Physics

Collision Calculator (1D, Elastic and Inelastic)

Two objects collide along a line. What happens to their velocities?

Your numbers

Your results

Elastic: final velocity 1 (m/s)
Elastic: final velocity 1 (m/s)
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Elastic: final velocity 2 (m/s)
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Inelastic: common velocity (m/s)
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Kinetic energy lost if inelastic (J)
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Total momentum (kg·m/s)
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Collision Calculator (1D, Elastic and Inelastic) by TheCalcTools

How the Collision Calculator (1D, Elastic and Inelastic) works

Enter the mass and velocity of each object, using signs for direction.

Momentum is conserved in both cases.

In an elastic collision kinetic energy is also conserved; in a perfectly inelastic collision the objects stick together.

The formula

v₁′ = ((m₁ − m₂)v₁ + 2m₂v₂) ÷ (m₁ + m₂)v₂′ = ((m₂ − m₁)v₂ + 2m₁v₁) ÷ (m₁ + m₂)

Worked example

Using the default values shown in the calculator:

Mass 1 (kg)2
Velocity 1 (m/s)3
Mass 2 (kg)1
Velocity 2 (m/s)0
  1. A 2 kg mass at 3 m/s hits a 1 kg mass at rest.
  2. Elastic: v₁′ = 1.00 m/s and v₂′ = 4.00 m/s.
  3. If they stick together they move at 2.00 m/s and lose 3.00 J of kinetic energy.

Result:

Elastic: final velocity 1 (m/s)1.000
Elastic: final velocity 2 (m/s)4.000
Inelastic: common velocity (m/s)2.000
Kinetic energy lost if inelastic (J)3.000
Total momentum (kg·m/s)6.000

Frequently asked questions

What is conserved in a collision?

Total momentum always, if no external forces act. Kinetic energy is conserved only in an elastic collision.

What does a negative velocity mean?

The object moves in the opposite direction to the one you chose as positive.

Sources and further reading

More in Physics · All calculators

This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.