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neilparker62

Homework Helper

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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.

$$ Δp = 2μΔv $$

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.

$$ Δp = μΔv $$

$$ P_f=P_i\pmΔp $$

$$ E_f=\frac{(P_i\pmΔp)^2}{2m} $$

$$ ΔE = ½μΔv^2 $$

*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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