Calculator Inputs
Use negative velocity for motion in the opposite direction. The calculator assumes a one-dimensional perfectly elastic collision.
Example Data Table
| Case | Mass 1 (kg) | Mass 2 (kg) | u₁ (m/s) | u₂ (m/s) | v₁ (m/s) | v₂ (m/s) |
|---|---|---|---|---|---|---|
| Equal masses | 2 | 2 | 6 | 0 | 0 | 6 |
| Heavy target | 1 | 4 | 10 | 0 | -6 | 4 |
| Opposite directions | 2 | 3 | 8 | -2 | -4 | 6 |
| Moving together | 5 | 3 | 4 | 4 | 4 | 4 |
Formula Used
v₁ = ((m₁ − m₂) / (m₁ + m₂))u₁ + (2m₂ / (m₁ + m₂))u₂
v₂ = (2m₁ / (m₁ + m₂))u₁ + ((m₂ − m₁) / (m₁ + m₂))u₂
Total momentum: p = m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
Total kinetic energy: KE = ½m₁u₁² + ½m₂u₂² = ½m₁v₁² + ½m₂v₂²
These equations apply to one-dimensional elastic impacts. They assume no kinetic energy loss, no rotation, and no external force during the short collision interval.
How to Use This Calculator
- Enter both masses using the same selected mass unit.
- Type the initial velocities with positive or negative signs for direction.
- Choose your preferred velocity unit and set decimal precision.
- Optionally rename the objects, such as cart and ball.
- Press Calculate Collision to show results above the form.
- Review final velocities, impulses, conservation checks, and detected scenario.
- Use the export buttons to save the current results as CSV or PDF.
Why These Results Matter
Elastic collision analysis helps you verify physics lab outcomes, compare test data against theory, and understand how mass and direction influence rebound behavior. The calculator presents final velocity, total momentum, kinetic energy, impulse, and approach-separation speed relationships in one place for faster interpretation.
Because signed velocities are supported, the tool is useful for head-on interactions, moving targets, and direction-sensitive practice problems. The conservation checks also help identify rounding noise versus genuine modeling mistakes.
Frequently Asked Questions
1. What does this calculator assume?
It assumes a one-dimensional perfectly elastic collision. Momentum and kinetic energy stay constant, and the objects do not rotate or deform permanently.
2. Can I enter negative velocity values?
Yes. Negative values represent motion in the opposite direction. This is important for head-on collisions and moving-target scenarios.
3. Why are the results shown in m/s and kg?
The calculator converts all inputs into SI units before solving. This keeps the equations consistent and makes the conservation checks reliable.
4. What happens when both masses are equal?
In an ideal one-dimensional elastic impact, the two bodies exchange velocities. This common case appears often in classroom demonstrations and lab carts.
5. Why is there a small momentum or energy difference?
Tiny differences usually come from decimal rounding in displayed output. The underlying calculations still satisfy conservation within floating-point tolerance.
6. Can this calculator solve inelastic collisions?
No. This page is built only for elastic collisions. Inelastic events need a different model because some kinetic energy is transformed.
7. What is the relative speed check?
For elastic collisions, the separation speed equals the approach speed in magnitude. Comparing them is a quick way to verify the solution.
8. Can I use this for lab reports?
Yes. It is useful for draft calculations, sanity checks, and result summaries. Still, always cite your own measured data and method.