# Mass of a compressed spring

I was wondering if:

1. The mass of a compressed spring is greater than that of an uncompressed spring
2. The mass of a body on the surface of the Moon is greater than that on Earth

according to the equation $E= mc^2$

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vaguely related: physics.stackexchange.com/questions/32067/… – John Rennie Feb 12 '13 at 10:10

1) Yes. When you compress a spring you do work on it, adding energy to it. This energy is stored in the configuration of the molecules that make up the spring. As you rightly point out, the $E=mc^2$ relation for an object at rest can then lead us to conclude that the rest mass of a compressed spring exceeds the rest mass of an uncompressed spring. But you should do the calculation to determine by how much!
2) Yes, but... When considering the energy of a bound gravitational system, it is best to think of the system as a whole. Consider the following thought experiment: You begin with a ball held at some height above the surface of the earth. Let's say that the rest mass of the elevated ball + earth system is $m_1$. Then you allow the ball to drop to the surface of the earth. When it hits the ground, some energy is released as sound, thermal vibrations, and eventually thermal radiation. Some of this energy will escape into space. Again, because of the $E = mc^2$ relation for objects at rest, the rest energy of the dropped ball + earth system, $m_2$, will be less than $m_1$.