Discussion

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

gravitational potential energy

ΔU_g = mgΔh

• 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				three-dimensional							compact notation
F(r) = −	dU			F(r) = −	∂U	ˆi −	∂U	ˆj −	∂U	ˆk	F(r) = − ∇U
	dr				∂x		∂y		∂z

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

bounded and unbounded states, binding energy

stability of equilibrium

stable equilibrium	unstable equilibrium	neutral equilibrium
[diagram]	[diagram]	[diagram]
local maximum	local minimum	constant potential energy