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Finding spring constant in elevator

  1. Nov 23, 2008 #1
    1. The problem statement, all variables and given/known data
    In a 'worst-case' design scenario a 2000-kg elevator with broken cables is falling at 25m/s when it first contacts a cushioning spring at the bottom of the shaft. The spring is supposed to stop the elevator, compressing 3m as it does so. During the motion, a safety clamp applies a constant 17,000N frictional force to the elevator. As an energy consultant, you are asked to determine what the force constant of the spring should be.

    3. The attempt at a solution
    The way I set up the problem was like this:

    Work done by noncons force + GPE initial+ KE initial+ EPE initial= GPE final + KE final+ EPE final
    EPE initial is 0. I set my zero as the point when the mass is coming to rest on the spring for a slight instant before compressing the spring. I assume the 25m/s is a constant velocity...? If so, then KE inital and KE final cancel. So I am left with:
    -fd + mgy0= mgyf + .5kx^2
    thing is, then I have two unknowns, because I don't know the spring constant and I don't know what height it starts off at...If someone could point me in the right direction, I would greatly appreciate it:)
  2. jcsd
  3. Nov 23, 2008 #2

    Chi Meson

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    No, 25 m/s is not constant. It was 25 m/s at the point where the elevator first contacts the spring, then, at full compression, the speed is zero.

    The energy going into the problem is KE+GPE. The height for GPE is the 3m it will compress.

    The dissipated energy is-Fd, ans you noted, where d is the same 3m. The remaining energy is in the spring.
  4. Nov 23, 2008 #3
    Why is d 3m for -Fd? I thought the d would be the entire distance the elevator was falling? Because isn't Work done the total distance over which the friction acts?
  5. Nov 23, 2008 #4
    in the same vein, why would the h for the GPE be 3m as well? assuming that this is the initial GPE, wouldnt h be the height at which the elevator starts falling at? How do we know it starts at a height of 3m?
  6. Nov 24, 2008 #5


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    Your equation should reflect both terms.

    KE of the initial 1/2mv² = 1/2kx² + 17000 * x

    Looks like everything is known but the spring constant k, which happily is what they asked you to find.
    Last edited: Nov 24, 2008
  7. Nov 24, 2008 #6

    Chi Meson

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    The problem "starts" at the moment the elevator contacts the spring. At this point it is moving at 25 m/s. The energy of the system is assessed at this moment. Whatever happened before is irrelevant. At this moment, it has KE (due to 25 m/s) and GPE (due to 3m above final position).
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