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Homework Help: A force acting on a particle moving in the xy plane is given by

  1. Oct 9, 2012 #1
    1. The problem statement, all variables and given/known data


    2. Relevant equations

    W=∫ Fx dx

    3. The attempt at a solution

    I think you gotta split this one in terms of axis.

    ∫(2yi + x2j) dx

    Pretty lost on it.
  2. jcsd
  3. Oct 9, 2012 #2


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    Well, they do not say in which direction the vectors i and j point, so let us assume that vector i is parallel to the x-axis and vector j is parallel to the y-axis, which is the usual convention.

    To start you off,
    Path OAC:
    From O to A, can you find the force on the particle along this path knowing that y = 0. In what direction does the force point from the equation given for force.? Does the force do any work along this path? Note that the particle is moving along the x-axis which is what vector direction, i or j. Can you find an equation for the path of the particle in terms of vectors i oj or both?

    from A to C, same questions.

    You might want to review dot and cross product as that that is what this problem seems to be designed for.

    PS. Your picture shows up a bit large.
  4. Oct 9, 2012 #3
    Understood, so quick question, is the blue line the force? Then the other lines simply components of the force?

    Still a little lost. We want to calculate the work required to mvoe the object to the right first. Force is constant right? So would you use fΔrCosθ?
  5. Oct 9, 2012 #4


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    No, the force is not along the blue line.

    No, the force is not constant.

    The force depends upon the location of the particle according to [itex]\displaystyle \vec{F}=2y\hat{\text{i}}+x^2\hat{\text{j}}\ .[/itex]

    You are to calculate the work done by that force in moving the particle from point, O, to point, C, along each of the colored paths.
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