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Momentum and collisions

The momentum of a body is its mass times its velocity, and it is conserved in a collision when external forces can be neglected, no matter how much kinetic energy is lost. In a perfectly inelastic collision the bodies stick together afterward, and some kinetic energy always turns into heat and deformation.

p = mv

momentum

m_1v_1 + m_2v_2 = m_1v_1' + m_2v_2'

conservation of momentum in a collision

Symbols

$p$	momentum	kg·m/s
$v,\ v'$	speed before/after	m/s

Example

A 1200 kg car at 15 m/s hits a stationary 800 kg car and they stick together. $v' = \dfrac{1200\cdot 15}{2000} = 9.0$ m/s.

Use momentum in collisions, not kinetic energy – that is only conserved in perfectly elastic collisions.

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