Use Green’s Theorem to find the work done by the force F(x, y) = x(x + y) i + xy2 j in moving a particle from the origin along the x-axis to (1, 0), then along the line segment to (0, 1), and then back to the origin along the y-axis.
To find: The work done by force using Green’s Theorem.
Force is and particle moving from origin along x-axis to , then line segment to and finally return to origin along the y-axis.
Consider a positively oriented curve C which is piece-wise smooth, simple closed curve in plane with domain D. Then work done by force moving over curve C is,
is continuous first-order partial derivative of P,
is continuous first-order partial derivative of Q, and
P and Q have continuous partial derivatives.
The curve C is typically a triangle, which is piecewise-smooth, and simply closed curve with domain and curve C is positively oriented. Therefore, the Green’s theorem is applicable.
Compare the two vector fields and .
Find the value of .
Find the value of .
Re-modify the equation (1)
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