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Work and Hooke's Law

  1. Mar 4, 2014 #1
    1. The problem statement, all variables and given/known data
    A vertical spring of negligible mass and spring constant k=1000N/m has a small object of mass M=5.0kg placed on its top. The spring is held compressed by distance of 25 cm from equilibrium position. The spring is released. Find speed of mass at equilibrium position.


    2. Relevant equations

    W spring=1/2kdeltax^2
    W gravity=deltax*5*9.8
    Total energy gain of mass=19J
    Energy transferred into potential: 12.25J=mgh
    Energy transferred into kinetic: 6.75J ---->v=1.64m/s


    3. The attempt at a solution

    The answer booklet says the answer is 2.76m/s!
    Where did I go wrong?
     
  2. jcsd
  3. Mar 4, 2014 #2
    I don't know. The 19J seems too low. I got about 32 J. You didn't subtract the potential energy change twice, did you?

    Chet
     
  4. Mar 4, 2014 #3

    NascentOxygen

    User Avatar

    Staff: Mentor

    When evaluating this, don't overlook that power of 2.
     
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