Surface Area and Friction in Static Friction?

[stu12345]

Homework Statement

How does the surface area of an object affect the force of static friction? I'm trying to figure out whether two different objects with equal mass and different surface areas requires the same amount of applied force or different amounts.

Homework Equations

I know of this one.

Ff = coefficient of friction(Fn)

The Attempt at a Solution

I'm not sure how to answer this.

 

[rock.freak667]

Does Fn depend on area?

 

[stu12345]

Well each object in contact with a flat surface will have equal masses just different surface areas. I'm using a same flat surface for each object with equal masses but different surface areas.

 

[rock.freak667]

Well each object in contact with a flat surface will have equal masses just different surface areas. I'm using a same flat surface for each object with equal masses but different surface areas.

Right, well in most cases, the normal force would be the weight right? So would the frictional force formula have area in it?

 

[stu12345]

Ya it would have area.

 

[rock.freak667]

Ya it would have area.

No, it would not, if F_n=mg and F_f=μF_n then area does not appear.

Once your materials are the same, then μ is the same and if the masses are the same, then the frictional force produced by them are the same, regardless of area.

 

[stu12345]

Ah ok. Thanks so much.

 

[SammyS]

No, it would not, if F_n=mg and F_f=μF_n then area does not appear.

Once your materials are the same, then μ is the same and if the masses are the same, then the frictional force produced by them are the same, regardless of area.

As long as you can treat the coefficient of friction, μ, as simply being a constant which depends only upon the two materials which are present, then surface area will not make any difference. That's the simple model used in physics courses.

However, coefficient of friction, μ, actually does depend on the temperature of the materials. We seldom include that in our model. The greater the surface area, the less the increase in temperature (The thermal energy is dissipated over a wider area.) so that μ will tend to change less than in the case less surface area. Of course, this is more a factor with sliding friction, which tends to produce heat.

It's also the case that for materials which deform rather easily, like rubber used in tires, the pressure at the point of contact affects μ in a rather complicated way.

This is just "scratching the surface". - pun intended

Generally, when solving a physics problem with friction involved, frictional force does not depend on surface area. In any case, F_f = μ F_n works very well.