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?