← Power and the energy ledger

Where kinetic energy goes in an inelastic collision

A moving railcar rolls into a stationary one. The couplers latch, and the pair moves off together, slower.

Measure the kinetic energy before and after the coupling: the after-total is smaller.

Momentum survives the coupling. Part of the kinetic energy does not. Where does it go?

A collision where the objects latch together and move as one is an inelastic collision.

At the latch, metal grinds on metal for an instant, and both couplers end slightly warmer.

before: one car movingtrackrailcar 1movingrailcar 2at restafter: the pair, slowertrackrailcar 1railcar 2moving, slowerslightly warm
Before: one car moving. After: the pair, slower, with warm couplers.

Part of the kinetic energy converts to thermal energy in the metal at the contact.

Another part goes into permanently changing the metal's shape. A dent or a crumple that stays is called permanent deformation, and making it takes energy.

So in an inelastic collision, part of the kinetic energy converts to thermal energy and permanent deformation, while total energy remains conserved.

Count every form: the kinetic energy after, plus the thermal energy and the deformation energy, equals the kinetic energy before.

A crash-test car striking a barrier shows the shares vividly: the crumple zone folds once and stays folded, the metal warms, and the car's kinetic energy is accounted for in full.

before the impactbarriercrash-test carmovingafter the impactthe same car, stoppedfolded, and it stays folded
The crumple zone folds once and stays folded: permanent deformation.

Two shopping carts couple on impact and move off together, with less total kinetic energy than before. Did the coupling destroy energy?

Part of the kinetic energy converted to thermal energy where the metal ground together.

Part went into permanent deformation: bent metal that stays bent.

Counting those forms, the total energy after the coupling equals the total before it.

No. The kinetic energy that left the motion is now thermal energy and deformation; the total energy is conserved.

Two bumper cars collide and lock together for a moment, moving off as one with less total kinetic energy than before. What happened to the kinetic energy the pair no longer carries?

Two warehouse dollies bump and latch together, and the pair rolls on more slowly. Flor says: 'Counting the thermal energy and the energy of deformation, the total energy after the latch equals the total before it.' Is she correct?

A beanbag dropped on a floor lands dead the same way: its kinetic energy becomes thermal energy and a permanent change of shape in the filling.

The account of an inelastic collisionform of energybeforeafterkineticall of itlessthermalnonesomedeformationnonesometotalthe samethe same
The kinetic column falls; thermal and deformation rise; the total holds.

A clay ball thrown at a wall sticks to it. State what happens to the clay's kinetic energy.

The clay stops, so its kinetic energy leaves the motion entirely.

Part converts to thermal energy in the clay and the wall.

Part goes into the clay's permanent change of shape: it is flattened, and it stays flattened.

The clay's kinetic energy becomes thermal energy and permanent deformation; none of it is destroyed.

A horseshoe dropped onto damp sand lands and stops without bouncing. Which statement is true of its kinetic energy?

Your turn

A van rolls into a parked trailer and their bumpers lock together. What happens to the kinetic energy the pair no longer carries?

In an inelastic collision, which quantity is conserved?

Two show sleds collide on ice and latch together, and careful measurement finds less total kinetic energy after the latch. Which statement explains the measurement?