Answer:
[tex]W=2\sqrt{26} \,J[/tex]
Explanation:
Given that:
Relation of force with position, [tex]F=4x+2xy[/tex] N
Initial position of the object, [tex](x_0,y_0)=(0m,0m)[/tex]
second position of the object, [tex](x_2,y_2)=(1m,0m)[/tex]
final position of the object, [tex](x_f,y_f)=(1m,1m)[/tex]
Now, from the schematic we get the displacement as:
[tex]s=\sqrt{2}\,m[/tex]
Now we calculate :
The force in X direction for initial displacement
[tex]F_x=4\times 1+2\times 1\times 0[/tex]
[tex]F_x=4\,N[/tex]
The force in Y direction for initial displacement
[tex]F_y=4\times 1+2\times 1\times 1[/tex]
[tex]F_y=6\,N[/tex]
Now the resultant force in the direction of displacement:
[tex]F_R=\sqrt{F_x\,^2+F_y\,^2}[/tex]
[tex]F_R=\sqrt{4^2+6^2}[/tex]
[tex]F_R=2\sqrt{13}\,N[/tex]
Therefore work:
[tex]W=F_R\times s[/tex]
[tex]W=2\sqrt{13}\times \sqrt{2}[/tex]
[tex]W=2\sqrt{26} \,J[/tex]
