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Homework Help: Elevator and spring problem

  1. Feb 23, 2005 #1
    Problem: An elevator cable breaks when a 754 kg elevator is 20.8 m above the top of a huge spring (k = 6.93×104 N/m) at the bottom of the shaft. Calculate the amount the spring compresses (note that here work is done by both the spring and gravity).

    i calculated the speed of the elevator just before it hits the spring which is
    Vinitial = 20.19 m/s

    the equation i used was (1/2)mV^2-(1/2)mVinitial^2= -(1/2)kx^2 + mgx
    x is the distance the spring was compressed
    and at distance x the current velocity = 0 because it is not moving at all anymore
    therefore the equation becomes -(1/2)mVinitial^2= -(1/2)kx^2 + mgx
    i plugged in all the numbers and solved by the quadratic equation.. but still came up with the wrong answer...
    can someone help?
     
  2. jcsd
  3. Feb 23, 2005 #2
    use conservation of energy... before the cable breaks, the elevator is steady, with a potential energy mgh... after the elevator hit the spring and compressed it, the velocity is also zero, potential energy become 1/2kx^2

    mgh=1/2kx^2
    x=sqrt(2mgh/k)
     
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