Sign of potential energy of SHO

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Discussion Overview

The discussion revolves around the sign of potential energy in the context of simple harmonic oscillators (SHO) and springs. Participants explore the implications of work done by conservative forces versus external agents, and how these relate to potential energy calculations during stretching and compressing of springs.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants propose that the potential energy U is calculated as U = -w, where w is the work done, leading to different signs depending on the direction of motion (away from or towards the mean position).
  • Others argue that the potential energy is always positive when the spring is either stretched or compressed, suggesting a misunderstanding in the application of the formula dU = -dW versus dU = dW for external work.
  • A later reply questions the interpretation of displacement, noting that the angle in the dot product affects the sign of work done, which in turn influences the sign of potential energy.
  • Some participants clarify that the potential energy is zero at the mean position and increases as the displacement from the mean position increases, regardless of direction.
  • There is a discussion about the distinction between the sign of work done during stretching versus decompressing, with some asserting that the change in potential energy is positive when moving away from the mean position and negative when moving towards it.
  • One participant introduces the concept of potential energy being defined through force and its relation to configuration, emphasizing that potential energy can be derived from the work done on the system.

Areas of Agreement / Disagreement

Participants express differing views on the sign of potential energy and the interpretation of work done in relation to stretching and compressing springs. There is no consensus on the correct application of the formulas or the implications of the signs of potential energy.

Contextual Notes

Limitations in the discussion include potential misunderstandings of the definitions of work and displacement, as well as the assumptions made regarding the reference points for potential energy. The discussion also reflects varying interpretations of the relationship between work done and changes in potential energy.

  • #31
OP remains as convinced as ever that the HO potential changes sign, and is now asserting that there is some sort of global physicist conspiracy to ignore this inconvenient "fact". Please see:

https://www.physicsforums.com/showthread.php?t=730150
 
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  • #32
devang2 said:
Thanks a lot for the answer . No one has pointed so for where i have gone wrong if i use basic formula dU =-W to calculate potential energy and use dot product to calculate work . This method leads to positive and negative signs when the particle moves away and toward the mean position respectively
That equation is incorrect - where did you get it from?
The correct relation is dW=-dU or dU=dW - depending on the context - as explained to you in post #5.
More precisely: http://en.wikipedia.org/wiki/Potential_energy#Work_and_potential_energy
... but it is not the definition.

One of the upshots of that equation is that there is no absolute zero for potential energy.
When we talk about a particular value of potential, we are using a shorthand for the difference in potential between two places.

There are conventions for some situations for where we put that zero by default.
For instance, for gravity, close to the Earth's surface, we put U=0 on the ground.
In that case you will see that U<0 below the ground, and U>0 above the ground.

If you start below the ground, and move upwards, then v>0, dU>0, and U goes from negative values to positive values.

But if we are talking about gravity at a long distance, it is more convenient to put U=0 at an infinite distance away. In that case, U<0 everywhere.

If you move towards a mass, dU<0, but U<0
If you stay still, or execute a circular orbit dU=0 but U<0
If you move away from the mass dU>0 but U<0

For a mass on a spring, it is convenient to put U=0 at the center of the motion simply because U increases to either side. This makes U>0 everywhere for the mass.
If the mass moves towards the center, then dU<0 and U>0
If the mass moves away from the center, then dU>0 and U>0
 
  • #33
Given the OP's history on this topic, there is no reason to continue either of these threads.
 

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