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 is…
- Gravitational potential energy can be computed through one of two equations
- The simplified equation…
∆Ug = mg∆h
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
- 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 ⋅ 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
- 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