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Energy Conservation: Block & Spring

  1. Feb 12, 2009 #1
    1. The problem statement, all variables and given/known data
    An object of mass M = 4 kg slides from rest a distance d = 4 m down a frictionless inclined plane where it encounters a spring. It compresses the spring a distance D = 1 m before stopping. The inclined plane makes an angle q = 20° with the horizontal.

    2. Relevant equations
    When the block just touches the spring, how much gravitational potential energy has it lost?
    U=53.7 J
    After the mass has fully compressed the spring, what is its total loss of gravitational potential energy?
    U=67.1 J
    What is the value of the spring constant?
    k=??

    3. The attempt at a solution
    U=Ui-Uf
    U=53.7-67.1=-13.4
    U=(1/2)kx^2
    k=2U/x^2
    k=2(-13.4)/(5)^2
    k=1.07????
    the answer is wrong. am i suppose to use the conservation of mechanical energy? because i am lost.
     
  2. jcsd
  3. Feb 12, 2009 #2

    Delphi51

    User Avatar
    Homework Helper

    It is wrong to take the difference between 53.7 and 67.1.
    The ramp is frictionless, so all of the PE (67.1 J) goes into the spring energy.
     
  4. Feb 12, 2009 #3
    thank you, i figured it out.
     
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