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Help calculating work in an xy plane

  1. Oct 20, 2014 #1
    1. The problem statement, all variables and given/known data
    A force Farrowbolditalic.gif = (1.9 N/m2)x2i is applied to a particle initially at rest in the xy plane. Find the work done by this force on the particle and the final speed of the particle as it moves along a path as follows. The given force is the only force doing work on the particle.

    a) in a straight line from point (2.1 m, 2.1 m) to point (2.1 m, 7.5 m)
    _________ J

    b) in a straight line from point (2.1 m, 2.1 m) to point (4.8 m, 6.6 m)
    __________ J

    2. Relevant equations
    W = F x d

    3. The attempt at a solution
    a) Due to the equation that I found above, I have used the distance formula to calculate d:
    = 5.4
    Then I did F x d = 1.9 * 5.4 = 10.26 (Wrong)

    b) Same this as above:
    = 2.7
    F x d = 1.9 * 2.7 = 5.13 (Wrong)
    -------------------------------------------------
    On top of these incorrect attempts, I am also confused with what the problem is asking... It says to find the word done by the force, and the final speed of the particle, but the answer boxes contain a J for Joules which is a unit of work. How would I put work and speed in one box?
     
    Last edited by a moderator: Apr 30, 2017
  2. jcsd
  3. Oct 20, 2014 #2

    rude man

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    Is the correct statement of the force F = 1.9 x2 i Newtons?
    (where i is the unit vector in the x direction.)

    PS it does not say to find the final speed. Both answers will be in Joules.
     
  4. Oct 20, 2014 #3
    Yes that is the correct statement, sorry about that. I have corrected it.

    It does say in the question "Find the work done by this force on the particle and the final speed of the particle as it moves along a path as follows", but it looks like the questions are asking for work, so I guess I'll just ignore that part.
     
  5. Oct 20, 2014 #4

    haruspex

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    Force and displacement are vectors. What, exactly, is the formula for the work done in terms of those vectors?
     
  6. Oct 20, 2014 #5
    Oh! It looks like it's the dot product of the force and the displacement vector.

    EDIT: Okay, I got a) correct: W = F dot d = 0 + 0 = 0
    Now for b) I get 5.13x2 and it is wrong. I think it might have something to do with the x
     
    Last edited: Oct 20, 2014
  7. Oct 20, 2014 #6

    rude man

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    You have to integrate F dot dx to get part (b).
     
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