Integrating Force: Understanding \oint and \int

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Homework Help Overview

The discussion revolves around the integration of force in relation to potential energy, specifically questioning the relationship expressed as \(\int{F}={-U}\) and exploring the distinctions between the integral symbols \(\oint\) and \(\int\).

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are examining the relationship between force and potential energy, with one suggesting that force is the negative derivative of potential energy. There are inquiries into the meaning of the integral signs used in different contexts, particularly regarding closed versus open integrals.

Discussion Status

The discussion is active, with participants providing insights into the definitions and applications of the integral symbols. There is an exploration of the concepts without a clear consensus on the implications of the relationships discussed.

Contextual Notes

Some participants are referencing specific equations and relationships, indicating a focus on the mathematical aspects of force and energy integration. The nature of the homework constraints or specific requirements is not detailed.

UrbanXrisis
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does the integration of Force equal negative potential energy?

[tex]\int{F}={-U}[/tex]

Also, what is the difference between [tex]\oint[/tex] and [tex]\int[/tex]?
 
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Yeah, it should seeing as F = - dU/dx.

The integral sign with a circle is an integral around a closed loop/surface I think, whereas the normal integral sign isn't.
 
so: W’=F=-dPE/dt
 
The [tex]\oint[/tex] is often used for a curve integral (whether or not the curve is looped (closed) or not).
 

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