more its weight is spread out.

The friction per area depends on the pressure between the surfaces …*the harder they're pressed together, the more friction you'd expect.

Pressure is force divided by area.

Halve the area, and the pressure is halved, so the friction per area is halved, so the total friction is still the same.

4. Jul 5, 2008

### nicksauce

The OP's first point (it seems) was that F = uN, implies that F does not depend on area. I was saying that this was false, as u could implicitly depend on area, as u also implicitly depends on many other things (material, roughness of surface, possibly temperature). You covered the rest, by explaining how F should not depend on area.

5. Sep 19, 2008

### chandangang

if area is halved then pressure wud double (force remains same throughout-normal reaction force).
could u put forward ur point properly

6. Sep 19, 2008

### stewartcs

The coefficient of friction in the standard friction model is dependent on the material properties mainly and to the environment to a certain extent, not the area.

CS

7. Sep 19, 2008

### stewartcs

F does not depend on the area.

CS

8. Sep 19, 2008

### stewartcs

CS

9. Sep 19, 2008

### rcgldr

In the real world it depends on the surfaces involved. In the case of tires, maximum static friction force does not increase lineary with normal force, the ratio is called load sensitivity:

For tires, a larger area reduces the force per unit area, increasing friction (there is a point of diminishing returns due to unsprung weight).

Also in the second half of the second video on this web page, 4 objects of the same density are placed on a smooth board, and the smallest object slides last, although I'm not sure if this is friction force or something related to air between the objects and board.

http://www.gyroscopes.org/1974lecture.asp

10. Sep 19, 2008

### Pyrrhus

Friction is a complex phenomenon. One explanation of friction in dry surfaces (or very lightly lubricated) was introduced by Coulomb (it is a very simplified explanation, and what you are talking about). The static friction and kinetic friction coefficients are usually found to approximated values on engineering handbooks. Also, as you noticed Coulomb's theory doesn't care for the contact surface, which indeed can affect on the movement of a body in some cases.

In simple words, within its range of applicability Coulomb's theory of dry friction has given good results. For cases where Coulomb's theory is not applicable such as lubricated surfaces, other theories must be employed.

11. Sep 20, 2008