Explanation Given: F ( x , y ) = y 2 i + x 2 j x 2 + y 2 = 2 Calculation: Given that F ( x , y ) = y 2 i + x 2 j Here, M = y 2 N = x 2 Now find ∂ M ∂ y = 2 y ∂ N ∂ x = 2 x Now, in polar coordinates, x = r cos θ , y = r sin θ , d A = r d r d θ Therefore, from Green’s theorem, the work done is given by ∮ C F ⋅ d R = ∫ ∫ R ( ∂ N ∂ x − ∂ M ∂ y ) d A = ∫

6th Edition

ISBN: 9781465208880

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 13.4, Problem 32PS

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To find: The work done using the Green’s theorem by the force filed F(x,y)=y2i+x2j e counter clockwise along the circle x2+y2=2

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Chapter 13.4, Problem 31PS

Chapter 13.4, Problem 33PS

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The work done using the Green’s theorem by the force filed F ( x , y ) = y 2 i + x 2 j e counter clockwise along the circle x 2 + y 2 = 2

Solution Summary: The author explains that the work done using the Green’s theorem is given by ldisplaystyle

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To find: The work done using the Green’s theorem by the force filed F(x,y)=y2i+x2j e counter clockwise along the circle x2+y2=2

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Chapter 13 Solutions