It is indeed helpful to come at length upon a physical system...
Brian's message made me think about a peculiarity of static friction.
Is it associated with heating? Is it associated with the macroscopic
work done by the applied force?
What happens when we push a box before it starts sliding? The
applied force increases continuously and so does the static force
of friction. If F_st =mu_st * N then mu_st must increase gradually.
What is behind the increase mu_st from zero to the maximum
quoted in tables? Perhaps the center of mass does move a little,
heat is produced and work is done, like in kinetic friction. It is
like stretching and breaking tiny elastic springs, I suppose.
Ludwik Kowalski