Quick P. Energy Derivation Question

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SUMMARY

The discussion centers on the work-potential energy theorem, specifically the relationship expressed as dV = -Fdr. The negative sign indicates that when positive work is performed by conservative forces, the potential energy (V) decreases while kinetic energy increases. This convention is critical for maintaining consistency in the definitions of potential energy and conservative forces, rather than being a matter of logic.

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When deriving the work-potential energy theorem, my book states that dV (derivative of the potential energy) is equal to the negative of Fdr without a corresponding explanation. What is the justification behind the negative sign?
 
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As such,there is no explanation,its about definition.

The important thing is,for conservative forces,you can define a potential.Even if you had define dV=Fdr,you would have a consistent theory.The fact that dV=-Fdr,and not Fdr,is not logic,its convention.

In essence,it means that,when positive work is done by the field forces on body,its potential energy decreases,and kinetic energy increases.
 

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