Given :
Force, [tex]\vec{F}= (2\hat{i} + 5\hat{j})\ kN[/tex].
Force is acting at point A( 2 m, 3 m ) and B( 3 m, 5 m )
To Find :
The work done by force F .
Solution :
Displacement vector between point A and B is :
[tex]\vec{d} = (3-2)\hat{i} + (5-3)\hat{j}\\\\\vec{d} = \hat{i} + 2\hat{j}[/tex]
Now, we know work done is given by :
[tex]W = \vec{F}.\vec{d}\\\\W= (2\hat{i} + 5\hat{j}).(\hat{i}+\hat{2j})\\\\W = (2\times 1) +( 5\times 2) \ kJ\\\\W = 12 \ kJ[/tex]
W = 12000 J
Therefore, work done by force is 12000 J .
