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Math Help - Work

  1. #1
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    Work

    Calculate the work done in moving the particle under the action of a force F(x,y,z) = (2x+3y)i + xyj along the arc of the circle x^2 + (y-1)^2 = 1 of (0,0) to (1,1).


    I am confused on the parameterization

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  2. #2
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    Quote Originally Posted by Apprentice123 View Post
    Calculate the work done in moving the particle under the action of a force F(x,y,z) = (2x+3y)i + xyj along the arc of the circle x^2 + (y-1)^2 = 1 of (0,0) to (1,1).


    I am confused on the parameterization

    A standard parameterization of the unit circle centered at (0,0), x^2+ y^2= 1 is x= cos(\theta), y= sin(\theta) because x^2+ y^2= cos^2(\theta)+ sin^2(\theta)= 1.

    That can be shifted to center (0, 1) using x= cos(\theta), y- 1= sin(\theta) so y= 1+ sin(\theta). To go from from (0,0) to (1,1), which is counter clockwise, integrate from \theta= 3\pi/2 to 2\pi.
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  3. #3
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    Quote Originally Posted by HallsofIvy View Post
    A standard parameterization of the unit circle centered at (0,0), x^2+ y^2= 1 is x= cos(\theta), y= sin(\theta) because x^2+ y^2= cos^2(\theta)+ sin^2(\theta)= 1.

    That can be shifted to center (0, 1) using x= cos(\theta), y- 1= sin(\theta) so y= 1+ sin(\theta). To go from from (0,0) to (1,1), which is counter clockwise, integrate from \theta= 3\pi/2 to 2\pi.
    Ok. Thank you
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