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Conservation/Conversion of energy

  1. Nov 17, 2009 #1
    1. The problem statement, all variables and given/known data
    A mass of 4.5kg is dropped from a height of 3.3m above a spring. spring const is 25N/cm. How much is the spring compressed.


    2. Relevant equations

    F = 4.5*9.8 = 44.1

    PE = mgh = 4.5*3.3*9.8 = 145.53

    v = sqrt(2(9.8)(3.3)) = 8.04m/s

    3. The attempt at a solution

    The above are the few things I was able to grab out of the given information. The issue I'm having is plugging this into an equation to find the spring
     
  2. jcsd
  3. Nov 17, 2009 #2

    Delphi51

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    Homework Helper

    Energy is conserved in this problem. If you write
    initial energy = final energy
    and then fill in the details of the kinds of energy involved you will be able to solve for the spring compression.
     
  4. Nov 17, 2009 #3
    so I get that mgh = 1/2mv^2+mgh?

    145.53 = .5(4.5)(8.04)^2+(4.5)(9.8)h

    .7m?

    I don't think I did it right
     
  5. Nov 17, 2009 #4
    Well I looked into a few of the formulas on the book and I get to a quadratic equation, but I'm still missing something here and I'm not sure what it is.

    .5(.25)Y^2-(4.5)(9.8)Y+4.5(9.8)(-3.3)
    0.125Y^2-44.1Y+145.53.

    356? That's not possible so any adive on this will be appreciated.

    Thnsx
     
  6. Nov 18, 2009 #5
    Got it done. My equation above is right, the only problem was that I had to convert N/cm to N/m.

    Thanks
     
  7. Nov 18, 2009 #6

    Delphi51

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    Homework Helper

    You didn't consider the spring!
    Initially you have the mgh. When the mass hits the spring, it comes to a stop and you only have spring energy ½kx².
     
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