Potential energy

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Potential energy Discussion

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

gravitational potential energy

ΔUg = 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
    F(r) = −dU
    dr
  • three dimensional, expanded notation
    F(r) = −U  −U  −U 
    xyz
  • 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

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