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Energy lost in inelastic collision
Intermediate
Kinetic energy loss in a perfect inelastic collision.
ΔK = ½μ(u₁−u₂)²The kinetic energy lost in a perfectly inelastic collision is ΔK = ½μ(u₁ − u₂)² with reduced mass μ. It depends only on relative speed.
Two 1 kg masses meeting head-on at 2 m/s each lose 4 J, all of it.
Zero loss if relative velocity is zero.
In more detail
In an inelastic collision, the loss of kinetic energy equals the drop between the total kinetic energy before and after. The lost energy is converted into thermal energy, sound and deformation.
Real-world uses
- Crash investigators estimate the energy absorbed by a vehicle from its deformation.
- Metal forming processes use inelastic impacts to shape parts.
- Engineers estimate the energy lost when two vehicles lock together after a crash, using the reduced mass of the pair.
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Frequently asked questions
How do I calculate the lost energy?
Subtract the total kinetic energy after the collision from the total before.
Can the lost energy be recovered?
Not directly. It spreads into the environment as thermal energy.
Why is energy lost even if momentum is conserved?
The bodies deform and heat up during the collision, converting kinetic energy into other forms.
Related topics in Momentum & Collisions
Equal masses collide elastically · Light hits heavy object · Heavy hits light object · Reduced mass · Collisions in two dimensions · Billiard ball collisions