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Highest point a mass can be dropped from without exceeding ultimate force of wire

  1. Sep 13, 2010 #1
    1. The problem statement, all variables and given/known data
    An object of mass .5 kg is hung from the end of a steel wire 2m in length and .5mm in diameter. The mass is lifted a distance h and then dropped (creating a 'jerk') What is the largest value of h if you don't want the wire to break?
    Ultimate Strength: 1.1E9 N/m^2
    Young's Modulus: 2E11n N/m^2
    g=9.8 m/s^2
    A=Pi(r^2) = Pi(0.0625) mm^2 = Pi(6.25E-5) m^2

    2. Relevant equations
    F = -kx = ma
    h=mgLo/AY
    k= -AY/Lo

    3. The attempt at a solution
    I know the ultimate strength may not be exceed w/o wire breaking. So
    Force(down) < or = 2E11 N/m^2

    But, I am unsure of what the force(down) would be with the given information.
    Force(down)=mgh ?
    = (AY/Lo) x , where x=2h ?
     
  2. jcsd
  3. Sep 13, 2010 #2

    diazona

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    Homework Helper

    When the object reaches the bottom of the wire (2m below the hang point), it's going to start stretching the wire. You can think of the stretching wire as a spring. How far it stretches depends on how fast the object is moving when the wire starts to stretch, and that in turn depends on how high the object was dropped from.

    So one way to solve this problem would be to consider it in two parts: first figure out how fast the object is going when it reaches the end of the wire, then figure out from that how far the spring stretches. (Alternatively, it is possible to solve the problem without explicitly finding the speed of the object)

    If you've ever solved a problem that involved calculating the lowest height reached by a bungee jumper, you'll find that this is nearly the same thing.
     
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