newtonian mechanics - Forces other than the fundamental interactions, e.g. friction

Forgive me for the silly question, but I just don't get it.

I just completed an elementary course in mechanics, and I am curious to know what I am about to ask.

We have, all year, dealt with many forces like gravity, friction, normal forces, tensions etc.

But only one of them is listed as a fundamental force, that is, gravity.

I know that the only forces that exist in nature are the four fundamental force, and all of these are, apparently, non-contact forces.

But then how do you account for, for example, friction? We know that $F_\text{frictional}=\mu N$, But how do we arrive at that? Is this experimental?

I cannot see how contact forces like friction can exist, when none of the fundamental force is a contact force.

Again, forgive me for my ignorance.

Answer

AlanZ2223 has given a nice summary of what's going on. I'll just make a couple of points that are orthogonal to his and that wouldn't fit in comments.

The electrical force is a non-contact force; it falls off with distance like $1/r^2$. But most of the objects we deal with in everyday life are electrically neutral, i.e., they contain equal amounts of positive and negative charge. You would think that this would mean the attractions and repulsions would exactly cancel out, but that's not quite true. When two electrically neutral objects are close together, they can influence each other to rearrange their charges somewhat, so that the cancellation isn't perfect due to the different distances and angles involved in all the force vectors that are being added. This is called a residual interaction. The residual electrical interaction falls off much more quickly than $1/r^2$ at large distances -- more like $1/r^6$. This is the basic reason why bulk-matter forces, which are electrical, appear to be zero-range contact forces.

The other thing to realize is that it is not possible to explain forces such as the frictional and normal forces purely by using classical mechanics and an electrical interaction. If you try to do that, you'll find that bulk matter isn't stable, and that one piece of bulk matter won't prevent another from penetrating into it. In fact, you need two ingredients to explain these forces: (1) electrical interactions, and (2) the Pauli exclusion principle. If you try to explain it using only one of these ingredients without the other, it doesn't work.