Question
A force acting on a particle moving in the xy plane is given by Fx = (2yi +x^2j)N, where x and y are in meters. The particle moves from the origin to a final position having coordinates x=5.00m and y=5.00m, as in Fig. Calculate the work done by F along (a) OAC, (b) OBC, (c) OC.(d) Is F conservative or nonconservative? Explain.
Answers
If you tried to copy and paste, that does not work here. Therefore I do not know your paths.
If the force is conservative the curl of the force vector is zero and it can be describedas the gradient of a potential. assuming you mean F = 2y i +x^2 j
i j k
d/dx d/dy d/dz
2 y x^2 0
[d/dx(x^2) - d/dy(2y)] k = (2x-2)k
see http://www.wolframalpha.com/widget/widgetPopup.jsp?p=v&id=85afa8b72bd564fc6c84dde9f0393305&title=MathsPro101%20-%20%20Curl%20and%20Divergence%20of%20Vector%20Fields&theme=gray&i0=2y&i1=x%5E2&i2=0&i3=curl&podSelect=&includepodid=VectorAnalysisResult
so
not a conservative field and the work done will depend on the path taken
If the force is conservative the curl of the force vector is zero and it can be describedas the gradient of a potential. assuming you mean F = 2y i +x^2 j
i j k
d/dx d/dy d/dz
2 y x^2 0
[d/dx(x^2) - d/dy(2y)] k = (2x-2)k
see http://www.wolframalpha.com/widget/widgetPopup.jsp?p=v&id=85afa8b72bd564fc6c84dde9f0393305&title=MathsPro101%20-%20%20Curl%20and%20Divergence%20of%20Vector%20Fields&theme=gray&i0=2y&i1=x%5E2&i2=0&i3=curl&podSelect=&includepodid=VectorAnalysisResult
so
not a conservative field and the work done will depend on the path taken
yes
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