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Mechanics
Mechanics

Elastic Collision (1D)

v1′=m1−m2m1+m2v1+2m2m1+m2v2v_1' = \frac{m_1 - m_2}{m_1 + m_2}v_1 + \frac{2m_2}{m_1 + m_2}v_2

Final velocity after elastic collision where KE is conserved.

Variables

v₁'
Final velocity of object 1
After collision
m/s
m₁
Mass of object 1
First object mass
kg
m₂
Mass of object 2
Second object mass
kg
v₁
Initial velocity of object 1
Before collision
m/s
v₂
Initial velocity of object 2
Before collision
m/s

Derivation

Solve conservation of momentum and KE simultaneously.

Your notes

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Common questions

What is the Elastic Collision (1D) formula?

Elastic Collision (1D) is written v₁' = m₁ - m₂/m₁ + m₂v₁ + 2m₂/m₁ + m₂v₂. Final velocity after elastic collision where KE is conserved. It belongs to Mechanics, under Momentum.

What are the units in v₁' = m₁ - m₂/m₁ + m₂v₁ + 2m₂/m₁ + m₂v₂?

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 + m₂v₁ + 2m₂/m₁ + m₂v₂.