# 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

- the energy associated with the
- 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 is…
- Gravitational potential energy can be computed through one of two equations
- The simplified equation…
∆

assumes that…*U*=_{g}*mg*∆*h*- 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
*U*= −_{g}*Gm*_{1}*m*_{2}*r*

- The simplified equation…
- 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**·*d***r**= 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**·*d***r**> 0

- For conservative forces, the work done…
- 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*

- one dimensional equation

- A conservative force is the gradient of a potential energy function for every location in space.
- 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

- the motion of a particle in a field