Friction charges by how hard the surfaces press together, and by nothing else — not by contact area, not by how heavy it looks. $f_k = \mu_k N$, read aloud f equals mu-k N, where $\mu$ is the Greek letter mu, said “mew”. $f_k$ is the friction force in newtons, $N$ is the normal force in newtons — on a level floor, exactly the weight — and $\mu_k$ is the coefficient, a force over a force, so every unit cancels and it travels naked. If your μ ever turns up wearing newtons, a rearrangement upstream is lying to you.

The subscripts name a STATE, not a first-and-second: s is static, still at rest, and k is kinetic, already sliding. Static gets its own relation, $f_{s,\max} = \mu_s N$, and read the name carefully — it is a ceiling, not a value. Below it, static friction supplies exactly as much as the push demands and no more. Reach it and the grip is spent; the crate breaks loose and the smaller kinetic coefficient takes over. That is why the hardest part of moving a couch is the first centimetre.

Now tilt a surface until the load just lets go. At that instant the down-slope pull equals the ceiling: $mg\sin\theta = \mu_s\, mg\cos\theta$. The mass cancels clean off both sides and leaves $\mu_s = \tan\theta$ — the angle of repose, where $\theta$ is the steepest slope in degrees that still holds. Measure the angle a gravel pile stands at and you have measured its coefficient of friction, without weighing a single stone.