Laws of Motion

Newton’s second law relates the net force on the block to its acceleration:

Friction itself isn’t one formula but two, depending on whether the block is moving. While it’s still at rest, static friction simply matches whatever force is trying to move it, up to a maximum:

Only once the applied force exceeds that ceiling does the block move, and friction switches to a fixed kinetic value:

with the normal force $N = mg$ on a horizontal surface.

“Friction equals $\mu N$” is one of the most confidently misapplied lines in this chapter. It’s true for kinetic friction, once something is already sliding. It is not true for static friction, which isn’t a fixed value at all: it’s a reaction force that self-adjusts to exactly cancel whatever you apply, right up until it hits its ceiling of $\mu_s N$.

That’s why a stationary crate you push gently doesn’t experience a friction force of $\mu_s mg$, it experiences a friction force equal to your push, no more. Set $F_{\text{applied}}$ below the limiting value in the simulation above and watch the friction arrow track it exactly, not sit fixed at $\mu_s N$.

It’s also why $\mu_k$ is usually smaller than $\mu_s$: it takes more force to break a surface loose than to keep it sliding, which is the entire reason a heavy wardrobe is hardest to move in the first half-second.