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Impulse and momentum

Momentum is mass times velocity. A force acting for some time changes the momentum, and the product of force and time is called impulse. In a collision with no external forces the total momentum is conserved.

p = m v

momentum

F\,\Delta t = \Delta p

impulse-momentum theorem

m_1 v_1 + m_2 v_2 = m_1 v_1' + m_2 v_2'

conservation in a collision

Symbols

$p$	momentum	kg·m/s
$F$	average force	N
$\Delta t$	duration	s
$v'$	velocity after the collision	m/s

Example

A 1000 kg car at 20 m/s stops in 0.5 s:

$F = \Delta p/\Delta t = 20\,000/0.5 = 40$ kN.

A longer stopping time gives a smaller force. That is why airbags and crumple zones save lives.

Practise work, energy and momentum for free →

← Conservation of energy

Part of Statics and Dynamics: Work, energy and momentum.