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- Thread starter Precursor
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*the statement "move them to infinitely apart" simply mean break them apart, NOT necc. moving them to the edge of the universe. In addition, the statement assumes that universe has no retarding force, so I guess...moving them across space won't take any additional energy.

Hope it helps

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Precursor> What do you know about inverse square laws? This might help.

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So, according to the inverse square law, there is always a force acting between charged particles, but the farther away from each other the weaker the force. But at an extremly far distance away, the force acting between the charged particles is negligible. Does that mean the binding energy is finite?Precursor> What do you know about inverse square laws? This might help.

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So, as the distance increase, the force between 2 particles becomes less and less until it's negligible (as you said). Then the work necc. to keep them farther apart toward infinity also becomes negligible.

After all, binding energy (when you really go down into the basis) is just a force (strong force I believe). [there are 4 well known accepted forces: gravity, Electromagnetic, Strong, and weak (nuclear decay and stuff)]

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But doesn't the force between 2 particles become negligible only when they are at an infinite distance apart, which makes the work neessary to move them that far apart, an infinte amount of energy? This seems to be going in circles...ISo, as the distance increase, the force between 2 particles becomes less and less until it's negligible (as you said). Then the work necc. to keep them farther apart toward infinity also becomes negligible.]

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Delphi51

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It appears that way, but instinct doesn't work well with non-linear things.But doesn't the force between 2 particles become negligible only when they are at an infinite distance apart, which makes the work neessary to move them that far apart, an infinte amount of energy?

You really need calculus to figure it out. The work necessary is the integral (as r goes from initial value R to infinity) of F dr. If you have done integration, you'll find it easy. And finite.

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Precursor: this is a good question. The fallacy is in your assumption that the amount of energy required to separate the nucleons infinitely apart (which is a theoretical construct ..but can be physically understood as being some perfected realization of the situation where the nucleons are separated outside of each other's force fields) is itself infinite. This energy is still finite.

How do you understand this physically? Consider this example: suppose you roll down a ball on a frictionless surface ..following Newton's law, it will head off to infinity eventually. But you would have only expended finite energy. The point is that you should not assume that sending things off to infinity will require infinite energy.

Before I proceed - we are talking about NUCLEAR forces here ..in fact, Coulomb forces would cause repulsion, rather than cause the nucleons to be bound together.

The energy deficit can be equated to the MASS deficit through Einstein's equation.

As far as I can tell, the question you're asking has nothing to do with non-linear effects.

Once all this has sunk in I can tell you more about what really binding energy physically means then.

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When thinking of physics concepts, I tend to think about them "physically" as you mentioned. Your post really struck me for that. Is it incorrect to think of physics in a physical mindframe?

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Although the strong force (the force that binds protons and neutrons together in a nucleus) is not an inverse square force, it also drops off with distance. You can use the same argument for the non-infinite energy being required to separate protons / neutrons as you can for non-infinite energy being required to separate a spaceship from the Earth, even if the maths involved is different.

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Delphi51

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More to it than just dropping off. If the force dropped off as F = k/r, then the energy would be integral from r=R to infinity of k/r*dr = ln(infinity) - ln R = infinity.the fact that the force drops off with distance means that you don't require an infinite amount of energy / have an infinite escape velocity.

The fact that it drops off as F = k/r^2 (what I meant by non-linear, where one's physical intuition is unreliable) that makes it come out to less than infinity: E = Integral from r=R to infinity of k/r^2*dr = k/R.

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