Question about potential for this mechanical force problem

AI Thread Summary
The discussion revolves around a mechanical problem involving the determination of critical force and stability in a structure under load. The user seeks clarification on why external energy is represented with a negative sign and the meaning of total potential being stationary. They explain that the total energy consists of internal energy from a spring and external work done by forces. The user acknowledges a mistake in terminology, clarifying that they meant "external work" instead of "external energy." The focus remains on understanding these concepts to solve the mechanical problem effectively.
Zouatine
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Hi! hope you are doing well ,

I'm trying to solve this problem ( mechanical problem) about structure with load F as it showing in the next figure , i want to determine to critical force F , the stability force ( which means if my load is bigger than the critical load my system will be unstable) ,so to get i have to do by Energy method which means i have to use potential ,in this step i have some questions :

1- why the External Energy must be with negative sign ?
2 - what does mean the total potential is Stationary ?

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This sounds like homework. It it?
 
hi thank you for your comment!

,no it's not , solution of the exercise i already know it , i said i have to use Energy method , which mean the first step to solve it : Total Energy = Internal Energy + External Energy ,
Internal Energy is the energy in the Spring , and for External Energy is the Energy cause by external Force , which it's = Force * Displacement ( cause by this force F), but my question here why we have to do sign mince in the formula of External Energy because the formula must be External Energy = - Force * Displacement, ?
when we get the total Energy we must to derivation of Total Energy corresponding to displacement =0 .
d(Total Energy )/d(displacement) =0 because the potential is Stationary , and here is my second question what does mean the potential is Stationary ?

i know the process how to solve but i have these two questions , thank you hope my problem is clear now
 
What exactly do you mean by "External Energy"? This is not a term I've ever heard before, so perhaps you could define it before we try to talk about it.
 
hello , thank you for your comment , sorry i made a mistake , i want to say external work , External Work= Work has done by the External Forces , Thanks and sorry again ,
 
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