I am thinking of a system of isolated, moving, and colliding particles in a frictionless box. The collisions were inelastic. My question is:

Supposing that the initial total momentum of the system is not zero. Since the collisions are inelastic, kinetic energy will not be conserved (converted to heat, sound, etc.). But since the isolated system experiences no net external force, the momentum could not change (Newton’s Second Law). Hence, total momentum of the system will remain constant. If I let the particles in the system collide for awhile, eventually, they will build up heat, but then again the momentum could not change. The particles would not stop until the box overheats.

What’s the problem with the scenario and my line of thinking?

  • 2
    $\begingroup$ You can't create more energy than what is already in the box. At some point, all of the particles in the box will be stuck together, and those particles will be moving at the same speed as the box. Momentum will remain conserved, and no collisions will be occurring. $\endgroup$ – David White Mar 28 '20 at 17:09
  • $\begingroup$ Which means the momentum completely transferred to the box itself? Right? $\endgroup$ – Lyle Mar 28 '20 at 17:12
  • $\begingroup$ No ... it means that the momentum transfers to the box and the particles. As you run this thought experiment through your mind, be careful to stay in the same imaginary reference frame that you started in. $\endgroup$ – David White Mar 28 '20 at 17:15
  • $\begingroup$ Oh thanks! Forgot about reference frames in this scenario. Sorted things out that way. $\endgroup$ – Lyle Mar 28 '20 at 17:25

In many-particle problems one has to distinguish the constants characterizing the movement of the system as a whole (it energy, the three components of the center-of-mass momentum, and the three components of the angular momentum), and the relative movement of the parts in the system.

So, indeed, the relative movement of the particles will eventually cease and its temperature will increase, but the seven integrals of motion (constants) mentioned above will conserve (if there are no external forces).

The concept of the particles that convert their kinetic energy into heat is suspect, since heat is the kinetic energy of the particle movement. So I suppose what is meant as particles is really macroscopic objects.


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