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Homework Help: Quick question regarding work?

  1. Nov 15, 2012 #1
    1. The problem statement, all variables and given/known data
    A force in the xy plane is given by F = A(10ai + 3xj), where A and a are constants, F is in newtons and x is in meters. Suppose that the force acts on a particle as it moves from an initial position x = 4m, y = 1m to a final position x = 4m, y = 4m. Show that this force is not conservative by computing the work done by the force for at least two different paths.

    2. Relevant equations
    W = integral of f dx

    3. The attempt at a solution
    I basically integrated and got W = A(10axi + 3/2 x^2j)
    I'm not sure how to exactly calculate the work done across the paths though.

  2. jcsd
  3. Nov 15, 2012 #2
    A force is non conservative if taking different routes leads to a conflict in potential between start/end points.

    Try this question by calculating the work done by moving the particle directly from (4,1) to (4,4). Now move it in a different motion, no complex path is required. For example move it from (4,1) to (x2,y2) then from there to (4,4).
  4. Nov 15, 2012 #3
    yeah I forgot how to compute the work from one point to another point.
  5. Nov 15, 2012 #4
    Work is equivalent to the dot product of Force and Distance.
  6. Nov 15, 2012 #5
    yeah I know you have to integrate the force vector across the displacement since it varies with displacement. I don't know how exactly you do that across the points. Do you have to do line integrals or something?
  7. Nov 15, 2012 #6


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    Staff: Mentor

    Yes, you have to do line integrals. From the statement of the problem, you need to choose two different paths and do a line integral along each of them.
  8. Nov 16, 2012 #7
    thanks. how exactly do you compute the line integral again?
    We didn't get up to it yet, we're only doing double integrals in multi.
  9. Nov 16, 2012 #8
    any ideas
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