Definition:Work

Definition

Let $P$ be a particle whose position vector at time $t$ is $\mathbf r$.

Let a force applied to $P$ be represented by the vector $\mathbf F$.

Suppose that, during the time interval $\delta t$, $P$ moves from $\mathbf r$ to $\mathbf r + \delta \mathbf r$.

The work done by $\mathbf F$ during $\delta t$ is defined to be:

$\delta W = \mathbf F \cdot \delta \mathbf r$

where $\cdot$ denotes the dot product.