Momentum in collisions

Collision problems revolve around one central promise: total momentum is conserved when external forces are negligible. The rest of the problem is deciding whether kinetic energy is also conserved.

The two questions to ask

1. What is the total momentum before the collision?
2. Does the collision conserve kinetic energy, or do the objects stick together?

Momentum

p = m v

Always conserved in collision problems

Perfectly inelastic

v_f = (m1 v1 + m2 v2) / (m1 + m2)

Objects move together after impact

Elastic vs inelastic

Elastic collisions conserve both momentum and kinetic energy.
Inelastic collisions conserve momentum but convert some kinetic energy into heat, sound, or deformation.
Perfectly inelastic collisions are the extreme case where the objects move together afterward.

Interactive lab

Collision Physics

Body A

Mass: 2 kg

Velocity: 4 m/s

Body B

Mass: 2 kg

Velocity: 0 m/s

Collision Type

Final speed

0.00 m/s

Final speed

4.00 m/s

KE Lost

0.00 J

Momentum

8.0 kg m/s

Momentum conserved(8.0 = 8.0 kg m/s)

KE conserved(Elastic collision)

Next step

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Quick reference

Momentum conservation: p_before = p_after
Elastic cue: KE_before = KE_after