Conservation of Momentum
The law of conservation of momentum states that the total momentum of a closed system remains constant before and after any interaction, provided no external forces act on it. Momentum is the product of mass and velocity (p = mv) and is a vector quantity. This is one of the most fundamental conservation laws in physics, derived from Newton's third law (every action has an equal and opposite reaction).
In collisions, momentum is always conserved, but kinetic energy may or may not be conserved depending on the type of collision. Elastic collisions conserve both momentum and kinetic energy, while inelastic collisions conserve only momentum. Most real collisions are partially inelastic, with some kinetic energy converted to heat, sound, and deformation energy.
Momentum Equations
Collision Types
| Type | Momentum | Kinetic Energy | Example |
|---|---|---|---|
| Perfectly Elastic | Conserved | Conserved | Billiard balls, atomic collisions |
| Inelastic | Conserved | Partially lost | Most real collisions |
| Perfectly Inelastic | Conserved | Max loss | Objects stick together |
| Explosion | Conserved | Increases | Chemical energy released |
Real-World Examples
- Newton's cradle demonstrates elastic collisions where momentum and energy transfer through a chain of balls.
- Car crashes are inelastic collisions where kinetic energy is converted to deformation, heat, and sound.
- Rocket propulsion uses conservation of momentum: exhaust gases expelled backward propel the rocket forward.
- Ballistic pendulums measure projectile speeds by analyzing the momentum transfer in a perfectly inelastic collision.
Frequently Asked Questions
Can momentum be negative?
Yes. Momentum is a vector quantity with both magnitude and direction. In a one-dimensional calculation, one direction is positive and the opposite is negative. An object moving to the left when rightward is positive has negative momentum. The conservation law states that the total vector sum of all momenta remains constant.
Why is kinetic energy lost in inelastic collisions?
In inelastic collisions, some kinetic energy is converted to other forms: thermal energy (heating the objects), sound energy, and deformation energy (permanently deforming the objects). Total energy is always conserved, but kinetic energy specifically is not. In a perfectly inelastic collision, the maximum possible kinetic energy is lost while still conserving momentum.
Are perfectly elastic collisions possible in real life?
At the macroscopic level, no collision is perfectly elastic because some energy is always lost to sound, heat, or deformation. However, collisions between hard objects like billiard balls or steel bearings are very nearly elastic (95%+ kinetic energy conserved). At the atomic level, collisions between atoms and subatomic particles can be truly elastic.