Potential Energy Diagrams and Stability

Potential energy diagrams help describe how a mechanical system moves. Because energy is a scalar quantity, the system’s behavior is easier to interpret from the diagram. A skater on a parabolic ramp is a clear example. The ramp height changes with horizontal position, so the potential energy changes as well.

An energy diagram is a plot of potential energy as a function of the position of an object when a conservative force is acting upon it. Because of the net conservative forces on the object, the total mechanical energy of the system is constant.

Consider a skater at a rest point A on a frictionless parabolic ramp of height y