MathLiveWork done by a force along a path
Gives the mechanical work done by a force as the line integral of the force dotted with the infinitesimal displacement along the path Γ. It is used when the force varies along the path or the path is curved.
A = \int_{\Gamma} \boldsymbol{F} \cdot \mathrm{d}\boldsymbol{r}What the symbols mean
| work done (joules, \mathrm{J}) | |
| path along which the force acts | |
| force vector (newtons, \mathrm{N}) | |
| infinitesimal displacement vector along the path (metres, \mathrm{m}) |
About this formula
- FieldPhysics
- TopicClassical mechanics
- LevelUniversity
- Also calledwork integral, physical work, mechanical work, line integral of force, work done by variable force, work formula physics
- SourceWikidata Q42213
Write it in Obsidian
MathLive is a free visual math editor for Obsidian. Run Find a formula, type “work done by a force along a path”, and it goes into your note as editable LaTeX. You can also scan formulas from screenshots, PDFs and handwriting.