Potential Energy and the Conservation of Energy

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Discussion Overview

The discussion revolves around the relationship between potential energy and the conservation of energy, exploring theoretical concepts and definitions related to energy in physics. Participants examine the nature of potential energy, its dependence on conservative forces, and the implications for energy conservation in various contexts.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • One participant suggests that potential energy arises from the conservation of energy, stating that work done against gravity results in stored energy.
  • Another participant agrees with the initial statement, indicating a general acceptance of the idea presented.
  • A different participant challenges the clarity of the initial explanation, arguing that potential energy is not directly related to conservation of energy and emphasizing the importance of path independence in defining potential energy functions.
  • This participant provides examples of potential energy in gravitational and electrical contexts, suggesting that potential energy can be defined based on specific conditions and forces.
  • Another participant counters the claim that potential energy is unrelated to conservation of energy, asserting that potential energy is essential for the conservation of total energy, which includes both potential and kinetic energy.
  • This participant also notes that potential energy arises only in the presence of conservative forces and differentiates between conservation of energy and conservation of mechanical energy.
  • One participant points out a potential misunderstanding regarding the definitions of energy conservation, suggesting that mechanical energy conservation requires only conservative forces.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between potential energy and conservation of energy. While some argue for a connection, others contest this notion, leading to an unresolved debate on the topic.

Contextual Notes

Participants reference specific conditions under which potential energy can be defined and the implications of conservative versus non-conservative forces on energy conservation, indicating a nuanced understanding of the topic that remains open to interpretation.

scotty_le_b
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Would I be right in saying the following:
Potential energy arises from the conservation of energy. To lift a mass you must exert a force counteracting the force of gravity. As it moved and a force was exerted work was done on it. As it is not moving it has no kinetic energy. Due to the conservation of energy the energy cannot be destroyed so there must be a stored type of energy...Potential energy.
 
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Sounds good to me.
 
scotty_le_b said:
As it moved and a force was exerted work was done on it. As it is not moving it has no kinetic energy.

This seems rather confused. Either it is moving, or it isn't. It can't be moving and not moving at the same time.

I would say potential energy has nothing to do with conservation of energy. If you have a situation where the amount of work done on something when it moves between two positions A and B does not depend on the exact path or on the speed that it moves, but only on the positions of A and B, then you can define a "potential energy function" that let's you calculate the amount of work done easily.

Gravity is a good example. If you are working close to the sirface of the Earth you can assume gravity is a constant force, and define its potential energy as mgh. Or if you want to consider the inverse square law, you can use a potential energy function that is proportional to 1/r where r is the distance between two objects. (Note, 1/r was not a typo for 1/r2)

You can also define potential energy for other types of force. For example, guess why the voltage between two points in an electrical circuit is sometimes called the "potential difference"...
 
What I meant by that it was moved up to say a shelf then on the shelf it was not moving. Sorry
 
AlephZero said:
This seems rather confused. Either it is moving, or it isn't. It can't be moving and not moving at the same time.

I would say potential energy has nothing to do with conservation of energy. If you have a situation where the amount of work done on something when it moves between two positions A and B does not depend on the exact path or on the speed that it moves, but only on the positions of A and B, then you can define a "potential energy function" that let's you calculate the amount of work done easily.

Gravity is a good example. If you are working close to the sirface of the Earth you can assume gravity is a constant force, and define its potential energy as mgh. Or if you want to consider the inverse square law, you can use a potential energy function that is proportional to 1/r where r is the distance between two objects. (Note, 1/r was not a typo for 1/r2)

You can also define potential energy for other types of force. For example, guess why the voltage between two points in an electrical circuit is sometimes called the "potential difference"...

How can you say potential energy has nothing to do with conservation of energy? IMO, potential energy is NECESSARY for conservation of energy. The potential energy + kinetic energy (in your gravitational situation, classically) is the total energy. Sometimes the potential is zero, sometime kinetic is zero, and sometimes neither is zero (and we can actually arbitrarily define the potential to be zero at any point).

Without potential energy, I don't think conservation of energy would not be satisfied.
 
khemist said:
How can you say potential energy has nothing to do with conservation of energy? IMO, potential energy is NECESSARY for conservation of energy. The potential energy + kinetic energy (in your gravitational situation, classically) is the total energy. Sometimes the potential is zero, sometime kinetic is zero, and sometimes neither is zero (and we can actually arbitrarily define the potential to be zero at any point).

Without potential energy, I don't think conservation of energy would not be satisfied.

Amusingly, your last sentence is a double negative. Anyway...

Potential energy only arises in the presence of conservative forces. Total energy of a system is always conserved, even when the forces present are not conservative. Perhaps you are confusing conservation of energy with conservation of mechanical energy (which requires that only conservative forces be present)?

Mechanical energy = kinetic energy + potential energy.

EDIT: AlephZero's second paragraph basically defines what a conservative force is.
 

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