Finding a force from a simple potential

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Homework Help Overview

The original poster attempts to determine the acceleration of an atom based on a given potential function, U(r), which is defined in terms of parameters ε and σ. The problem involves concepts from classical mechanics and potential energy, specifically relating force to the gradient of the potential.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the calculation of the force from the potential, with some questioning the correctness of the derivative taken by the original poster. There is also a mention of potential confusion regarding the definition of r in the context of the problem.

Discussion Status

There is ongoing clarification regarding the calculation of the derivative of the potential and its relation to the force. Some participants have pointed out potential errors in the original poster's approach, while others have offered insights into the correct interpretation of the variables involved.

Contextual Notes

Participants note that the potential depends solely on the radial distance r, which is defined as the distance between two points, leading to discussions about the implications of this definition on the calculations being performed.

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Homework Statement


I need to find the acceleration of an atom, given the potential:

U(r) = ε[(σ/r)^12 - (σ/r)^6]

where r = |x1 - x2|, ε = 1e-20 J, and σ = 3e-10 m.

Homework Equations



I know F=-dU/dr and F=ma so
a=(-dU/dr)/m but I think my dU/dr is wrong.

The Attempt at a Solution



dU/dr = (6εσ^6/r^7) - (12εσ^12)/r^13

so F = (12εσ^12)/r^13 - (6εσ^6/r^7)
 
Last edited:
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Welcome to Physics Forums.

The negative gradient of a scalar potential will give you the force acting on the atom. Note that this is not simply the same as taking the derivative of U with respect to r.
 
Yes, your dU/dr is wrong. Maybe if you write r^{-12} you'll see what your mistake is.
 
Hootenanny said:
Welcome to Physics Forums.

The negative gradient of a scalar potential will give you the force acting on the atom. Note that this is not simply the same as taking the derivative of U with respect to r.

Since U only depends on r, that's NOT the mistake OP makes.
 
borgwal said:
Since U only depends on r, that's NOT the mistake OP makes.
I assumed we were in spherical coordinates and r was the radial distance from the origin. Of course on later reflection after you pointed it out, I noticed that r was define as the segment between two points.

My mistake.
 
sorry, the formula i gave for my solution should NOT BE dU/dr. it is the Force. dU/dr has the opposite sign. I will edit.
 
emoboya3 said:
sorry, the formula i gave for my solution should NOT BE dU/dr. it is the Force. dU/dr has the opposite sign. I will edit.
emoboya3 said:
dU/dr = (6εσ^6/r^7) - (12εσ^12)/r^13

so F = (12εσ^12)/r^13 - (6εσ^6/r^7)
Looks good to me now :approve:

Apologies for the mix-up before.
 
Much appreciated to all. And sorry for my lack of etiquette. I'm still learning.
 
emoboya3 said:
And sorry for my lack of etiquette.
There was nothing at all wrong with your posting etiquette, whatever gave you the impression that there was?
 

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