Finding a force from a simple potential

[emoboya3]

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)

[Hootenanny]

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.

[borgwal]

Yes, your dU/dr is wrong. Maybe if you write r^{-12} you'll see what your mistake is.

[borgwal]

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.

[Hootenanny]

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.

[emoboya3]

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.

[Hootenanny]

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.

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.

[emoboya3]

Much appreciated to all. And sorry for my lack of etiquette. I'm still learning.

[Hootenanny]

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?