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Finding a force from a simple potential

  1. Nov 20, 2008 #1
    1. The problem statement, all variables and given/known data
    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.


    2. Relevant equations

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

    3. 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: Nov 20, 2008
  2. jcsd
  3. Nov 20, 2008 #2

    Hootenanny

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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.
     
  4. Nov 20, 2008 #3
    Yes, your dU/dr is wrong. Maybe if you write r^{-12} you'll see what your mistake is.
     
  5. Nov 20, 2008 #4
    Since U only depends on r, that's NOT the mistake OP makes.
     
  6. Nov 20, 2008 #5

    Hootenanny

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    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.
     
  7. Nov 20, 2008 #6
    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.
     
  8. Nov 20, 2008 #7

    Hootenanny

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    Looks good to me now :approve:

    Apologies for the mix-up before.
     
  9. Nov 20, 2008 #8
    Much appreciated to all. And sorry for my lack of etiquette. I'm still learning.
     
  10. Nov 20, 2008 #9

    Hootenanny

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    There was nothing at all wrong with your posting etiquette, whatever gave you the impression that there was?
     
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