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Work done by the spring pls. help

  1. Jun 14, 2009 #1
    work done by the spring URGENT!! pls. help

    1. The problem statement, all variables and given/known data
    An ideal spring is hung vertically from the ceiling. When a 2.0 kg mass hangs at rest from it, the spring us extended 6.0 cm from its relaxed length. A downward external force is now applied to the mass to extend the spring an additional 10 cm. while the spring is being extended by the forxe, the work done by the spring is?

    2. Relevant equations
    Ws=o.5kx^2
    Fs=kx
    Weight=mg
    3. The attempt at a solution
    so first i found k of the string by equating mg=kx with x=0.06 m where i got a value of 326.67 N/m. then i used Ws=o.5kx^2 with delta x=0.1m and tried to solve for work and my answer is coming out wrong. The answer is supposed to be -3.6 J ..i'm not getting that or close to it..pls help
     
  2. jcsd
  3. Jun 14, 2009 #2

    LowlyPion

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    Re: work done by the spring URGENT!! pls. help

    You need to account for the potential energy in the spring already as a result of the initial weight hanging on it don't you?
     
  4. Jun 14, 2009 #3
    Re: work done by the spring URGENT!! pls. help

    aare you saying that i should use this equation W=o.5kx^2 +mg where x=0.1 and k=326.67N/m
     
  5. Jun 14, 2009 #4

    LowlyPion

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    Re: work done by the spring URGENT!! pls. help

    No. I'm saying that the work that goes into increasing the potential energy in the spring is from .06 to .16, not from .00 to .10.
     
  6. Jun 14, 2009 #5
    Re: work done by the spring URGENT!! pls. help

    i'm sorry but i'm really confused by what you mean wouldnt delta x= 0.1[0.16-0.06] ??? or do you mean that when i'm solving for k value in the equation mg=kx my x should actually be the difference between 0.06-0.16 and not 0.06?
     
  7. Jun 14, 2009 #6

    LowlyPion

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    Re: work done by the spring URGENT!! pls. help

    Remember that

    W = F*d

    but in this case it's

    W = ∫ Fx dx = ∫ -k*x dx

    and your limits are from .06 to .16

    This comes out to W = -1/2*k*x2 from .06 to .16 or

    W = -1/2*k*(.162 - .12)
     
  8. Jun 14, 2009 #7

    LowlyPion

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    Re: work done by the spring URGENT!! pls. help

    You have the correct value of k by the way, so that's not the issue.
     
  9. Jun 14, 2009 #8
    Re: work done by the spring URGENT!! pls. help

    ok but then would the k value still be right as i used x=0.06 m?? cuz i used this equation W = -1/2*k*(.16^2 - .1^2) with the k value of 326.67 N and still am not getting the right answer
     
  10. Jun 14, 2009 #9

    LowlyPion

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    Re: work done by the spring URGENT!! pls. help

    Sorry. I typed it wrong.

    1/2*k*(.162 - .062)

    Is what it should be.
     
  11. Jun 14, 2009 #10
    Re: work done by the spring URGENT!! pls. help

    i'm getting -2.54J

    W=-0.5*(326.67N)(0.16^2-0.1^2)
    W=-0.5*(326.67)(0.0156)
    W=-2.548026 J
     
  12. Jun 14, 2009 #11
    Re: work done by the spring URGENT!! pls. help

    ok yea now i'm getting the answer thank you so much :)
     
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