# I Relationship between force and potential energy

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1. Jun 6, 2018

### I_laff I am aware that the negative derivative of potential energy is equal to force. Why is the max force found when the negative derivative of potential energy is equal to zero?

2. 3. Jun 6, 2018

### Chandra Prayaga Could you give an example problem or situation when this is done? Where did you see this? It is not correct.

4. Jun 6, 2018

### I_laff 5. Jun 6, 2018

### I_laff I was told by someone that when you set the derivative to zero, you get the max force.

6. Jun 6, 2018

### anorlunda ### Staff: Mentor

The answer to your question does not depend on any physics. It is a matter of simple math. Maxima and minima occur at the places where the slope of the curve is zero. Also, the sign of the slope flips as we pass a maximum or minimum. 7. Jun 6, 2018

### I_laff So if we set the derivative to zero, we can calculate the minima and maxima of a potential energy graph, how does that help us find the max force?

8. Jun 6, 2018

### sophiecentaur It doesn't. If there is a turning value of Potential Energy with distance, the force is zero. As the hyperphysics link tells you, the highest force is where the Potential Energy is changing fastest with distance.
If you were told otherwise by "someone" then perhaps they are not a reliable source of info (or they misinterpreted the question that you asked them).

9. Jun 6, 2018

### anorlunda ### Staff: Mentor

No. You don't set the derivative to zero, you find the potential energy where the derivative is zero. That place is a ax or min.

10. Jun 6, 2018

### Dale ### Staff: Mentor

This is incorrect. When the negative gradient of the PE is zero then the force is zero.

11. Jun 7, 2018

### I_laff 12. Jun 7, 2018

### ZapperZ Staff Emeritus
Where exactly in the hyperphysics link does it claim that ".... max force found when the negative derivative of potential energy is equal to zero ... "? I do not see it, and you're asking us to correct an non-existing error.

Force is the gradient of the potential energy. This means that the quicker the potential energy changes over distance, the higher the absolute value of the force. So it is not the absolute value of the potential energy, but rather the change in the potential energy that corresponds to the force.

Zz.

13. Jun 7, 2018

### I_laff I didn't say that Hyperphysics stated that the max force is when the derivative was set to 0. I said that I was told that it was, which confused me since it didn't make sense. My only mistake was assuming that the person who told me that the max force could be calculated by setting the derivative to zero was correct.

14. Jun 7, 2018

### ZapperZ Staff Emeritus
Look at Posts 1, 2, and 3 and read them again in sequence to see why it appears that you are using the Hyperphysics link to justify what you were told.

Zz.

15. Jun 7, 2018

### willem2 So the maximum occurs where the slope of the potential energy curve is steepest. You can find those points by differentiating the potential energy twice with respect to position and setting that equal to 0. Only in those points can the force be maximal. (there could also be a minimum, or an inflection point)

16. Jun 7, 2018

### ZapperZ Staff Emeritus
This is not correct either. 2nd derivative tells you how rapidly the slope is changing, and thus, how rapidly the force changes. It doesn't tell you how large the force is.

You can have an almost vertical straight line on the V vs x graph (i.e. 2nd derivative is zero but not at a max or min or inflection point), and yet, this is where a force can be a maximum.

Zz.

17. Jun 7, 2018

### I_laff I would've thought the quoted post below would've clarified what information was and was not from the Hyperphysics website.

18. Jun 7, 2018

### ZapperZ Staff Emeritus
I get that you were "told" by someone, but when asked for a source in Post 2, you cited Hyperphysics, as if you were using that page to justified what you were told by this "someone". That's why I asked where specifically on that Hyperphysics page matches what you were told by this "someone".

Many of us are familiar with Hyperphysics. I even used it as an additional educational source for my students. I don't ever recall them making this type of error, and that is why I was particular concerned in trying to find where exactly in there that matches the erroneous info that you were told. If nothing there matches what you were told, why did you cite it without understanding it?

Zz.

19. Jun 7, 2018

### I_laff Apologises if I misled you, I will be more careful when citing sources next time so it is obvious what is and is not from the source. I cited hyperphysics because it was from there that I read about the relationship between force and potential. The first reply to my post simply said that what I had stated was 'not correct'. They didn't specify what part of what I said was incorrect, so in reply to this I just posted where I got all my information from. I think my understanding of what hyperphysics was on about was adequate enough for me to cite it. Once again, I never said that hyperphysics stated the incorrect information I was told. You insinuated that this is what I meant from my posts, but that is not the case.

20. Jun 7, 2018

### sophiecentaur I thought we had already decided that this "person" was not a reliable source of information but that Hyperphysics is pretty well trustworthy.

21. Jun 7, 2018

### willem2 I don't get this at all. You say you disagree with me, but then you produce a case where the 2nd derivative is 0 and the force is a maximum, but this is not a max or min or inflection point? This appears to be a contradiction.
The force is the first derivative of the potential energy. The only place where the force can be a maximum is where the derivative of the force, or the second derivative of the potential energy is 0.