Discussion

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

gravitational potential energy

∆U_g = mg∆h

• 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

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