Potential energy greater total energy in the system?

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Discussion Overview

The discussion revolves around the relationship between potential energy (PE) and total energy (TE) in a system, particularly in the context of a graph depicting these energies. Participants explore classical mechanics concepts, questioning why the TE line appears below the PE curve at certain points and whether this indicates a misunderstanding or a convention in energy representation.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant notes confusion regarding the TE line being below the PE curve, questioning if this is a convention or a misunderstanding.
  • Another participant explains that, classically, movement is restricted to regions where total energy is less than potential energy, indicating that regions where TE is below PE are "forbidden" due to the implications for kinetic energy.
  • A participant emphasizes a desire to avoid quantum mechanics in the explanation, suggesting that the question may be poorly constructed.
  • Discussion includes the mathematical representation of potential energy, with one participant mentioning that while PE can take on values leading to imaginary speeds, the constraints imposed by total energy must be considered.
  • Another participant discusses gravitational potential energy, noting that it can be negative and explaining the work done in lifting an object, contrasting this with spring potential energy which cannot yield negative values without issues.

Areas of Agreement / Disagreement

Participants express confusion and differing interpretations regarding the representation of energy in the graph. There is no consensus on whether the observed phenomenon is a convention or indicative of a deeper misunderstanding.

Contextual Notes

Limitations include the lack of clarity on the specific graph being referenced and the assumptions regarding energy conventions in classical mechanics. The discussion does not resolve the implications of negative potential energy in different contexts.

shredder666
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First of all this is not a HW question, I already "handed" the assignment in and its graded

There was this question on my assignment, it asked questions off of a graph that had distance on the x-axis and energy on the y axis.
The potential energy was a curve, and basically took up the entire page.
the total energy was just a horizontal line and intercepts the PE curve at several points.

But the strange thing was that the TE line was below the PE curve at several intervals. Which just totally confuse me, cus the potential energy is greater than the total energy... or is that some sort of convention that i don't know about
 
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From a classical point of view, the movement of the object is restricted to the zone where total energy is less than potential energy.
The other regions are "forbidden" in the sense that, within those zones, the kinetic energy is less tan zero and it would lead to an imaginary speed.
QM predicts another behavior, but I think you're looking for a "classical" answer
 
yes, I am looking an answer that does not involve the word "quantum".
So I don't get why that portion is there, is it some sort of bad question making?
 
The potential energy is a function eg. the potential energy for a linear simple harmonic oscillator is 1/2kx2---the function is real for all real x---- but there are constraints on x put by limits of total energy. But the potential energy is still a function and it can have the corresponding value for an x that gives an imaginary speed----if that were possible.
 
shredder666 said:
But the strange thing was that the TE line was below the PE curve at several intervals. Which just totally confuse me, cus the potential energy is greater than the total energy... or is that some sort of convention that i don't know about
For gravitational potential energy the potential energy function is liner U=mgh. It can get negative.In order to lift something at point p1 that is below your reference point at O set to 0 you must do work w=-mgh(h distance from p1 to O).Since gravitation is a conservative force and you are measuring with respect to some point the increase in Kinetic energy from O to p1 is equal to w so your total energy will be unchanged.No problems and no quantums.For a spring this is not possible since U=(1/2)kx^2 so if you get -U there is a problem..
 

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