At what range does a conservative force contribute to the thermal U?

[etotheipi]

Suppose we define our system to contain a few deformable bodies that exert gravitational forces on each other, and are consequently moving towards each other in some vague sense.

We might want to express the total energy of the system as the sum of the mechanical energy and internal energy. From my perspective, the gravitational potential energies would contribute to the mechanical part, and the intermolecular electric/gravitational/etc potential energies within the bodies themselves would contribute to the internal energy. Just because from this perspective, the macroscopic/microscopic distinction is more obvious.

However, we could have just as easily zoomed way way out of the above scenario, and considered all of those deformable bodies to make up one larger deformable body, with a fixed COM (no external forces). Now, we can just as easily say the system has no mechanical energy, and only internal energy.

So how do we draw the line? I'm aware that I'm probably misinterpreting a few things so please do let me know if this is completely the wrong outlook. Thanks!

 

[HallsofIvy]

There is NO such line. The affect of force gets smaller with distance (typically as 1/r^2) but there is no point where it is 0. You will have to decide when you want to declare that the force is "negligible" yourself.

 

[etotheipi]

There is NO such line. The affect of force gets smaller with distance (typically as 1/r^2) but there is no point where it is 0. You will have to decide when you want to declare that the force is "negligible" yourself.

You're right, suppose instead we paused time and considered a snapshot of the scenario. The magnitudes of the gravitational forces between each deformable body would then be fixed.

It seems the gravitational PE between the various deformable bodies could be considered as a contribution to the thermal energy or the mechanical energy of that system.