# Dependence of friction on area.

• suryanarayan
In summary, the conversation discusses the nature of frictional force and its dependency on the area of contact. The points mentioned include the independence of friction from area due to the small contact area at a microscopic level, the limit at which an object starts dipping into another object, and the deduction that the points of contact can be considered as free bodies with friction and normal forces acting at each elemental area. The conversation also mentions different theories, such as the pressure-based theory and the role of fluid friction, and suggests doing further research on the topic.
suryanarayan
Hello Guys,
I have been pondering on the nature of the frictional force and its dependency on the area of contact for the past few days and I had already searched for plausible explanations for the same.Although I could gather a few discrete points ,I couldn't get a complete picture of it.
Some of the points I had found online are as follows
a) It is independent of area because the area of actual contact(at the microscopic level) is a very tiny fraction of the geometric area of the object. Thus any increase or decrease in geometric area is insignificant.
b)Friction is independent of area up to a limit, that limit being the point at which the object starts dipping into the other object.

Based on some literature survey, The following are my deductions on the nature of the frictional force
1)Regarding point 'a', if that is so a thin sheet and a small box of the same mass should have the same friction. But shouldn't an increase in the geometric area result in more chances of actual contacts as well.If so, this should surely increase the friction(because of more interlocking at the newly contacted sites.)
2)The point 'b' seems plausible from a practical point of view but gives no mathematical or cause for why friction exhibits such behavior,in the ideal and in the dipping case.
3)One theory that I derived from point 'a', is that the points of contact can be considered as free bodies with dF(friction) and dN(normal force) acting at area dA. Then the total friction would be the sum of the friction acting at all points. Thus if geometric area increases, the number of such area elements also would increase but with a reduction in the normal force at the elemental area.So this would tend to cancel out the effect in the increase of area and thus friction becomes independent of area. But the problem with this theory is that it assumes that the reduction in normal force and the increase in the number of elemental areas has a connection which exactly cancels them both out.
4)Another theory that I have is based on pressure.It states that
Friction,F=Pressure x Area x coefficient of friction. So when area increases force acting per unit area (pressure)decreases and this would cancel out.
But this does not explain why friction would depend on area when the object starts dipping into the other object and this theory does not reconcile with the point 'a'.

Please comment on this issue with both mathematical and logical explanations.
Thank you :)

There are many models to 'explain' the forces between objects in contact. The simplest model is not at all bad for describing many phenomena but it fails when things behave non-linearly. Your 'coefficient of friction' is a quantity that's based on linear deformation of two microscopically uneven surfaces in contact and it assumes that the effective contact area is proportional to the pressure between them and not on the total 'apparent' area of contact.
This model can't work accurately for more complex materials.

What about fluid friction?

e-pie said:
What about fluid friction?
Where would contact area fit in neatly? It's a much harder thing to consider, I think.

sophiecentaur said:
It's a much harder thing to consider,

Newton has an answer to everything I suppose.

T=m (del u/del y)IIx

m is shear viscosity, del means partial differentiation and T is Force per area. IIx in subscript means flow parallel to X axis.

sophiecentaur
sophiecentaur said:
There are many models to 'explain' the forces between objects in contact. The simplest model is not at all bad for describing many phenomena but it fails when things behave non-linearly. Your 'coefficient of friction' is a quantity that's based on linear deformation of two microscopically uneven surfaces in contact and it assumes that the effective contact area is proportional to the pressure between them and not on the total 'apparent' area of contact.
This model can't work accurately for more complex materials.
Can you give me a link to these models?

suryanarayan said:
Can you give me a link to these models?
I am about to go out of the house, to visit my Son for the week end. But you can easily find yourself a suitable web source by googling "Friction Theory" or suchlike. Slipping in the term linear or non-linear could perhaps select what you actually want. The advantage of doing your own searching is that you can select something at your own level. Friction and lubrication (Tribology) have been popular topics throughout the ages so there is a vast range of studies.

## 1. How does increasing or decreasing the surface area affect friction?

Increasing the surface area in contact between two objects generally increases the amount of friction. This is because there are more points of contact between the two surfaces, resulting in a larger force needed to move the objects against each other.

## 2. Is there a relationship between the surface area and the coefficient of friction?

Yes, there is a direct relationship between surface area and the coefficient of friction. As surface area increases, so does the coefficient of friction, meaning there is a stronger force resisting motion between the two surfaces.

## 3. Does the type of material affect the dependence of friction on area?

Yes, the type of material can greatly affect the dependence of friction on area. Different materials have different coefficients of friction, meaning they will have varying levels of resistance to motion depending on the surface area in contact.

## 4. How does the angle of the surface affect the dependence of friction on area?

The angle of the surface can greatly affect the dependence of friction on area. A steeper angle will result in a larger surface area in contact, therefore increasing the friction. However, as the angle of the surface decreases, the surface area in contact also decreases, resulting in less friction.

## 5. How do external factors, such as temperature, affect the dependence of friction on area?

External factors, such as temperature, can impact the dependence of friction on area. For example, an increase in temperature can cause materials to expand, resulting in a larger surface area and potentially increasing friction. However, this can also depend on the materials and their coefficients of friction, as different materials can have varying responses to changes in temperature.

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