1D Elastic Collision Calculator
Compute final velocities of a 1D elastic collision and verify momentum/energy.
Input Data
Mass1Kg
kg
Velocity1Ms
m/s
Mass2Kg
kg
Velocity2Ms
m/s
Results
Final v₁'.
1m/s
Final v₂'.
4m/s
m₁v₁+m₂v₂.
6kg·m/s
After collision.
6kg·m/s
Before KE.
9J
After KE.
9J
Energy lost (0 for elastic).
0%
At a glance:v₁' = ((m₁−m₂)v₁+2m₂v₂)/(m₁+m₂); symmetric for v₂'. KE conserved. Complements elastic-collision and coefficient-of-restitution.
Formula
v₁' = ((m₁−m₂)v₁+2m₂v₂)/(m₁+m₂).
$$v_1' = \dfrac{(m_1 - m_2)v_1 + 2m_2 v_2}{m_1 + m_2}$$$$v_2' = \dfrac{(m_2 - m_1)v_2 + 2m_1 v_1}{m_1 + m_2}$$How to Use
- Enter masses and initial velocities.
- The tool returns finals and conservation checks.
Case Studies
m₁=m₂=1, v₁=2, v₂=0
v₁'=0, v₂'=2.
FAQ
Equal masses?
They exchange velocities (v₁'=v₂, v₂'=v₁).
Related Tools
References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.