Work (Physics)

up:: 031 MOC Classical Mechanics

Given a force $\vec{F}$ which acts upon a body, one can calculate the work it exerts through a given path $L$ as the line integral

$$W_L={\int }_L\vec{F}\cdot d\vec{l}$$

Given a parameterization of $L$ via $\gamma (t)$, one can write the work done over $\gamma$ as

$$W_L={\int }_{t_0}^{t_f}\vec{F}(\gamma (t))\cdot {\vec{\gamma }}^{\prime }(t)dt$$

with ${\vec{\gamma }}^{\prime }(t)$ being its derivative with respect to $t$.

Properties

• The work of resultant forces equals the difference in kinetic energy
• Work of conservative forces is the opposite of potential energy difference