We explore the relationship between force and potential energy, where force is the slope of a potential energy curve. In a spring-mass system, the restoring force follows Hooke’s Law and points toward...We explore the relationship between force and potential energy, where force is the slope of a potential energy curve. In a spring-mass system, the restoring force follows Hooke’s Law and points toward decreasing potential energy. More generally, force equals the negative slope of the potential energy graph, with steeper slopes indicating stronger forces. In multiple dimensions, force aligns with the steepest slope, or gradient, of the potential energy surface.
