Potential Energy

Summary

Potential energy …
- is energy associated with position in a field (a force that exists at many locations)
- comes in four fundamental types, one for each of the fundamental forces, and several subtypes
  - gravitational
  - electromagnetic
    - electrostatic
    - chemical
    - elastic
  - strong
    - primary: between quarks, within nucleons (and other hadrons)
    - residual: between nucleons, within the nucleus
  - weak

Gravitational potential energy

can be computed through one of two formulas

the simplified formula

the more general formula

ΔU = mgΔh

U = −	Gm₁m₂
	r²

assumes that

is dealt with in a later section of this book

acceleration due to gravity is nearly constant
height change is small compared to the separation between centers

Forces and Potential Energy
- nonconservative forces
  - work done depends on path
  - W = ∮ F · dr > 0
  - cannot be associated with a potential energy function
- conservative forces
  - work done is independent of path
  - W = ∮ F · dr = 0
  - can be associated with a potential energy function

Forces and Potential Energy

work is the force-displacement integral
- this is the work energy theorem
a conservative force is the gradient of potential energy


one-dimensional				three-dimensional							compact notation
F(r) = −	dU			F(r) = −	∂U	î −	∂U	k̂ −	∂U		F(r) = − ∇U
	dr				∂x		∂y		∂z

Potential energy curves (or surfaces, or their higher order equivalents) are useful problem solving tools

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 Physics Hypertextbook

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© 1998–2011 Glenn Elert