Calculator Input
Use one mass unit and one velocity unit for both bodies. The calculator converts everything internally to SI units.
Example data table
| Scenario | m₁ | m₂ | u₁ | u₂ | Case | v₁ | v₂ | Total momentum |
|---|---|---|---|---|---|---|---|---|
| Sample 1 | 2 kg | 1 kg | 4 m/s | -1 m/s | Elastic | 0.667 m/s | 5.667 m/s | 7 kg·m/s |
| Sample 2 | 3 kg | 2 kg | 5 m/s | 0 m/s | Perfectly inelastic | 3 m/s | 3 m/s | 15 kg·m/s |
| Sample 3 | 1.5 kg | 0.5 kg | 6 m/s | -2 m/s | Custom e = 0.6 | 2.8 m/s | 7.6 m/s | 8 kg·m/s |
Formula used
This version models one-dimensional collisions. Use signed velocities to represent direction correctly.
How to use this calculator
- Select a common mass unit and velocity unit.
- Enter both masses and initial velocities.
- Choose whether to solve final velocities or enter them manually.
- Pick elastic, perfectly inelastic, or custom restitution when solving.
- Submit the form to see results above the calculator.
- Review the momentum table, impulses, kinetic energy change, and graph.
- Export the results using the CSV or PDF buttons.
Frequently asked questions
1) What does this calculator measure?
It computes individual and total momentum before and after a one-dimensional collision. It can solve final velocities from restitution or evaluate user-entered final velocities. It also reports impulses, kinetic energy change, center-of-mass speed, and conservation error.
2) When is total momentum conserved?
Total momentum is conserved when external impulse on the system is negligible. A mismatch between initial and final totals usually means measurement error, rounding, or an external force affected the collision.
3) What is the difference between elastic and inelastic collisions?
Elastic collisions conserve both momentum and kinetic energy. Inelastic collisions conserve momentum but lose kinetic energy. Perfectly inelastic collisions are the special case where both bodies move together after impact.
4) Can I enter negative velocities?
Yes. Negative velocities represent motion opposite to your chosen positive direction. Signed inputs are important because momentum, impulse, and restitution depend on both magnitude and direction.
5) What does the coefficient of restitution mean?
It measures how strongly the bodies separate after impact. A value of 1 means perfectly elastic, 0 means perfectly inelastic, and values between them indicate partial rebound.
6) Why does the calculator show kinetic energy change?
Momentum conservation alone does not guarantee kinetic energy conservation. Energy change helps identify elastic or inelastic behavior and shows losses to sound, heat, deformation, or internal motion.
7) Can I use different units?
Yes, but use one selected mass unit and one selected velocity unit for both bodies. The calculator converts them internally to SI, then reports momentum in kilogram-meters per second and energy in joules.
8) Is this valid for angled or two-dimensional collisions?
Not directly. This version assumes motion along one straight line. For angled impacts, resolve motion into components and analyze each axis separately, or use a vector collision model.