Is μN a fundamental law of nature or just an approximation for friction?

[AlchemistK]

Where did "μN" come from?

Friction on the molecular level is basically the attractive forces between the molecules, but while dealing with macroscopic objects we use the value "μN" as the magnitude of friction, where N is the magnitude of the normal reaction force, and it acts in the direction opposite to relative motion.
Where did "μN" come from? It does seem that its tougher to move an object the harder it is pushing down, but did this result only come experimentally? Is there a mathematical proof for it?

 

[f95toli]

Maybe I've completely misunderstood the question, but 1 μN=10^-6 N.
μ is the Greek symbol for micro, you will often come across μF (micro-farad) for capacitance etc.

 

[Doc Al]

Maybe I've completely misunderstood the question, but 1 μN=10^-6 N.
μ is the Greek symbol for micro, you will often come across μF (micro-farad) for capacitance etc.

μ also stands for the coefficient of friction.

 

[AlchemistK]

Ah yeah, sorry that title must be confusing, I'm referring to μN as the value of friction where μ is the coefficient of friction and N is the magnitude of the normal reaction force, not micro Newton in this case.

 

[Doc Al]

Where did "μN" come from? It does seem that its tougher to move an object the harder it is pushing down, but did this result only come experimentally? Is there a mathematical proof for it?

Look up the Coulomb model of friction, which I've always regarded as semi-empirical. As you might expect, that simple relationship fails under many conditions. See: Standard model of friction

 

[AlchemistK]

Thank you, that helped a lot. The part about "cold weld" was especially interesting.

 

[Ken G]

There are some limits. For one thing, as soon as you say that you are going to treat it as entirely a function of N, you immediately know that it has to be proportional to N. That's because two identical blocks sliding side by side must have the same frictional force on them, so if you treat them as a single block, they must have double the frictional force on them. But they would then also have double the normal force.

 

[AlephZero]

I think the best case for the Coulomb model of friction (with constant coeffiients of static and dynamic friction) is

1. It is simple enough to use when doing statics and dynamics analyses "by hand".
2. It is a fairly good approximation for the situations used in simple mechanics lab experiments.

The main problem is that students often get the idea that it is a "law of nature" comparable with say Newton's laws or the ideal gas laws, and that idea is just wrong.