Find the work done by the force field F=(2x^2+2y^2)i+(3x+3y)j as an object moves counterclockwise along the circle x^2+y^2=4 from (2,0) to (−2,0) and then back to (2,0) along the x-axis.

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Find the work done by the force field F=(2x^2+2y^2)i+(3x+3y)j as an object moves counterclockwise along the circle x^2+y^2=4 from (2,0) to (−2,0) and then back to (2,0) along the x-axis.

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Step 1

The work done is the dot product of force and displacement.

W=F.dwhere W is the work done and d is the diplacement.

Here displacement is along a circle of radius 2 units. The object moves from (2,0) to (-2, 0) in counterclockwise direction. Again moves back to the same initial point (2,0).

Hence net displacement is zero.

d=0.

 

 

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