The normal force is not always mg
The mistake
Setting N = mg on an incline, in an elevator, or under an applied force.
Why it feels right
On a level floor with no vertical acceleration, N = mg. Reusing that special case can feel automatic.
How to catch it
You wrote N = mg without checking the perpendicular force balance.
The first principle
N is found from Newton's second law perpendicular to the surface. On a slope N = mg·cos θ; in an accelerating lift N = m(g ± a).
worked mini-example
A 3.0 kg block rests on a 25° incline. Find the normal force.
Common wrong move
N = mg = 29.4 N.
Correct
N = mg·cos 25° ≈ 26.6 N.
Test the repair NL-07 · transfer
include N
Make a fresh prediction before referring to the worked example.