FirstPrinciplesa Physoly project
EN-07energytrap · Path vs. state confusion

Friction work depends on path length

  1. 01

    The tempting model

    Treating friction like gravity and using only vertical height change.

  2. 02

    Why it feels right

    Energy methods often compress a path into endpoints, so friction gets accidentally included.

  3. 03

    Where it breaks · how to catch it

    Two rough paths with the same endpoints lose the same mechanical energy in your solution.

  4. 04

    The correct model

    Kinetic friction is non-conservative: W_f = -f_k times path length. Longer rough paths dissipate more energy even with the same height change.

  5. 05

    Repair · see it, then test it

    worked example Two rough ramps reach the same height, one longer. Which loses more energy to friction?

    Tempting move

    Same, because the height is the same.

    Correct move

    The longer ramp, if f_k is comparable, because friction acts over more distance.

    Test the repair EN-07 · transfer
    include J

    Make a fresh prediction before referring to the worked example.

    Then practise it on the ladder

    R17Endpoint work by gravityadds: Conservative work depends on endpoints, not the path.R19Frictional loss over a pathadds: Friction work depends on path length.