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.

Work is a scalar quantity.

Symbol

The usual symbols used to denote work are $w$ or $W$.

Unit

The SI unit of measurement of work is the joule.

Also see

• Definition:Energy

• Results about work can be found here.

Sources

• 1961: D.S. Jones: Electrical & Mechanical Oscillations ... (previous) ... (next): Chapter $1$: Equilibrium: $1.1$ Introduction
• 1969: J.C. Anderson, D.M. Hum, B.G. Neal and J.H. Whitelaw: Data and Formulae for Engineering Students (2nd ed.) ... (previous) ... (next): $1.$ Units and Abbreviations: $1.2$ SI units $(2)$ Derived units
• 1970: George Arfken: Mathematical Methods for Physicists (2nd ed.) ... (next): Chapter $1$ Vector Analysis $1.3$ Scalar or Dot Product
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): work
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): work