The Memory Trick
💡 Total Momentum Before = Total Momentum After
In any closed system (no external forces), the total momentum before a collision or interaction equals the total momentum after: m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'. This holds true regardless of what happens during the collision — whether objects bounce apart or stick together.
Why It Works
Momentum conservation follows directly from Newton's Third Law — the forces two colliding objects exert on each other are equal and opposite, so any momentum one gains, the other loses in exactly equal measure.
Step by Step
The Three Types of Collisions
1
Elastic collisions
Both momentum AND kinetic energy are conserved. Objects bounce off each other without permanent deformation or heat loss.
Billiard balls colliding on a pool table — a close real-world approximation of a perfectly elastic collision.
2
Inelastic collisions
Momentum is conserved, but kinetic energy is NOT — some KE converts to heat, sound, or deformation.
A car crash: the vehicles crumple and heat up, losing kinetic energy, but the total momentum of the system is unchanged.
3
Perfectly inelastic collisions
The most extreme case of an inelastic collision — the objects stick together after impact and move with a shared final velocity, losing the maximum possible kinetic energy while momentum remains conserved.
A ballistic pendulum: a bullet embeds itself in a wooden block, and the two move together afterward.
🏥 Worked Example
A 1000 kg car moving at 15 m/s rear-ends a stationary 1200 kg car, and the two vehicles lock together (perfectly inelastic collision). What is their combined velocity right after impact?
1
Set up conservation of momentum: m₁v₁ + m₂v₂ = (m₁+m₂)v'.
2
Plug in values: (1000×15) + (1200×0) = (1000+1200)×v' → 15,000 = 2,200 × v'.
3
Solve: v' = 15,000/2,200 ≈ 6.8 m/s — much slower than the original 15 m/s, since the combined mass is much greater.
📌 Exam Application
Exams test correctly setting up the conservation equation for two-object systems, distinguishing which type of collision applies (elastic, inelastic, perfectly inelastic), and knowing that kinetic energy is only conserved in the elastic case.
⚠️ Most Common Conservation of Momentum Mistakes
The most common trap is assuming kinetic energy is always conserved alongside momentum — it's only conserved in perfectly elastic collisions. In every other type, momentum is conserved but kinetic energy is not.
✓ Quick Self-Test
1) State the conservation of momentum equation for a two-object collision. m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'. 2) In which type of collision is kinetic energy conserved? Only elastic collisions. 3) What happens to the objects in a perfectly inelastic collision? They stick together and move with a shared final velocity. 4) Is momentum conserved in an inelastic (but not perfectly inelastic) collision? Yes — momentum is always conserved in a closed system, regardless of collision type. 5) Where does the 'lost' kinetic energy go in an inelastic collision? It converts to heat, sound, and deformation of the colliding objects.
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