Understanding physical meaning

[Seeker69]

TL;DR

I'm missing to understand the physical meaning of frictional force formula

For example, talking about density formula; it conveys the essence that if a container with volume"V" can hold "m" mass of substance then " d" will be the density.

Jumping on to frictional force formula "F_f = μN", how do I know the physical meaning of the coefficient of friction from the equation?

 

[jfizzix]

$F_{f}=\mu N$
This is an empirical equation about the force of friction rather than one derived from first principles (e.g., summing up inter-molecular forces and such).

As such, the coefficient $\mu$ really is just a constant of proportionality between the friction force $F_{f}$ and the normal force $N$.

$\mu$ is a function of what kind of materials are in contact with each other, and whether we are talking about static friction or kinetic friction. The values of $\mu$ are found experimentally and tabulated rather than derived from more fundamental physics.

 

[Adesh]

Density is defined as “mass per unit volume”, so you see the definition of Density is purely mathematical, all it says is what will be the mass of a substance if we take a unit volume of that substance.

But when we come to friction it is defined as “the parallel component of the force when the bodies are in contact”, you can see that the friction is defined physically not mathematically. When experiments are done it was found that the parallel component of the force was proportional to the normal force acting on bodies in contact. The proportionality constant $\mu$ was also once again found empirically, and it was also found that it depends on nature of the materials in contact.

 

[A.T.]

Summary:: I'm missing to understand the physical meaning of frictional force formula

For example, talking about density formula; it conveys the essence that if a container with volume"V" can hold "m" mass of substance then " d" will be the density.

Jumping on to frictional force formula "F_f = μN", how do I know the physical meaning of the coefficient of friction from the equation?

It conveys the essence that if a contact compressed with force N resists sliding with force F_f then μ will be the coefficient of friction.