# Friction force does not depend upon contact area, but how?

#### krmr

Joined Nov 19, 2007
4
Friction force does not depend upon contact area, but how?

#### recca02

Joined Apr 2, 2007
1,212
Friction force does not depend upon contact area
though one finds this written in laws/properties of friction this is not true.

#### thingmaker3

Joined May 16, 2005
5,083
Friction force does not depend upon contact area, but how?
DaVince was a pretty sharp fellow, but not without flaw.

To keep from damaging your rims, of course! #### recca02

Joined Apr 2, 2007
1,212
if u want an answer why is it said that friction does not depend on surface are of contact
then u might want to have a look a this eqn

friction =coeff of friction*normal force.

coeff is const for two surfaces and normal force is the force component perpendicular to the surface on which the body stands.
so no 'area of contact' is seen in that equation.
it must mean it is free from area of contact.

however in actuality that is not the case.

cycle with flat tires is harder to ride apart from the danger it poses to the rim.

#### krmr

Joined Nov 19, 2007
4

#### Ryno3030

Joined Dec 1, 2007
9
The actual problem with the lack of surface area inclusion is the fact that entire surfaces do not express the coefficient of friction. The coefficient of friction is derived from irregularities in the surfaces of the objects in question. The friction coefficient should actually be thought of as an average. Using the average, the numbers behind the problem come astronomically close to the truly correct answer. If you wanted to take a really disgusting surface integral, then the surface area would play a part. Gotta love classical physics.

#### chandangang

Joined Sep 19, 2008
1
if u want an answer why is it said that friction does not depend on surface are of contact
then u might want to have a look a this eqn

friction =coeff of friction*normal force.

coeff is const for two surfaces and normal force is the force component perpendicular to the surface on which the body stands.
so no 'area of contact' is seen in that equation.
it must mean it is free from area of contact.

however in actuality that is not the case.

cycle with flat tires is harder to ride apart from the danger it poses to the rim.
cycles with flat tyres is difficult to ride since internal pressure reduces so the round shape is distorted so rotation of wheel is not possible
the reason is not friction which u have given.

#### triggernum5

Joined May 4, 2008
216
It is related to friction though.. Distorting a solid is resisted by internal friction.. Its one of the things that add heat to orbiting bodies..

#### siddharth mittal

Joined Oct 14, 2008
23
while deriving the equ. for friction we assumed that the body is PERFECTLY rigid that means it does not change its shape......so we need pressure to make that tyre almost rigid

#### triggernum5

Joined May 4, 2008
216
In the simple friction =coeff of friction*normal force, the coefficient is dependant on the surface area in contact.. Change the contact area, and the coefficient will need to be altered in the same way as if the object was switched..
A function could be derived that yields the proper coefficient based on the amount of contact area.. It wouldn't increase linearly with contact area though.. If that was the case you would have
friction =coeff_of_friction(contact_area)*normal force

#### markm

Joined Nov 11, 2008
16
friction = coeff * normal force

applies only to one object sliding on another, not to a rolling tire. Rolling friction does not occur between the tire and the road, but instead is the internal friction of the rubber as it distorts under the load. With lower pressure, the rubber bends more, and the energy lost to friction increases because there is more motion. I don't expect that a simple formula for that could be derived from first principles, but rather you should just measure it empirically.

The friction formula will apply fairly accurately to the friction in the wheel bearing, if it's a simple sleeve bearing. (The coefficient should be pretty low, if the bearing is properly lubricated.) It would also apply to a tire sliding on the road - locked brakes, skids, or tire-spinning acceleration - but it's only an approximation, which is far more accurate for two hard surfaces (like sleeve bearings, or a train sliding to a stop on locked wheels, steel on steel) than for a yielding and sometimes even sticky surface like rubber. Wet or icy roads often give you a coefficient that changes unpredictably every few inches, and also changes with speed and horizontal force, so it's pretty hard to predict how fast you can stop or take a corner...

#### BillO

Joined Nov 24, 2008
999
Wow!

Thanks Mark, reading this until you stepped in was giving me a headache.

No insult intended here, but it is interesting how people can have such a distorted view of the universe, and be sure it's right.

BTW Mark is right, with the exception that "internal Friction" might not be the best term to use.

My question to everyone else would be, why would the friction between the road and the bike's tire even enter into your discussion? When, if the wheel is rolling, the point of contact with the road is essentially stationary.

Another point. Fricton itself is a quantity that needs to be applied per unit area such that the FORCE required to overcome friction is related to pressure between the surfaces and the applicable coefficient of friction.

This should be self evident, but if it is not, let me know and I'll give an example or two.

#### georgecomputerscience

Joined Oct 21, 2009
1
According to the model developed by Charles-Augustin de Coulomb the dry force of friction can be expressed as This approximation mathematically follows from the assumptions that surfaces are in atomically close contact only over a small fraction of their overall area, that this contact area is proportional to the normal force (until saturation, which takes place when all area is in atomic contact), and that frictional force is proportional to the applied normal force, independently of the contact area (you can see the experiments on friction from Leonardo Da Vinci). Such reasoning aside, however, the approximation is fundamentally an empirical construction. It is a rule of thumb describing the approximate outcome of an extremely complicated physical interaction. The strength of the approximation is its simplicity and versatility  though in general the relationship between normal force and frictional force is not exactly linear (and so the frictional force is not entirely independent of the contact area of the surfaces), the Coulomb approximation is an adequate representation of friction for the analysis of many physical systems.

Source: http://en.wikipedia.org/wiki/Friction#Coulomb_friction

Summary: The Coulomb approximation is a model that allows us to avoid the complication of including the contact area when determining the force of friction. But if a more accurate result is needed, it would require to use a much more complicated model.