Energy conservation fails when external work is hidden

01
The tempting model
Applying KE + PE = const when friction, drag, or a motor is present.
02
Why it feels right
Total energy is conserved, but it is easy to mistake that statement for conservation of mechanical energy alone.
03
Where it breaks · how to catch it
You equated initial and final mechanical energy despite friction or an applied push.
04
The correct model
Mechanical energy is conserved only when non-conservative work is zero. Otherwise ΔKE + ΔPE = W_nonconservative (negative for friction).
05
Repair · see it, then test it
worked example A box slides down a rough ramp of height h. Is ½mv² = mgh?
Tempting move
Yes, energy is conserved.
Correct move
No — ½mv² = mgh − f·d; friction removes f·d as heat.
Test the repair EN-01 · transfer

A motor pulls a crate up a rough ramp at constant speed. Which mechanical-energy statement is complete?
Mechanical energy is conserved The motor's work becomes only gravitational potential energy Motor work supplies both increased gravitational potential energy and thermal energy Friction does no work

Make a fresh prediction before referring to the worked example.
Then practise it on the ladder
R19Frictional loss over a pathadds: Friction work depends on path length.