FirstPrinciplesa Physoly project
EN-06energytrap · Dimensional inconsistency

Spring energy uses displacement squared

  1. 01

    The tempting model

    Using kx or mgx as spring energy instead of ½kx².

  2. 02

    Why it feels right

    Spring force is kx, so energy feels like it should be the same expression.

  3. 03

    Where it breaks · how to catch it

    Your spring energy has units of newtons instead of joules, or changes sign when x changes sign.

  4. 04

    The correct model

    Spring potential energy is the area under F = kx: U_s = ½kx². Compression and extension with equal |x| store equal energy.

  5. 05

    Repair · see it, then test it

    worked example A spring with k = 200 N/m is compressed 0.10 m. Energy stored?

    Tempting move

    kx = 20 N.

    Correct move

    ½kx² = 1.0 J.

    Test the repair EN-06 · transfer
    include J

    Make a fresh prediction before referring to the worked example.

    Then practise it on the ladder

    R18Spring turning pointadds: Spring energy is quadratic in displacement.