Perfectly Inelastic Collision

v' = \frac{m_1 v_1 + m_2 v_2}{m_1 + m_2}

Objects stick together after collision. Maximum KE loss.

Variables

Final velocity

Combined velocity after collision

m/s

m₁

Mass of object 1

First object mass

Allowed values: 0 or more

m₂

Mass of object 2

Second object mass

Allowed values: 0 or more

v₁

Velocity of object 1

Before collision

m/s

v₂

Velocity of object 2

Before collision

m/s

Derivation

Conservation of momentum with v₁' = v₂' = v'.

Your notes

0/5000

Check value

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m₁ = 2 kg (Mass of object 1)
m₂ = 3 kg (Mass of object 2)
v₁ = 4 m/s (Velocity of object 1)
v₂ = 5 m/s (Velocity of object 2)

Result: v' = 4.6 m/s

Where this formula is listed

Mechanics formulas, under Momentum, alongside Impulse and Coefficient of Restitution.
In the mechanics list it comes after Elastic Collision (1D) and before Coefficient of Restitution.
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 Perfectly Inelastic Collision formula?

Perfectly Inelastic Collision is written v′ = (m₁v₁ + m₂v₂)/(m₁ + m₂). Objects stick together after collision. Maximum KE loss. It belongs to Mechanics, under Momentum.

What are the units in v′ = (m₁v₁ + m₂v₂)/(m₁ + m₂)?

In SI units, v′ is final velocity, measured in m/s; m₁ is mass of object 1, measured in kg; m₂ is mass of object 2, measured in kg; v₁ is velocity of object 1, measured in m/s; v₂ is velocity of object 2, measured in m/s.

How is the Perfectly Inelastic Collision formula derived?

Conservation of momentum with v₁' = v₂' = v'. The result is v′ = (m₁v₁ + m₂v₂)/(m₁ + m₂).