Understanding Potential Energy and Force for a Constant Potential Function

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Homework Help Overview

The discussion revolves around a potential energy function defined as U = C/x, where C is a constant. Participants are tasked with finding the force as a function of x and analyzing the direction of this force, as well as the behavior of potential energy with respect to changes in x for both positive and negative values of C.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the relationship between potential energy and force, questioning how to derive force from the given potential energy function. There are attempts to apply known formulas and concepts, such as the relationship between work and potential energy.

Discussion Status

The discussion is active, with participants providing guidance on how to relate potential energy to force. Some participants express uncertainty about the application of formulas, while others reiterate the fundamental concepts involved. Multiple interpretations of the problem are being explored without a clear consensus on the next steps.

Contextual Notes

Participants are navigating the implications of both positive and negative constants in the potential energy function, which may affect their analysis of force and potential energy behavior. There is also a mention of homework constraints regarding the expected approach to the problem.

yamama1
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Homework Statement


Potential energy function is given by U = C/x, where C is a positive constant.
a. Find the force as a function of x.
b. Is this force directed toward the origin or away from it?
c. Does the potential energy increase or decrease as x increases?
d. Answer b, and c if C is a negative constant.

Homework Equations


How do you relate U = C/x to force?

The Attempt at a Solution


I tried the formulas.
F = mg
U = mgy
But I am not sure how you relate both of them together
 
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welcome to pf!

hi yamama1! welcome to pf! :wink:

potential energy is (minus) the work done by a (conservative) force

in other words, PE = -∫F.dx,

and so F = … ? :smile:

(see the pf library for some details)
 


tiny-tim said:
hi yamama1! welcome to pf! :wink:

potential energy is (minus) the work done by a (conservative) force

in other words, PE = -∫F.dx,

and so F = … ? :smile:

(see the pf library for some details)


F = ma.
so PE = - ∫ma.
I don't know what that would equal to.
 
(just got up :zzz: …)
yamama1 said:
F = ma.
so PE = - ∫ma.
I don't know what that would equal to.

stick to the question … nobody's asked you for a

you're asked for F, you're given PE, and you have an equation relating PE and F …

so what is F (as a function of PE)? :smile:

(oh, and PE isn't -∫ma. it's -∫ma.dx = -∫mv(dv/dx)dx = -∫mvdv = -1/2 mv2)
 
apply F= -dU/dx
 

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