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Homework Help: Vector calculus

  1. May 25, 2010 #1
    1. The problem statement, all variables and given/known data

    A force is applied to a particle, defined by:

    F(x,y)= (y^2, 2xy) << This is a verticle bracket with the y^2 ontop of the 2xy

    The path of the particle is straight. The particle moves from (-1,2) to (1,3)

    i) Calculate the work that the force F does as the particle moves along the path C by evaluating the appropreate line integral directly


    I dont know where to start with this. I know that work: w = fd so to get the distance i must do some integration, but how do you integrate a vector like that?


    Can somone please help!? - would be much appreciated


    Many thanks
     
  2. jcsd
  3. May 25, 2010 #2

    LCKurtz

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    What do you mean by that? Force is a vector, not a fraction???
    w = fd only works for constant forces along straight lines. Perhaps you mean

    [tex] W = \int_C \vec F \cdot d\vec R[/tex]
     
  4. May 25, 2010 #3
    Hi there! thanks for your help

    sorry about the fraction thing.. what i ment was that it is a vector but written vertically not horizontally... so still a vector but not (y^2, 2xy) .. Im damn useless at LaTeX so i cant make it with a large bracket and the y^2 at the top and the 2xy at the bottom.. hope that makes sense

    Also i was only making a guess with the w=fd thing, im sure your expression is what im looking for as it uses vectors.

    What would be the next logical thing to do with it?

    Thanks again
     
  5. May 25, 2010 #4

    vela

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    Click on the formula below to see the LaTeX for writing the column vector.

    [tex]\textbf{F} = \begin{pmatrix} y^2 \\ 2xy \end{pmatrix}[/tex]
     
  6. May 26, 2010 #5

    LCKurtz

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    Parameterize the line as

    [tex]\vec R(t) = \langle x(t), y(t), z(t)\rangle[/tex]

    and use

    [tex]\int_C \vec F \cdot d\vec R = \int_a^b \vec F(t)\cdot \frac {d\vec R}{dt}\, dt[/tex]
     
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