The Physics
Hypertextbook
Opus in profectus

# Potential Energy

## Discussion

W J M Rankine coined the term potential energy 150 years ago.

gravitational potential energy

Ug = mgh

• acceleration due to gravity is nearly constant
• height change is small compared to the separation between centers

the more general form will be dealt with later

 Ug = − Gm1m2 r

work-energy theorem, two possibilities

• conservative forces
• work done is independent of path
• W = ∮F · dr = 0
• can be associated with a potential energy function
• nonconservative forces
• work done depends on path
• W = ∮F · dr > 0
• cannot be associated with a potential energy function

force and potential energy

• one dimensional  F(r) = − dU dr
• three dimensional, expanded notation  F(r) = − ∂U î − ∂U ĵ − ∂U k̂ ∂x ∂y ∂z
• three dimensional, compact notation

F(r) = − ∇U

constant total energy, horizontal line above curve, kinetic energy is difference between line and curve

bounded and unbounded states, binding energy

stability of equilibrium