Determining if force is attractive/repulsive from Energy diagrams

[DrummingAtom]

Homework Statement

The potential energy of a pair of atoms separated by a large distance x is given by U(x) = -C6/x6, where C6 is a positive constant. What is the force that one atom exerts on the other? Is this force attractive or repulsive?

Homework Equations

F(x) = -dU/dx

The Attempt at a Solution

The force I got is:

F = -6C₆/x⁷

I'm confused by the second question of is the force attractive or repulsive. Seeing that there's a negative sign, one must be moving toward the other. Although, the potential energy graph says it's going to be a large negative U at a small distance. Which shouldn't it be a small positive U at a small distance? Thanks for any help.

 

[Delphi51]

U = -C/x^6, right? The 6 after the C is just a subscript that gets in the way.
If you sketch the graph of that it is very large and negative at small values of x, and increases as x increases, approaching zero as x gets very large.
Clearly the potential energy decreases as x gets smaller. So the force will be to the left, toward decreasing energy. It is like a baseball being pulled toward the Earth where it will diminish in potential energy and increase in kinetic energy. So the F should be negative. Your expression for F looks good to me.

 

[zhermes]

Forces act to move things towards minima in the potential----i.e. the lowest (negative or positive) values. The potential you have, has a single (divergent) minima---and thus towards this point will forces always act.