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Hooke's Law & Energy conservation

  1. Jul 1, 2013 #1
    1. The problem statement, all variables and given/known data

    An engineer is designing a spring to be placed at the bottom of an elevator shaft. If the elevator cable should happen to break when the elevator is at a height h above the top of the spring, calculate the value of the spring constant k so that the passengers undergo an acceleration of no more than 5.0 g when brought to a rest. Let M be the total mass of the elevator and passengers.


    2. Relevant equations

    F=-kx, Hooke's law
    Energy conservation: spring energy, gravitational energy


    3. The attempt at a solution

    The maximum acceleration will occur at the maximum compression of the spring, because a is proportional to x. Since kx=ma=5mg, k=5mg/x.

    I then conserved energy to get 1/2kx^2 - mgx - mgh = 0.

    I solved both equations to get k = 15mg/(2h). But my solution key says 12mg/h. What's wrong?

    EDIT: Never mind, solved it. My force equation was off.
     
    Last edited: Jul 1, 2013
  2. jcsd
  3. Jul 2, 2013 #2

    Simon Bridge

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    Well done :)
    Perhaps you could show others where you went wrong with the force equation?
     
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