Math 2.0

Mechanics of particles and systems Foundations of particle mechanics Concept

Potential energy

Builds on Conservative vector fieldScalar potential

Summary

Potential energy is energy stored in the position of a system, such as a raised weight or a stretched spring. Mathematically, a potential energy of a conservative force field FF is a function VV with F=−∇VF = -\nabla V. So −V-V is a scalar potential of FF in the convention ∇ϕ=F\nabla \phi = F. The work done by the force along a path is the drop of VV from the start to the end. The sum of kinetic and potential energy is then constant along each motion.

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Euclidean space, object, no evidence levelEuclidean spaceobjectFunction, concept, no evidence levelFunctionconceptTotal derivative, concept, no evidence levelTotal derivativeconceptFunction of several variables, concept, no evidence levelFunction of several v…conceptVector-valued function, concept, no evidence levelVector-valued functionconceptDifferentiable function of several variables, concept, no evidence levelDifferentiable functi…conceptPartial derivative, concept, no evidence levelPartial derivativeconceptVector field, concept, no evidence levelVector fieldconceptGradient, concept, no evidence levelGradientconceptScalar potential, concept, no evidence levelScalar potentialconceptConservative vector field, concept, no evidence levelConservative vector f…conceptPotential energy, concept, no evidence levelPotential energyconcept
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Euclidean space object
  2. Function concept
  3. Total derivative concept
  4. Function of several variables concept
  5. Vector-valued function concept
  6. Differentiable function of several variables concept
  7. Partial derivative concept
  8. Vector field concept
  9. Gradient concept
  10. Scalar potential concept
  11. Conservative vector field concept
  12. Potential energy concept

Where this leads

17 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Potential_energy
About this page
TagDF7DKHTQ7A
URIm2://DF7DKHTQ7A
Kindconcept
WritingW0 stub
MSC70A05, 70F10
UsesConservative vector field, Scalar potential
Same as
Changed3 November 2026

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