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Test Question (Potential Energy): Need help finding answer

  1. Apr 18, 2005 #1
    I can't figure out what I did wrong on this test question.

    A 4kg block is dropped from a height of 0.8m above a spring, k=120N/m. Find the maximum compression of the spring.

    I have the PE at the top is equal to KE at the bottom.
    PEtop=31.4J
    KEbottom=31.4J

    The potential energy in the spring when compressed should equal the KE at the bottom. Based upon that I should be able to find the maximum distance the spring will compress.

    KEbottom=Wspring
    31.4J=.5*120*x^2
    Rearranging x=sqrt(2*31.4/120) and I get x=-0.723m

    What am I doing wrong here? Can someone point it out.

    Thanks, peace
     
  2. jcsd
  3. Apr 18, 2005 #2

    SpaceTiger

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    Remember that the spring is compressing in the vertical direction, so there is more gravitational potential energy to take into account:

    Initial gravitational potential energy = Final spring potential energy

    [tex]mg(x_0+x_{spring})=\frac{1}{2}kx_{spring}^2[/tex]
     
    Last edited: Apr 18, 2005
  4. Apr 18, 2005 #3
    Your equation will give me the exact same answer I got.
    mg(0.8 + 0) =.5kx^2
     
  5. Apr 18, 2005 #4

    SpaceTiger

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    No, in my response, x_spring is the same as x in your response. On the left side, you set the second term to 0, when it should be mgx. It's a quadratic equation.
     
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