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Perfectly inelastic collision
Beginner
The bodies stick together and move with a common velocity.
v = (m₁u₁+m₂u₂)/(m₁+m₂)The bodies stick and move with a common velocity v = (m₁u₁ + m₂u₂)/(m₁ + m₂). This loses the maximum kinetic energy compatible with momentum conservation.
A 2 kg and a 1 kg cart at 3 m/s and 0: v = 2 m/s.
Maximum loss, but not all kinetic energy unless the centre of mass is at rest.
In more detail
In a perfectly inelastic collision, the objects stick together and move with a common velocity. This gives the maximum possible loss of kinetic energy for given masses.
Real-world uses
- A bullet embedded in a wooden block forms a perfectly inelastic collision.
- Train couplings that lock together after impact are modelled this way.
- A bullet fired into a wooden block becomes embedded, and the block and bullet move off together.
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Frequently asked questions
What is the common velocity?
Total momentum before divided by total mass after.
Is kinetic energy conserved?
No. A large fraction is lost in this type of collision.
Is the kinetic energy lost in a perfectly inelastic collision?
Yes. Momentum is conserved, but a large part of the kinetic energy is converted into heat and deformation.
Related topics in Momentum & Collisions
Recoil of a gun · Elastic collision · Inelastic collision · Coefficient of restitution · Elastic head-on collision velocities · Equal masses collide elastically