Energy conservation fails when external work is hidden
The mistake
Applying KE + PE = const when friction, drag, or a motor is present.
Why it feels right
Total energy is conserved, but it is easy to mistake that statement for conservation of mechanical energy alone.
How to catch it
You equated initial and final mechanical energy despite friction or an applied push.
The first principle
Mechanical energy is conserved only when non-conservative work is zero. Otherwise ΔKE + ΔPE = W_nonconservative (negative for friction).
worked mini-example
A box slides down a rough ramp of height h. Is ½mv² = mgh?
Common wrong move
Yes, energy is conserved.
Correct
No — ½mv² = mgh − f·d; friction removes f·d as heat.
Test the repair EN-01 · transfer
Make a fresh prediction before referring to the worked example.