Possibly a stupid question, but suppose I wind up a spring. I am therefore storing energy in it.
Does this increase in energy increase the mass of the spring?
Or suppose I put a box on a high shelf. I am therefore storing potential energy in it. Does the mass of the box increase?
Finally, I throw something up into the air. The increased distance between the object and the earth means that I am storing energy. If I can throw the something high enough to make it escape into space, where does the energy go?
I’m nowhere near the level I would need to be to answer these questions, but I have a feeling that energy is too light to affect the weight of anything appreciably.
Yep, the mass of a tight spring is more (trivially!) than the mass of a loose spring, because of Relativistic effects.
No, the mass of a raised object is not more than the mass of a lowered one: the earth’s gravitational field is where the energy is stored, not in the object.
An object hurled out to escape velocity (“to infinity, and beyond!”) continues to gain potential energy forever (at a vastly diminishing rate.) This energy is compensated for by the fact that the object’s speed, away from the earth, is always decreasing (slightly…) For instance, take Voyager: it won’t travel quite as far today as it did yesterday. The earth is still pulling on it, slowing it down. (Gosh, maybe as much as an inch per decade at its current distance…)
If an object hurled out to space gains potential energy, is the universe as a whole gaining potential energy as it expands? If so, where is the energy coming from?
Well yes, in a way. The store of mechanical potential energy is increased but the store of chemical potential energy (assuming chemical rockets did the lifting) is decreased by even more with the difference being converted into the entropy of the process.
I see I misunderstood your question. I think that the potential energy gained by expansion of the universe comes at the expense of the thermal energy in the big bang. The universe as a whole, as I understand it, is slowly getting colder.