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Math Help - Work

  1. #1
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    Work

    I have this vector field equation, the first part of the question is to find the potential equation for it, I found it.
    The second part of the question is to find the work of the field through this path.
    My idea is to plug t in the r equation, because I'm not sure but I think (x,y,z)=(component of r), is that right? and that way I find the start point of the path and the end point, plug it into the potential equation and that's it, is that right?
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  2. #2
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    Quote Originally Posted by asi123 View Post
    I have this vector field equation, the first part of the question is to find the potential equation for it, I found it.
    The second part of the question is to find the work of the field through this path.
    My idea is to plug t in the r equation, because I'm not sure but I think (x,y,z)=(component of r), is that right? and that way I find the start point of the path and the end point, plug it into the potential equation and that's it, is that right?
    If F = \nabla \phi then W = \int_{C} F \cdot dr = \phi(x_2, y_2, z_2) - \phi(x_1, y_1, z_1) where (x_1, y_1, z_1) are the coordinates of the start of C and (x_2, y_2, z_2) are the coordinates of the end of C.

    To get the coordinates of the start and endpoints of C, substitute t = 0 and t = 2 \pi into r.

    So yes, that's right.
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    If F = \nabla \phi then W = \int_{C} F \cdot dr = \phi(x_2, y_2, z_2) - \phi(x_1, y_1, z_1) where (x_1, y_1, z_1) are the coordinates of the start of C and (x_2, y_2, z_2) are the coordinates of the end of C.

    To get the coordinates of the start and endpoints of C, substitute t = 0 and t = 2 \pi into r.

    So yes, that's right.

    10x, it seemed so easy, and they gave 10 points for it (it's a question from a test), so I got confuse...
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