# B Collisions Toolkit

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1. Nov 6, 2018

### neilparker62

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. Nov 6, 2018

### Staff: Mentor

Thanks for sharing!