# Why do completely inelastic collision have MAXIMUM energy loss?

1. Oct 31, 2013

### MathewsMD

I understand that energy is lost, but it doesn't necessarily show that this is MAXIMUM energy loss, just that there is energy lost. How would you go about proving that more energy cannot be lost, as long as momentum is conserved (no net external force)?
I honestly feel like I'm just missing something here, so any clarification on the matter would be much appreciated!

2. Oct 31, 2013

### tiny-tim

Hi MathewsMD!

Suppose two objects collide head-on so that their centre of mass was stationary before the collision.

Clearly the minimum KE afterwards is zero (because zero is possible, and < zero isn't! ).

Zero corresponds to the two bodies sticking together, ie a perfectly inelastic collision.

Now transform into any other frame of reference.

3. Oct 31, 2013

### arildno

In addition to tiny-tim's version, You may also think of a collision as a two-phase process:

In phase 1, their relative velocity at the contact point goes to zero, the objects deforming to maximal extent (and gaining maximal potential energy, as in two springs).

In phase 2, the RESTITUTION phase, the potential energy associated with deformation is switched back into kinetic energy, to a CERTAIN DEGREE. For fully elastic collisions, ALL energy converted from kinetic in phase 1 was contained in potential energy, and thus for full restitution, energy is always conserved.

INELASTIC collisions may be thought of as the extreme case where NONE of the energy going into deformation was stored in potential energy (it dissipates as heat instead); i.e, you experience maximal energy loss.

4. Oct 31, 2013

### AlephZero

That is a bit over-simplified. Some of the energy may be stored permanently in the bodies without being converted to heat - for example, as "locked in" stresses and strains resulting from plastic deformation of the bodies.

The key point is that none of the internal energy is transferred back into KE which corresponds to rigid body motion of the objects, i.e. "you experience maximal kinetic energy loss."

Of course if you account for all forms of energy, the energy is conserved whatever type of collision occurs.

5. Nov 1, 2013

### arildno

Sure it is oversimplified.
I cut out the mechanical energy loss from the generation of sound waves as well.
The point is that there is no potential energy storage in the idealized inelastic collision, thus meaning there will be a net loss of mechanical energy in the system, whatever type of other forms of energy the initial kinetic energy is converted into.