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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
$$ ΔE = ½μΔv^2 $$
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
$$ ΔE = ½μΔv^2 $$
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