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Mass launched into the air by a spring

  1. Jan 13, 2019 #1
    1. The problem statement, all variables and given/known data
    A child's toy consists of a piece of plastic attached to a spring in the figure below. The spring is compressed against the floor a distance of 2.00 cm, and the toy is released. If the toy has a mass of 117 g and rises to a maximum height of 45.0 cm, estimate the force constant of the spring. (Assume the toy rises 45.0 cm above the equilibrium position of the spring.)

    2. Relevant equations
    0.5kx^2 = mgh

    3. The attempt at a solution

    k = 2mgh/(x^2)

    k = 2*0.117*9.81*45/(0.02^2)

    k = 258248.25 N/m

    Apparently this answer is off by a multiple of 10... not sure what's wrong. Can anybody help me? Thanks
  2. jcsd
  3. Jan 13, 2019 #2


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    Gold Member

    You forgot to convert 45 cm to meters. Also, some of the stored potential energy in the spring is used to raise the toy from where it starts to the equilibrium position. I am not sure if that will account for a factor of 10 though. More like a factor of 100.
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