About the Momentum Calculator
What is the Momentum Calculator?
Momentum – mass times velocity – is always conserved in a collision when no outside force acts. This calculator uses that law to find what happens after two objects collide.
In an elastic collision, kinetic energy is also conserved and the objects bounce apart. In a perfectly inelastic one, they stick together and some energy turns into heat and sound.
How to use the Momentum Calculator
- Mass of Object 1 (kg) (sample: 2)
- Velocity of Object 1 (m/s, + right / − left) (sample: 3)
- Mass of Object 2 (kg) (sample: 1)
- Velocity of Object 2 (m/s) (sample: 0)
- Collision Type (sample: Perfectly elastic (bounce))
- Press Calculate Momentum & Collision (results also refresh as you type). The result card shows the Total Momentum, along with Object 1 velocity after, Object 2 velocity after, Kinetic energy before and Kinetic energy lost.
Formula used
m₁v₁ + m₂v₂ = m₁v₁′ + m₂v₂′
- Inelastic = v′ = (m₁v₁ + m₂v₂) ÷ (m₁ + m₂)
- Elastic = v₁′ = ((m₁ − m₂)v₁ + 2m₂v₂) ÷ (m₁ + m₂)
Use negative velocities for motion in the opposite direction.
Worked example
These are the sample values already filled in the calculator above, and the result it returns for them:
| Input | Sample value |
|---|---|
| Mass of Object 1 (kg) | 2 |
| Velocity of Object 1 (m/s, + right / − left) | 3 |
| Mass of Object 2 (kg) | 1 |
| Velocity of Object 2 (m/s) | 0 |
| Collision Type | Perfectly elastic (bounce) |
| Result | Value |
|---|---|
| Total Momentum | 6 kg·m/s |
| Object 1 velocity after | 1 m/s |
| Object 2 velocity after | 4 m/s |
| Kinetic energy before | 9 J |
| Kinetic energy lost | 0 J |
Tips for using the Momentum Calculator
- Real collisions lie between elastic and perfectly inelastic.
- Equal masses in an elastic head-on collision simply swap velocities.