# In $\textbf{f} = -\boldsymbol{\nabla} u$, what is $u$?

I know that force is the negative gradient of the potential:

$$\textbf{f} = -\boldsymbol{\nabla} u$$

where force $\textbf{f}$ is a vector and $u$ is a scalar.

This is a relatively soft question, but what is $u$? I frequently hear it referred to as "the potential." But is it actually the potential energy?

For example, suppose I have a system consisting of several classical particles that interact. Suppose that I can calculate the potential energy at the position of each particle, because I know how they interact (e.g., by gravity, by Coulomb's Law, by the Lennard-Jones potential, and so on). Can I then determine the force $\textbf{f}_\boldsymbol{1}$ on particle 1 by simply calculating the negative gradient of the potential energy $u_1$ at the position of particle 1?

-