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B Collisions Toolkit

  1. Nov 6, 2018 #1


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    Homework Helper

    Just thought I'd post a couple of formulas which I have found useful when assisting (or should I say attempting to assist!) with collisions problems in the "Homework" forums. These formulas work on the basic premise that a collision is essentially a "Newton 3 event" in which equal and opposite impact forces act for a (usually) short period of time resulting in equal and opposite impulses on the colliding objects.

    Collision impulse during perfectly elastic collisions:

    $$ Δp = 2μΔv $$
    where μ is the reduced mass of the colliding objects:
    $$ μ=\frac{m_1m_2}{m_1+m_2} $$
    and Δv is their relative velocity along the line of impact.

    Collision impulse during perfectly inelastic collisions:

    $$ Δp = μΔv $$

    Post collision momentum and energy (applies to both colliding objects)

    $$ P_f=P_i\pmΔp $$
    $$ E_f=\frac{(P_i\pmΔp)^2}{2m} $$

    Energy loss during perfectly inelastic collisions

    $$ ΔE = ½μΔv^2 $$
    Last edited: Nov 6, 2018
  2. jcsd
  3. Nov 6, 2018 #2


    Staff: Mentor

    Thanks for sharing!
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