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The Law of conservation of Mechanical Energy states that in a closed system with no non-conservative forces acting, the energy of the system will always remain constant. This makes sense for an elastic collision where Mechanical energy is conserved. However, if an inelastic or completely inelastic collision takes places in a closed system with no dissipative forces acting on it, how is mechanical energy not conserved?

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Energy is conserved in inelastic collisions. Bulk kinetic energy is not conserved.

The sources I learned from never introduced a "Law of conservation of Mechanical Energy". I assume it applies in a restricted mechanics where thermalization is disallowed and all energy must be expressed in terms of macroscopic coordinates.

In that case the energy lost from (or added to) the kinetic channel must be hiding in strain potentials of some kind (elastic potential energy or some non-linear generalization).

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  • $\begingroup$ ok, so the energy lost during the inelastic collisions is thermal energy, which is not accounted for in the conservation of mechanical energy? $\endgroup$ – William Cooper Jan 14 at 17:59
  • $\begingroup$ You can still have inelastic behavior in the restricted mechanics. You just have to stick the energy into some macroscopic strain. An artificial text-book example is a spring attached to a ratchet: you compress it during the collisions, but the mechanism doesn't let it expand again, so energy is trapped. For a more "real world" case, the folding of sheet metal in a car collisions can trap considerable amounts of potential enery (it will also disapate some heat, but your author seems to have disallowed that). $\endgroup$ – dmckee --- ex-moderator kitten Jan 14 at 18:04
  • $\begingroup$ Thank you very much! $\endgroup$ – William Cooper Jan 14 at 18:05
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In most collisions heat is generated and/or work is done deforming material around the point of contact. (Consider the condition of a car after a collision with another car.)

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  • $\begingroup$ ah, so there is work done in deforming the car. $\endgroup$ – William Cooper Jan 14 at 18:12

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