Potential energy Summary

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Potential energy Summary

  • Potential energy is…
    • the energy associated with the arrangement of objects
    • the energy due to position of a quantity in a field
  • Potential energy comes in four fundamental types, one for each of the fundamental forces, and several subtypes
    • Gravitational potential energy is…
      • the energy associated with the arrangement of masses
      • the energy of a mass in a gravitational field
    • Electromagnetic potential energy is…
      • the energy associated with the arrangement of charges
      • the energy of a charge in electric and magnetic fields
      • the origin of several subtypes of energy.
        • Chemical potential energy is associated with the arrangement of atoms in a molecule.
        • Elastic potential energy is associated with the deformation of elastic materials.
    • Strong nuclear potential energy is…
      • the energy associated with the arrangement of protons and neutrons is a nucleus
      • the energy associated with the arrangement of quarks in a meson or hadron
      • the energy of a color charge in a strong nuclear field
    • Weak nuclear potential energy is…
      • the energy associated with beta decay reactions
      • the energy associated with flavor change processes in fundamental particles
  • Gravitational potential energy can be computed through one of two equations
    • the simplified equation…

      ΔUg = mgΔh

      assumes that…

      • acceleration due to gravity is nearly constant
      • height change is small compared to the separation between centers
    • the more general equation is dealt with in a later section of this book
      Ug = −Gm1m2
      r
  • Work and Forces

    • For conservative forces, the work done…
        • is path independent (does not depend on the path taken)
        • can be associated with a potential energy function

      W = ∮F · dr = 0

    • For nonconservative forces, the work done…
        • is path dependent (depends on the path taken)
        • cannot be associated with a potential energy function

      W = ∮F · dr > 0

  • Potential Energy and Forces

    • conservative force is the gradient of a potential energy function for every location in space.
      • one dimensional equation
        F(r) = −dU
        dr
      • three dimensional equation, expanded notation
        F(r) = −U  −U  −U 
        xyz
      • three dimensional equation, compact notation
        F(r) = − ∇U
  • Potential energy curves (or surfaces, or their higher order equivalents) are useful problem solving tools; for example…
    • the motion of a particle in a field
      • constant total energy, horizontal line above curve
      • kinetic energy is difference between line and curve
      • bound and unbound states, binding energy
    • stability of equilibrium

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