In both elastic and inelastic collisions, total momentum is conserved in an isolated system. The difference is that total kinetic energy is conserved in an elastic collision but not in an inelastic collision. This is SL and HL content in A.2 Forces and momentum.
The Reasoning
During any collision, the forces between the bodies are internal forces. If the resultant external force is negligible, the total linear momentum remains constant:
However, momentum conservation does not require kinetic energy conservation. In an inelastic collision, some kinetic energy is transferred into internal energy, deformation, thermal energy, or sound. Total energy is still conserved.
The classification therefore depends on the system’s kinetic energy before and after impact, not on whether each object changes speed. Kinetic energy may move between objects while its total remains constant. By contrast, deformation or heating indicates that some initial kinetic energy has been transformed, making the collision inelastic.
| Feature | Elastic collision | Inelastic collision |
|---|---|---|
| Total momentum | Conserved in an isolated system | Conserved in an isolated system |
| Total kinetic energy | Conserved | Not conserved |
| Bodies stick together | Not necessarily | Only in a perfectly inelastic collision |
| Typical model | Colliding particles or idealized balls | Vehicle collision or deforming objects |
Consider two objects. Object A moves at , while B is stationary.
In an elastic collision, A could stop and B could move at . Initial and final momentum are both , while initial and final kinetic energy are both:
If they stick together, momentum conservation gives:
The final kinetic energy is , so the collision is inelastic.
A common misconception is that all inelastic collisions involve objects sticking together. Sticking occurs only in a perfectly inelastic collision.
Exam Technique
For IB questions, calculate total momentum before and after first, then compare total kinetic energy. Momentum alone cannot determine whether a collision is elastic; an examiner expects an explicit kinetic-energy comparison.
