Static friction is not always at its maximum
The mistake
Using f = μs·N whenever there is friction.
Why it feels right
The expression μsN is often presented without emphasizing that it gives a maximum, not the friction in every static situation.
How to catch it
You wrote f = μs·N for a body that isn't on the verge of slipping.
The first principle
Static friction is a range: it takes whatever value (≤ μs·N) is needed for equilibrium. Only at the threshold of sliding does it reach μs·N.
worked mini-example
A crate (weight 200 N, μs = 0.4) is pushed with 50 N and stays put. Find friction.
Common wrong move
f = μs·N = 80 N.
Correct
f = 50 N — exactly balancing the push, which is below the 80 N maximum.
Test the repair NL-04 · transfer
include N
Make a fresh prediction before referring to the worked example.