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Math Help - work - calculus

  1. #1
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    Question work - calculus

    given the force vector field F = <y,a> .
    Find the work in moving an object through the vector field along the closed curve C formed by the arc of the ellipse x=acost , y=bsint, lying in the first quadrant, the x-axis, and the y-axis.

    Please help me. thank you very much.
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  2. #2
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by kittycat View Post
    given the force vector field F = <y,a> .
    Find the work in moving an object through the vector field along the closed curve C formed by the arc of the ellipse x=acost , y=bsint, lying in the first quadrant, the x-axis, and the y-axis.

    Please help me. thank you very much.
    have you checked the previous post about work?
    so,
    r(t) = x(t)i + y(t)j = (a \cos t)i + (b \sin t)j
    where t is from 0 to \, \frac{\pi}{2}
    and
    F(x,y) = yi + aj

    note that
    W = \int_C F \cdot dr = \int_C <y,a> \cdot <dx,dy>
    \, = \int_0^{\frac{\pi}{2}} y(t)dx(t) + a dy(t)

    can you continue?
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by kittycat View Post
    given the force vector field F = <y,a> .
    Find the work in moving an object through the vector field along the closed curve C formed by the arc of the ellipse x=acost , y=bsint, lying in the first quadrant, the x-axis, and the y-axis.

    Please help me. thank you very much.
    Quote Originally Posted by kalagota View Post
    have you checked the previous post about work?
    so,
    r(t) = x(t)i + y(t)j = (a \cos t)i + (b \sin t)j
    where t is from 0 to \, \frac{\pi}{2}
    and
    F(x,y) = yi + aj
    Assuming kalagota is right and F(x,y) = yi + aj is what is meant by F = <y,a> what field of study did you get this notation from. I'm sure that I'm not the only person at least partialy mystified by this notation

    RonL
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  4. #4
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by CaptainBlack View Post
    Assuming kalagota is right and F(x,y) = yi + aj is what is meant by F = <y,a> what field of study did you get this notation from. I'm sure that I'm not the only person at least partialy mystified by this notation

    RonL
    we also that notation for vector fields, i.e. if we have a Field vector
    F(x,y)
    then it is equivalent to saying that
    F(x,y) = <x,y>
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by kalagota View Post
    we also that notation for vector fields, i.e. if we have a Field vector
    F(x,y)
    then it is equivalent to saying that
    F(x,y) = <x,y>
    Yes, but in this context who is the "we" you refer to?

    That is what area of study uses this notation (I ask because it is not used
    in any thing I have studies in this way).

    RonL
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by CaptainBlack View Post
    Yes, but in this context who is the "we" you refer to?

    That is what area of study uses this notation (I ask because it is not used
    in any thing I have studies in this way).

    RonL
    i've seen that notation before. it is from vector calculus, and you see it even in calc 3. in general we can use \left< x_1, x_2, ..., x_n \right> to represent a vector with n components. if the components are functions, as opposed to just numbers, we obtain a vector field, that is, a function that assigns an nth dimensional vector to each point
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  7. #7
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by CaptainBlack View Post
    Yes, but in this context who is the "we" you refer to?

    That is what area of study uses this notation (I ask because it is not used
    in any thing I have studies in this way).

    RonL
    "we" as in all students of math/physics in our university..
    we used it in our calc 3 also..
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