Trying to understand potential energy with this tricky question

[farleyknight]

Some of you might recognize my screen name as the math guy that doesn't "get" physics. Well maybe you can help me straighten out my understanding of at least one law, and I'll just bother the forum for others as I learn them at my own pace.

Wikipedia gives the definition of potential energy:

Potential energy is energy stored within a physical system as a result of the position or configuration of the different parts of that system.​

So depending on the way objects are placed, we can "store" energy. Okay, seems fair enough to me. Then take this example.

I'm going to "store" some elastic potential energy into a spring. Consider an idealized room, where we can analyze just the potential energy without other forces getting in the way. Well, almost all forces. You'll see in a second. I place a spring on the floor of this room and it points straight up. I place two heavy books on top of it, in such a way that one book would cause the spring to bounce back but two books is enough mass to keep it in a compressed state.

With me so far? Now, I leave the room and let it sit there for years, no.. decades. The metal of the spring now begins to rust. It is no longer elastic, it's coils are now welded together by oxidation. I return and lift the first book from the spring and it does not move. The energy is now gone.

My question is, where is the energy that was stored? We know by the conservation of energy that energy is neither created or destroyed in a closed system. Granted, when I entered and left the room I broke that closed-ness but I hope I'm correct that during the period of time when the spring began to rust that the stiffness of the spring became less and potential energy was lost.

So what exactly is going on? Is the idealization of elastic potential energy that I'm given too simple to take into account this case? If so, then for what it's worth, I don't really "understand" the law, just a simplified version that's only applicable in special cases, correct? How do you extend this definition to include such cases?

 

[aquapurity]

If the coils of the springs are welded together by oxidation, then this would effectively be replacing the two books. The potential energy is still in the spring, but the strength of the welding is equal to or greater than the gravitation strength of the two books, therefore effectively continuing to bottle up the potential energy. No?

 

[Yuqing]

Elastic potential energy on a microscopic level is the energy stored within the electric fields of the molecules. Compression arranges the lattice in such a way that attraction or repulsion forces sum to a net macroscopic "elastic" force. My reasoning is that since the structural energy is still present, the new oxidized metal has a greater amount of intrinsic energy within it's bonds/structure.

 

[rcgldr]

In real life, even without rusting, most springs would end up becoming permanently deformed over very long periods of time, somewhat behaving like a liquid where the internal structure changes over time. I assume the potential energy leakage would be in the form of heat.

 

[Blankato]

This has been something that has always confused me, perhaps I should have started my own thread, but this is more efficient and directly related.
Consider a similar example, going into space on a spacecraft . As the ship climbs its gaining or 'storing' potential energy right? Right, now consider two possibilities:
Possibility A:
The unmanned ship stalls out 1 mile up and falls to the ground, thus 'losing' all the potential energy that has been 'stored'.

Possibility B:
The unmanned ship achieves orbit, and even morose, goes beyond the immediate gravitational pull of Earth. (as the Viking orbiter did)

In both possibilities has the ship lost all of the potential energy stored? If not, in possibility B, what has happened to the energy 'stored'?
Furthermore, if the energy remains 'stored' in possibility B, does that mean that everything in the universe has energy stored from everything else?

 

[vanesch]

In real life, even without rusting, most springs would end up becoming permanently deformed over very long periods of time, somewhat behaving like a liquid where the internal structure changes over time. I assume the potential energy leakage would be in the form of heat.

I would think so too. Another possibility (which comes ultimately down to heat in the end) is that the energy is stored in some form of chemical energy, for instance, in more lattice defects or so. Upon rusting, the liberated energy by the chemical reaction will then slightly higher. But I admit not knowing the exact "pathway" of the potential energy of the spring towards heat.

As a general remark in this thread, what's maybe misleading with the wiki definition is that one might think that there is some "storage" of potential energy in the *object*. That doesn't need to be the case. In the case of gravitational potential energy, the energy is not somehow "stored" in the object (as a physical modification of the object or so). It is just a mathematical trick to have a shortcut to the effect of the force of gravity, and if you insist on a "location" of the potential energy the second best answer would be "in the gravitational field" (the best answer would be: in the calculation on your sheet of paper )

 

[dacruick]

rusting is an exothermic reaction, so if it rusts it will give off head, increasing the temperature in the room.