Negative Energy in Newtonian Mechanics: Explained

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Discussion Overview

The discussion centers around the concept of negative energy in Newtonian mechanics, particularly in the context of potential energy and its implications for systems like the electron in Bohr's atomic model. Participants explore the meaning of negative energy, its dependence on reference points, and the relationship between kinetic and potential energy.

Discussion Character

  • Conceptual clarification
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about the meaning of negative energy, specifically in relation to Bohr's atomic model and requests clarification using Newtonian mechanics.
  • Another participant explains that negative potential energy arises from the convention of setting the potential energy at infinite separation to zero, indicating that at lesser separations, potential energies are negative.
  • This explanation suggests that negative energy means the system has less energy than it would at infinity, which is a commonly accepted convention.
  • A later reply discusses the frame dependence of kinetic energy, asserting that potential energy is gauge invariant, meaning it can be shifted by a constant without affecting physical measurements.

Areas of Agreement / Disagreement

Participants generally agree on the convention of setting potential energy at infinity to zero and the implications of negative potential energy. However, there is some debate regarding the frame dependence of potential energy versus kinetic energy, indicating a lack of consensus on this aspect.

Contextual Notes

The discussion highlights the arbitrary nature of defining potential energy and the implications of this choice on understanding energy states in physical systems. There is also an acknowledgment of the limitations in measuring energy at a specific point, focusing instead on energy differences between points.

Who May Find This Useful

Undergraduate students of physics, particularly those studying mechanics and atomic models, may find this discussion relevant for understanding the concepts of energy in various contexts.

gdpudasaini
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Actually i never got this concept clearly in my mind. What is the meaning whern we say that the energy of a body is negative? For example in Bhor's atomic model we have calulated the total energy of an electron to be negative. Please explain me by using Newtonian Mechaincs as i am the undergraduate student of physics.
 
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This is to do with potential energy.We cannot specify what an absolute potential energy is at any particular particle separation but we can calculate the amount by which potential energy changes with separation.For attracting particles the PE is a maximum at infinite separation and we choose to refer to this separation and to give the PE at infinity a value of zero.At lesser separations the PEs are negative.The choice of infinity and zero are arbitary but generally accepted as being the most useful choices in that they are easiest to work with.When you calculate that the energy of the electron is negative what that really means is that it has less energy than it would have if it were at infinity.
 
Dadface said:
This is to do with potential energy.We cannot specify what an absolute potential energy is at any particular particle separation but we can calculate the amount by which potential energy changes with separation.For attracting particles the PE is a maximum at infinite separation and we choose to refer to this separation and to give the PE at infinity a value of zero.At lesser separations the PEs are negative.The choice of infinity and zero are arbitary but generally accepted as being the most useful choices in that they are easiest to work with.When you calculate that the energy of the electron is negative what that really means is that it has less energy than it would have if it were at infinity.

Thanks a lot for your wonderful reason. I got it. So you mean PE and KE are frame dependent, right?
 
KE is definitely frame depended. However, potential energy is a little bit more interesting. It's actually what is called gauge invariant. One cannot measure the energy of something at a given point, only the energy between points. So, we can take electric potential energy (that defines the electric field E = grad V) and add a constant to it an nothing changes physically.
 

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