List of formulas related to Green’s formula and work of force:
Green’s formula
Green’s formula connects integrals over the boundary of a region and double integrals over the region itself. It has the form:
[
\oint_C (P \, dx + Q \, dy) = \iint_D \left( \frac{\partial Q}{\partial x} – \frac{\partial P}{\partial y} \right) dA
]
Where:
- ( C ) is a closed curve that bounds the region ( D ),
- ( P ) and ( Q ) are functions defined on the domain ( D ).
Work of force
The work (A) done by a force (F) in moving an object a distance (s) is defined as:
[
A = F \cdot s \cdot \cos(\theta)
]
Where:
- ( A ) — work,
- ( F ) — magnitude of force,
- ( s ) — displacement,
- ( \theta ) — the angle between the direction of force and the direction of displacement.
If the force is constant and directed along the displacement, the formula simplifies to:
[
A = F \cdot s