Work:

Work is said to be done if certain amount of force applied on a body displace it by a certain distance along the direction of force. Mathematically,

[latex]W = \vec{F}. \vec{S}[/latex]

It means work is scalar product of force and displacement.

i.e., [latex]W = FS\cos\theta[/latex]

when, [latex]\theta = 0^o[/latex].

[latex]W = FS[/latex]

When, [latex]\theta = 90^o[/latex], W = 0.

Unit of work is Joule in SI unit and erg in CGS unit so that, 1 Joule = [latex]10^7[/latex] erg.

Workdone by variable force:

Let us consider, a body moving due to the application of variable force. In certain time, the body transit from P to Q to find workdone in this transition. Let us divide the section PQ into large number of rectangular strips with infinitely small thickness [latex]\Delta x[/latex].

Now, the small workdone by the body moving A to B is:

[latex]\Delta W = F_i \times \Delta x[/latex], where, i = workdone on moving [latex]i^{th}[/latex] strip [AD = area of [latex]i^{th}[/latex] strip]