Several similar questions have been asked, e.g. this one, but all of them used the example of muscle work, so it was clear where the energy went. However, suppose we suspend an object on a rope from the ceiling. We come 20 years later and find the object hanging where we left it. I understand that no mechanical work is being performed here. However, it seems counter-intuitive that this holding of the object is achieved for free. So, what has been happening energy-wise during these 20 years and what observable changes did that result in?
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2$\begingroup$ Suppose you instead find an object that has been sitting in the same place on the floor for twenty years. Is staying immobile on the floor "for free" more intuitive than staying immobile hanging from a chain? If so, can you articulate the difference? $\endgroup$– rob ♦Commented Aug 7, 2018 at 11:05
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$\begingroup$ I don't understand the significance of the question "What observable changes did that result in?" Aren't we declaring that the object is known to have been hanging there completely still and untouched for 20 years? Because then, by definition, without any need for reasoning, the answer must be "no changes". $\endgroup$– user191954Commented Aug 7, 2018 at 11:52
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1$\begingroup$ Muscles experience fatigue; ropes and other such things do not. The only reason it feels counter-intuitive that no work is spent is because you yourself cannot hold an object for 20 years without getting kind of tired. But a rope, a scaffolding, or — as @rob pointed out — a floor cares little about such things. $\endgroup$– MichaelKCommented Aug 7, 2018 at 11:53
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$\begingroup$ I think you are mixing the dictionary definition of energy (work) and the physics definition of energy (work). They both are as different as it can be and that is why it is counter intuitive to you. $\endgroup$– GlobalCommented Aug 7, 2018 at 12:19
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$\begingroup$ For another take on muscle fatigue, consider that a dead flamingo is still stable standing on one leg. $\endgroup$– rob ♦Commented Aug 7, 2018 at 15:36
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1 Answer
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Nothing.
You seem to wonder why no energy is spent. But why would it?
In general, a force does not spend energy. Some forces do (the human body, a rocket, kinetic friction, gravity during free fall) and some forces don't (normal force, tension forces, gravity when stationary). It is not a general rule that energy is spent for a force to exist.
Those that do spend energy, do so because of the "machine" that creates them (the human body spending nutritions, the rocket spending fuel) or because they do work on an object by their very nature (kinetic friction expelling heat, gravity converting stored potential energy to/from kinetic energy).
But the rope in your example doesn't spend any energy. All that may happen is deterioration of the material due to corrosive chemical processes. In a vacuum that wouldn't happen. In ideal conditions, the rope can keep up its tension force forever.
