Spring energy

[beowulff]

@Precambrianmollusc

Do you agree the area under the tension extension graph as you stretch the spring is the energy stored in the spring?
This is not a complication but a very simple way of describing the energy in a spring - see link high school physics.

Sure, but it’s irrelevant.
The energy in the spring was fixed at the start. It can never go up, since the spring ends are restrained (by the OP). The energy will be released into the solution as the sprinf dissolves. End of story.

[naita]

@Precambrianmollusc

But what about the fact the spring constant is 800 and according to our calculation the energy in a spring is ½ K X^2. You have to remember that that was derived from integrating under the line on the extension/tension graph. So the formula (1/2 kX^2) assumes we started with a spring of k 800 and moved from (0,0) along the line k=800 to point B (0.0125,10) doing work and accumulating energy in the spring as we move along that line from O to B. The final area under that triangle is indeed 0.0625J

Compare the area under the graph going from O to A to B , it is indeed more than going straight from O to B, so the dissolved spring has more energy than just stretching an ideal spring of k= 800 from O to point B. they do not have the same energy.

Nonsense. If I have a spring where the load was added while it had k=1000, and then dissolved to k=800, and one where the load was instead added at that point, they’ll contain the same energy. Looking at this at the atomic level, what novel mechanism are you proposing that allows two otherwise identical springs to contain different amounts of potential energy.

Now we are at point B. Let’s relax the spring and go all the way back to (0,0) . Indeed we will follow the straight line from B back to O, after all we all agree the new spring constant is 800, because it is a thinner spring and all. Now the energy we give back is the area under the O to B triangle ( 0.0625J), but the spring has 0.075J in it. That difference in energy is given out, as many have said, as heating of the spring.

Important to note, when we are at B, following the dissolve spring route (O A B) the energy in the spring is 0.075 (O to A to B area) , we only give up that energy as we relax the tension and extension and move back along B to O line, with the delta in the areas being given up as heat. The Energy is not carried away when the spring is dissolving Ie moving from A to B, in fact as the string stretches we are getting more energy into the spring, 0.025J of work in this case.

Again, for emphasis, this requires the two springs to be somehow different on the atomic level. Unless you can justify your ideas on the atomic level your suggestion is equivalent to a situation where a load hanging from 800 tiny springs after 200 more tiny springs have been cut, is different from the setup where we started with the 800 tiny springs.

[naita]

@Precambrianmollusc

Do you agree the area under the tension extension graph as you stretch the spring is the energy stored in the spring?
This is not a complication but a very simple way of describing the energy in a spring - see link high school physics.

High school physics doesn’t involve springs with a changing k. If the k changes, the energy stored is the area under the graph when the tension is released.