The Physics
Hypertextbook
Opus in profectus

# 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…

Ug = mgh

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
• A 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 î − ∂U ĵ − ∂U k̂ ∂x ∂y ∂z
• 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

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