Elastic collision

What’s conserved?

In an elastic collision:

• Momentum is conserved
• Kinetic energy is also conserved

What does this mean?

• The sum of the individual objects’ momentums before the collision is equal to the sum of their momentums after the collision (no momentum is ‘lost’)
• The sum of the individual objects’ kinetic energies before the collision is equal to the sum of their kinetic energies after the collision (no kinetic energy is ‘lost’)

Equal masses: both objects moving

If both objects have the same mass:

• The velocity of each object is swapped after the collision.

For example, if object A is moving at +5 \, ms^{-1} and object B is moving at -3 \, ms^{-1} before the collision, then after the collision:

• Object A will be moving at -3 \, ms^{-1}
• Object B will be moving at +5 \, ms^{-1}

A special case of this is when one of the objects is stationary.

• The object that was moving will completely stop.
• The object that was stationary will start moving at the velocity of the

• object that was previously moving.

Unequal masses

If the two objects have different masses, then the velocities of both objects will change after the collision, but they won’t be swapped.

The momentums of the two objects will add up to the same total momentum before and after the collision, and so will their kinetic energies.

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