# Finding Force From Potential Energy

1. Nov 19, 2011

### Diff.Ed

1. The problem statement, all variables and given/known data
The potential energy of two neutral molecules may be modelled using the Lennard Jones potential,
$$U(x)=U_0(\frac{\sigma^{12}}{x^{12}} - \frac{\sigma^6}{x^6})$$
where $U_0$ and $\sigma$ are positive constants and $x$ is the distance between the two molecules.

a) Find the force at an arbitrary point x ?

2. Relevant equations

conservative forces and potential energy

3. The attempt at a solution
$$F(x) = -\frac{dU}{dx}= U_0(12\frac{\sigma^{12}}{x^{13}} - 6\frac{\sigma^6}{x^7})$$