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Notation within homework question

  1. Nov 14, 2009 #1
    1. The problem statement, all variables and given/known data

    A particle moving along the x-axis is subject to a conservative force such that the potential energy of the particle is given by U(x,y)=2x + x^3 where x and y are in meters, U is in joules. When the particle moves from (2,0) to the origin, the work done by the conservatice force is:
    A) b) c) d) (the choices don't matter... I have the right value, wrong sign)

    2. Relevant equations

    delta(U) = change in potential energy.

    3. The attempt at a solution

    Okay, my real question here is: What does this notation U(x,y) really mean?

    And I checked the solution for this problem, and it says U(initial) - U(final)...... Why is this? Since when is the change in a value equal to initial - final ?
  2. jcsd
  3. Nov 14, 2009 #2


    Staff: Mentor

    The notation U(x, y) is used to indicate that U is a function of two variables, x and y. The formula you show, however, is a function of x alone.
    Is there a typo in this formula? Should it be U(x, y) = 2x + y^3?
  4. Nov 14, 2009 #3


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    Hi mike_302! :smile:

    (try using the X2 tag just above the Reply box :wink:)

    Change in potential energy = minus the work done

    ie ∆PE = -W

    so the work done will be -∆PE = Uinitial - Ufinal
  5. Nov 14, 2009 #4
    Okay, I completely see why it's Ui-Uf now but that U(x,y) notation seems messed up because there's no typo :P That's how it is written, and I get the answer using JUST x, so I guess it should've said U(x)= ....

    Oh well!
  6. Nov 15, 2009 #5


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    No, because potential is a function of position, and has to be defined at every position …

    for example gravitational potential is U(x,y,z) = -gz. :wink:
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