Work

WORKDONE DUE TO CONSTANT FORCE

Let a constant force \(\overrightarrow F\)  be applied on the body such that it makes an angle  \(\theta\) with the horizontal and body is displaced through a distance s
By resolving force \(\overrightarrow F\) into two components :
                 

(i) F cos\(\theta\)  in the horizontal direction of displacement of the body.                     
(ii) F sin\(\theta\)   in the perpendicular direction of displacement of the body
Since body is being displaced in the direction of  \(F cos\theta\), therefore work done by the force in displacing the body through a distance s is given by 
             \( W = (F\cos \theta )s = Fs\cos \theta \)  
Thus, work done by a force is equal to the scalar or dot product of the force and the displacement of the body.
If a number of force \( \overrightarrow {F_1 } ,\,\overrightarrow {F_2 } ,\,\overrightarrow {F_3 } ......\overrightarrow {F_n } \) are acting on a body and it shifts from position vector  \(\vec r_1\)  to position vector \(\vec r_2\) then \( W = \left( {\overrightarrow {F_1 } + \overrightarrow {F_2 } + \overrightarrow {F_3 } + .....\overrightarrow {F_n } } \right).\left( {\overrightarrow {r_2 } - \overrightarrow {r_1 } } \right) \)