### What is work?

Scalar product of force and displacement is called work.

$$ W = \vec{F}.\vec{S}\cos \theta $$

Work is a scalar quantity. The dimensional formula of work is [ M^{1}L^{2}T^{-2} ]. SI unit of work is joule. CGS unit of work is erg.

Relation between joule and erg is

1 joule = 10^{7} erg.

In terms of rectangular components, work is

W = x F_{x} + y F_{y} + z F_{z}

### Types of work

#### Positive work

If angle between \(\vec{F}\) and \(\vec{S}\) lies between 0^{0} and 90^{0}, then work done is positive.

#### Negative work

If angle between \(\vec{F}\) and \(\vec{S}\) lies between 90^{0} and 180^{0}, then work done is negetive.

#### Negative work

The work done is zero, if

- there is no displacement
- no force is acting on the body
- angle between \(\vec{F}\) and \(\vec{S}\) is 90
^{0}