Mass, Energy, and Springs

[UncleFred]

After having read the older thread on batteries changing weight (or not) after charging,

Do batteries get heavier when you charge them?

I found myself understanding one principle less the further I read.

So, let me focus on one aspect;

If I compress a spring, does it’s mass change? (presumably due to energy being stored in it.)

I realize that (at a high level) is a mechanical storage and not exactly the same situation as the chemical storage discussed in the article, but posters seemed to state that any change in energy was related to a change in mass. ( Yes, I know about e=mc^2, but am not sure to what extent it applies here.)

[naita]

I was just going to quote Chronos’ early answer in that thread:

In principle, there is a slight increase in mass (E = mc2: It’s not just for nuclear reactions). In practice, though, the change is so small as to be completely imperceptible.

but then I read further through the thread and found a directly applicable quote to add to it:

Yup, potential energy stored in a spring works the same way.

[Mangetout]

I can’t get my head around how potential energy would effect a change in mass (I get that it’s implied by e=mc^2) - but if (say) I lift a rock off the ground and its mass increases because of the potential energy, what happens when I lift it so far that it is in a position to fall into Jupiter? (relative to which, it has greater potential energy because of Jupiter’s higher gravitation.

Mass would have to be calculated relative to every other object in the universe.

[naita]

@Mangetout

I can’t get my head around how potential energy would effect a change in mass (I get that it’s implied by e=mc^2) - but if (say) I lift a rock off the ground and its mass increases because of the potential energy, what happens when I lift it so far that it is in a position to fall into Jupiter? (relative to which, it has greater potential energy because of Jupiter’s higher gravitation.

Mass would have to be calculated relative to every other object in the universe.

In the case of potential energy due to gravity, the mass increase applies to the whole system. So moving the rock to Jupiter involves a constant increase in energy, and thus mass, of the Earth-Rock-system, and a decrease in the Rock-Jupiter system.

I’m fairly confident the relative weak strength of gravity makes this change in mass insignificant.

[Crafter_Man]

@naita

I was just going to quote Chronos’ early answer in that thread…

I also recall Chronos (and others) saying mass can’t be converted to energy, and energy can’t be converted to mass. E = mc[sup]2[/sup] not withstanding.

[Chronos]

It can’t be converted for the same reason that I can’t be converted into a human. Mass is always energy.

[Mangetout]

@naita

In the case of potential energy due to gravity, the mass increase applies to the whole system. So moving the rock to Jupiter involves a constant increase in energy, and thus mass, of the Earth-Rock-system, and a decrease in the Rock-Jupiter system.

I’m fairly confident the relative weak strength of gravity makes this change in mass insignificant.

The size of the values involved is not what I’m concerned about - it’s the fact that we’d have to calculate a component of the mass of any object as part of a system of that object vs all the other objects in the universe.

[Chronos]

Yup, that’s one of the many ways in which gravity is messy and complicated.