# Work

The physics term for the amount of energy required to move an object over a given path subject to a given force.

#### Formulas

For an object moving distance $$d$$ with constant force $$F$$ acting in the direction of motion,

${\rm{Work}} = Fd$

If the force is a scalar that is not constant, and the motion runs from position $$x = a$$ to $$x = b$$ on the number line, then

\eqalign{{\rm{Work}} &= \int_a^b {f\left( x \right)dx} \\x &= {\rm{position}}\\f\left( x \right) &= {\rm{force \,at \,position\; }}x}

If the force $${{\bf{F}}}$$ is a vector function and the object moves along curve $$C$$, then

\eqalign{{\rm{Work}} &= \int\limits_C {{\bf{F}}\left( {{\bf{x}}} \right) \cdot {\bf{dx}}} \\{\bf{x}} &= {\rm{position \,vector}}\\{\bf{F}}\left( {{\bf{x}}} \right) &= {\rm{force \,vector \,at \,position \;}}{\bf{x}}}

### Words used here

Distance

Constant

Definite integral

Vector

Dot product