1. The problem statement, all variables and given/known data During class, we were considering position dependent forces and we used the following differential equation to describe what is happening to the object in this case: m*(d2x/dt2) = F(x) (i.e. ma=F(x)) Then, we were introduced the potential V(x) which we defined as: F(x) = -(dV/dx) = -mg I am a bit confused where did the negative sign come from and why it is equal to -mg as I though F(x) is the force dependent only on position (and not g). Also, I do not quite understand what physical meaning does potential V have. Does it just show the energy level of an object at a particular position in space? I hope this is not confusing and thank you for your help in advance! 2. Relevant equations As stated before the following equation was introduced, the meaning of which I cannot really understand: F(x) = -(dV/dx) = -mg 3. The attempt at a solution I suspect the sign has something to do with the direction in which the position changes.