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Frictional resistance to the relative motion of two solid objects is usually proportional to the force which presses the surfaces together as well as the roughness of the surfaces. But when we talk about co-efficient of friction we write mathematically, $F_f = μN$. I don't know if there is any method that can calculate me the roughness of object but this question lies with my thoughts ,always, about friction that if it depends upon both the factors viz., roughness of the object and pressing force (normal force) then why only one of the factor is taken when calculating friction mathematically? Is it so for we are unable to calculate roughness of the surface?

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In the equation $F_f=\mu F_N$, where $F_f$ is the frictional force, $F_N$ is the normal force, and $\mu$ is the coefficient of friction, $\mu$ is sort of a way of expressing the quantity that you're looking for.

You ask why this equation does not include an expression of the "roughness" of a surface, but it's not obvious to me how you would concisely describe this property as a single number in the manner that you ask. When two surfaces are in contact, both surfaces will have surface irregularities, and you would be hard pressed to describe them both completely and concisely because they are irregular-ities (emphasis on the irregular part.

However, the coefficient of friction, $\mu$ still does a pretty good job of describing the amount of friction generated by two surfaces. It is a dimensionless number, because by rearranging the above equation, we can see that its just a ratio of the frictional force produced between two objects compared to the normal force between the two objects: $$\mu =\frac{F_f}{F_N}$$

Although we can't say precisely that $\mu$ is a direct measure of roughness (ice on steel, for example, has a pretty low coefficient of friction, even though ice is actually quite rough at the microscopic level) it is a measure of the relative amount of friction generated between two surfaces, for a given normal force.

Also, I would like to add that the equation $F_f=\mu F_N$ is just a helpful approximation for physicists, and is not an exact solution to the amount of friction between two surfaces. If you look at the top-voted answer to this question you'll see that a full description of friction is actually quite complicated, and $F_f=\mu F_N$ is only a first order approximation of how friction between two surfaces really behaves.

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