FirstPrinciplesa Physoly project
MOM-08momentumtrap · Dimensional inconsistency

Impulse is area under force-time, not peak force

  1. 01

    The tempting model

    Using the maximum force in a collision as if it were the impulse.

  2. 02

    Why it feels right

    Peak force is easy to read directly, while impulse requires the area over the entire collision interval.

  3. 03

    Where it breaks · how to catch it

    Your impulse has units of newtons instead of newton-seconds.

  4. 04

    The correct model

    Impulse is J = ∫F dt = Δp. A longer, smaller force can deliver the same impulse as a shorter, larger force.

  5. 05

    Repair · see it, then test it

    worked example A triangular force-time pulse has height 100 N and width 0.20 s. Impulse?

    Tempting move

    100 N.

    Correct move

    Area = ½(0.20)(100) = 10 N·s.

    Test the repair MOM-08 · transfer
    include N·s

    Make a fresh prediction before referring to the worked example.

    Then practise it on the ladder

    R23Impulse from a force-time graphadds: Impulse is area under the force-time curve.