Why Delta PE is Negative Work: Understanding the Relationship and Derivation

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Discussion Overview

The discussion revolves around the relationship between change in potential energy and negative work, exploring its derivation and implications within the context of physics. Participants engage with concepts related to energy conservation, the work-energy theorem, and the mathematical relationships involved.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant requests a proof that the change in potential energy corresponds to negative work, indicating a basic understanding of the concept.
  • Another participant suggests referring to a Wikipedia article for an explanation rather than a formal proof.
  • A participant notes that while proving the relationship in general is not possible, it is straightforward for gravity, and emphasizes the derivation from kinetic energy and conservation of energy principles.
  • One participant presents a mathematical formulation of the work-energy theorem, attempting to establish that the change in potential energy is equal to negative work.
  • Another participant reiterates the same proof and questions the understanding of the origin of the work-energy theorem.
  • A participant provides a detailed derivation of the work done in terms of kinetic energy, linking it back to the initial and final states of motion.

Areas of Agreement / Disagreement

Participants express differing views on the ability to prove the relationship in a general context, with some asserting that it is straightforward in specific cases like gravity. There is no consensus on the proof's correctness, as participants present varying degrees of confidence in their mathematical formulations and understanding of the underlying principles.

Contextual Notes

The discussion includes assumptions about the conditions under which the work-energy theorem applies, and there are unresolved questions regarding the generality of the proof for different forces beyond gravity.

Who May Find This Useful

This discussion may be of interest to students and educators in physics, particularly those exploring concepts of energy, work, and their mathematical relationships in mechanics.

CrazyNeutrino
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Can someone prove that the change in potential energy is negative work.
I have a very basic understanding of the concept. I do not understand where it is derived from.
 
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Unfortunately you can't prove that in the general case. For gravity it's easy. What you can prove is that work done=1/2*m*v^2= kinetic energy, and from conservation of energy (dE/dt=0) you can derive the remaining stuff.
 
Thanks that helps.!
 
So the proof would be...

mgy(b)+KE(b)=mgy(a)+KE(a)

That is: U(b)+K(b)=U(a)+K(a)
So U(b)-U(a)=K(a)-K(b)=-(K(b)-K(a)
So U(b)-U(a)=-W ( By work energy theorem )
Therefore:

ΔU=-W

Is this proof correct?
 
CrazyNeutrino said:
So the proof would be...

mgy(b)+KE(b)=mgy(a)+KE(a)

That is: U(b)+K(b)=U(a)+K(a)
So U(b)-U(a)=K(a)-K(b)=-(K(b)-K(a)
So U(b)-U(a)=-W ( By work energy theorem )
Therefore:

ΔU=-W

Is this proof correct?

Yeah it's ok. But another important question is wheather you know where work energy theorem comes from?
 
Yeah.
W= ∫from a to b of Fdx
=∫from a to b of madx
=∫from va to vb of mdv/dt vdt. (dx/dt =v so dx =vdt)
=∫from va to vb of mvdv
=1/2mv^2 evaluated at va and vb
= 1/2mvb^2-1/2mva^2
=KEb-KEa
Therefore
W=KEb-KEa
 
Last edited:

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