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Homework Help: Work and Energy Theorem- change in acceleration

  1. Apr 19, 2009 #1
    1. The problem statement, all variables and given/known data

    A toy car of mass 555g is moving with speed 1.21m/s and strikes a spring mounted to the wall. The spring slows the toy car to rest with a acceleration that varies from 0 - 3.055m/s2.
    Determine the spring constant.

    2. Relevant equations
    W = -1/2mv2 + 1/2 kx2

    3. The attempt at a solution
    I've seen equations like this but I don't understand the acceleration part. I think that because there is no friction the work is conservative so it equals zero. Then I solved the equation for x2 and substituted that back into the equation so that I could solve for k but the answer I got doesn't jive with the one my instructor gave me. What am I doing wrong?

    Thanks for your help.
    Last edited: Apr 19, 2009
  2. jcsd
  3. Apr 19, 2009 #2


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    W = -1/2mva + 1/2 kx2
    It should be W = -1/2mva^2 + 1/2 kx2
  4. Apr 19, 2009 #3
    Why is the acceleration part of the kinematic equation? And if there is a range (0-3.055) then what number should I insert?

    Otherwise was the way I was going about solving it right?

  5. Apr 19, 2009 #4


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    For kinetic energy you have used 1/2* m *va. It should be 1/2* m *va^2. Is it typo?
  6. Apr 19, 2009 #5
    oh yea, sorry but the acceleration should be included?
  7. Apr 19, 2009 #6


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    No. a is not a part of the equation. I think there is some confusion in your notation, since I trust you didn't intend that a was a subscript of v.

    KE = 1/2*m*v2
  8. Apr 19, 2009 #7
    my question is still how does the acceleration factor into this problem? I'm trying to work the problem out and I'm not getting the question right I don't understand what I am doing wrong.

    am I using the right formula?
  9. Apr 19, 2009 #8


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    You have 2 equations and 2 unknowns don't you?

    You don't know k or x.

    But they tell you that max a = 3.055 which means that

    Fmax = .555*3.055

    which is also

    Fmax = k*x

    You also know that

    1/2*m*v2 = 1/2*k*x2

    So Xmax = m*v2/Fmax

    and k = Fmax/Xmax
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