Elastic Collision (1D)
Final velocity after elastic collision where KE is conserved.
Variables
Derivation
Solve conservation of momentum and KE simultaneously.
Your notes
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- m₁ = 2 kg (Mass of object 1)
- m₂ = 3 kg (Mass of object 2)
- v₁ = 4 m/s (Initial velocity of object 1)
- v₂ = 5 m/s (Initial velocity of object 2)
Result: v₁' = 5.2 m/s
Other mechanics formulas with the same quantities
- Coefficient of Restitution (Momentum) shares Final velocity of object 1, Initial velocity of object 1, Initial velocity of object 2
- Perfectly Inelastic Collision (Momentum) shares Mass of object 1, Mass of object 2
Where this formula is listed
- Mechanics formulas, under Momentum, alongside Impulse.
- In the mechanics list it comes after Impulse and before Perfectly Inelastic Collision.
- Mechanics formula sheet, one of 58 formulas printed with symbol keys and SI units.
- The full formula index, grouped by category and topic.
Common questions
What is the Elastic Collision (1D) formula?
Elastic Collision (1D) is written v₁′ = ((m₁ − m₂)/(m₁ + m₂))v₁ + (2m₂/(m₁ + m₂))v₂. Final velocity after elastic collision where KE is conserved. It belongs to Mechanics, under Momentum.
What are the units in v₁′ = ((m₁ − m₂)/(m₁ + m₂))v₁ + (2m₂/(m₁ + m₂))v₂?
In SI units, v₁′ is final velocity of object 1, measured in m/s; m₁ is mass of object 1, measured in kg; m₂ is mass of object 2, measured in kg; v₁ is initial velocity of object 1, measured in m/s; v₂ is initial velocity of object 2, measured in m/s.
How is the Elastic Collision (1D) formula derived?
Solve conservation of momentum and KE simultaneously. The result is v₁′ = ((m₁ − m₂)/(m₁ + m₂))v₁ + (2m₂/(m₁ + m₂))v₂.