Hard potential energy function question

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Homework Help Overview

The discussion revolves around a potential energy function for a particle approaching a force region, specifically defined as V(x) = (ka^2)/((x^2)+(a^2)). Participants are tasked with deriving an expression for the force acting on the particle based on this potential energy function.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to substitute the potential energy function into various equations but is unsure of the next steps. Some participants question the relationship between potential energy and mass, while others inquire about the necessity of introducing a charge constant in their calculations. There is also a mention of using calculus to derive the force from the potential energy.

Discussion Status

Participants are actively exploring different interpretations of the problem. Some guidance has been offered regarding the use of the gradient to express force, and there seems to be a productive exchange of ideas, although no consensus has been reached on the approach to take.

Contextual Notes

There are indications of confusion regarding the relationship between potential energy, mass, and charge, as well as the application of calculus in this context. The original poster has expressed a need for hints rather than complete solutions.

Lucy Yeats
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Homework Statement


Potential energy function A particle of mass m, starting from x = −∞, approaches
a force region whose potential is given by
V (x) =(ka^2)/((x^2)+(a^2))
where V0 > 0 and a are constants.
(a) Derive an expression for the force on the particle as a function of

Homework Equations



E=F/Q, V=W/Q, E=V/d

The Attempt at a Solution



I tried to substitute it into the equations above, but it didn't work. A friend thought the answer involved calculus, but I'm not sure where to start. Any hints would be much appreciated...
 
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Is it correct that potential x mass = potential energy?
 
Do I need to introduce a constant for the charge, of can I express F without this? Help, please! Thanks! :-)
 
Lucy Yeats said:
Is it correct that potential x mass = potential energy?

No.

Check your thread which directly asks this question.
 
Lucy Yeats said:
Do I need to introduce a constant for the charge, [STRIKE]of[/STRIKE] or can I express F without this? Help, please! Thanks! :-)

You don't need the charge.

You can express F without introducing a charge.

Do you know how to take the gradient?

F = - V .

Otherwise, F = - dV(x)/dx .
 
Thanks SammyS, you post about the gradient answers the question perfectly!

:-)
 

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