Prove a system is at equilibirum?

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Discussion Overview

The discussion revolves around methods to prove that a system is in equilibrium, particularly in the context of physics. Participants explore different approaches and definitions related to equilibrium, including mechanical and thermal aspects.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant seeks clarification on how to prove a system is in equilibrium and requests insights on two methods.
  • Another participant suggests that in physics, equilibrium is defined by the conditions that the sum of forces in all directions and the sum of moments about any point are zero.
  • A participant reiterates the conditions for equilibrium, specifically mentioning the equations ΣFx = 0 and ΣFy = 0, and questions if these are sufficient for proof.
  • It is noted that mechanical equilibrium is characterized by net forces being zero, and different types of equilibrium, such as thermal equilibrium, are acknowledged.
  • Another viewpoint introduces the concept that an equilibrium state can also be characterized by an energy minimum or plateau, suggesting a method involving the calculation of energy as a function of position.

Areas of Agreement / Disagreement

Participants express varying methods and definitions related to proving equilibrium, indicating that multiple competing views remain without a consensus on a singular approach.

Contextual Notes

Participants have not fully defined the specific context of equilibrium they are discussing, which may affect the applicability of the proposed methods. Additionally, the discussion includes different types of equilibrium that may require distinct approaches.

flaren5
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I am aware of the meaning when "the system is in equilibrium".

What are two ways to prove it?

Any insight would be greatly appreciated...

Thank you.
 
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In what context are you referring to? Like in physics, for a system to be in equilibrium, the sum of forces in the x,y,z directions are zero and the sum of moments about any point is zero.
 
That sounds to be what I am referring to...I'm assuming it has to do with:
ΣFx = 0 and ΣFy = 0...
Is that how I would prove it?...I was wondering what the explanation is for two ways of proving when a system is in equilibrium.

I hope that explains better to what I am looking for.

Thank you.
 
flaren5 said:
That sounds to be what I am referring to...I'm assuming it has to do with:
ΣFx = 0 and ΣFy = 0...
Is that how I would prove it?...I was wondering what the explanation is for two ways of proving when a system is in equilibrium.

I hope that explains better to what I am looking for.

Thank you.

Well that is how you would show a system is in equilibrium. Mechanical equilibrium is defined such that the net forces acting on an object are zero. There are also different kinds of equilibrium such as thermal equilibrium.
 
In general an equilibrium state is characterised by an energy minimum (or plateau).

Generally you calculate the energy of the system as a function of position, differentiate it and set equal to zero. That gives the position of equilibrium.
 

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