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HELP Energy problem

  1. Nov 2, 2008 #1
    HELP!!!Energy problem

    1. The problem statement, all variables and given/known data
    A 20kg object is acted on by a conservative force given by F=-3.0x-5.0x^2, with F in newtons and x in meters. take the potential energy associated with the force to zero when the object is at x=0
    a) what is the potential energy of the system associated with the force when the object is at x=2.0m?
    b)If the object has a velocity of 4.0m/s in the negative direction of the x axis when it is at x=5.0m, what is its speed when it passes through the origin?
    c)What are the answers to a) and b) if the potential energy of the system is taken to be -8.0J when the object is at x=0.

    3. The attempt at a solution
    a)I can get the equation for finding out PE by integrating F=-3.0x-5.0x^2, which is -1.5x^2-5/3x^3
    sub 2.0 into x
    then the answer I got is -19.3
    b) I don't really know how to approach this question, but I know that I have to somehow relate the conservative energy to speed...maybe to kinetic energy???1/2mv^2???
    c)
    a. -8=-1.5x^2-5/3x^3
    x=-2.04m
    but the question says when x=0, so I don't know what did i do wrong with this question
    b. I didn't know how to do b), so I don't really know how to det the answer for this too.

    I need some help on this. Thank you very much.
     
  2. jcsd
  3. Nov 2, 2008 #2
    Re: HELP!!!Energy problem

    (b) is simple, just put in x=2 into your answer of part (a).
     
  4. Nov 2, 2008 #3
    Re: HELP!!!Energy problem

    Then isn't the answer same as a)
     
  5. Nov 2, 2008 #4
    Re: HELP!!!Energy problem

    Oh yeah, sorry :). For part (b) you have to use energy conservation. Kinetic energy (T=mvv/2) plus potential energy is a constant at any x, so just make an equation at for two points.
     
  6. Nov 2, 2008 #5
    Re: HELP!!!Energy problem


    E=K+PE
    find PE by plugging in the x value
    and plug in the x values and m into K then I got the energy...
    sorry, but how can you get the speed from the answer I got for the energy
    And also do you know whether i did part c right or not?
     
  7. Nov 2, 2008 #6
    Re: HELP!!!Energy problem

    Consider points x_1=0 and x_2=5.
    Then by energy conservation:

    [tex]\frac{mv_1^2}{2} + V(x_1) = \frac{mv_2^2}{2} + V(x_2)[/tex]

    You have one of the speeds, so just solve for the other one.
     
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