Falling objects

  1. JBP

    JBP 3

    Hi there,

    I've spent some hours on trying to make a simulator (in Excel) for calculating the forces involved in a climbers fall.

    I've found the following link (http://toad.stack.nl/~stilgar/calc.php) but can't figure it out - Maybe because my grades back in high-school were terrible :uhh:

    Could anyone please help me making the formulas?

    The following variables will be available:

    - Lenght of rope (in meters)
    - Fall factor / Height of fall
    - Dynamics of rope (in percent @ 80kg)
    - Weight of climber (in kg)

    Thanks in advance
     
  2. jcsd
  3. You weren't clear as to what you were asking. I assume that you're asking what force a rope would exert on a person when the person, who has the rope tied around his waist falls and is prevented from falling all the way to the ground by the rope. That force is F = dp/dt where p is the momentum of the person who is falling and dt is the time inteval during which the person's momenum changes by the amount dp. I also don't know what you mean by "Dynamics of rope (in percent @ 80kg)". you need to know the properties of the rope such as Young's modulus for the rope.

    Pete
     
  4. JBP

    JBP 3

    Hi Pete,

    When I look at Your answer I can see that what I'm missing is the Young's modulus for the rope.
    So lets start with that. I've found this formula:

    E = (L*F)/(l*A)

    E: Young's Modulus
    L: Length of the rope
    l: Change in lenght
    F: Force
    A: Area of the rope

    I donĀ“t know what units to use, please correct me in this example:

    L = 100 meters
    l = 7 meters (dynamics = 7%)
    F = 784,8 newtons (80 kg x 9.81)
    A = 314,29 mm^2 (10mm x 10mm x pi)
    E = 35,67 (100*784,8 / 7*314,29)
     
  5. doesnt the rope act as a spring, it decelerates the faller. Dont you need the ropes spring coefficient?
     
  6. JBP

    JBP 3

    Nenad,

    I see Your point - do You know how to find/calculate the spring effect?
     
  7. well, you need to know the spring constant (k). This is in N/m. Then you can use the equation E = 1/2kx^2, where k is the spring constant, and x is the amount of strech from the resting possition of the rope. The force exerted on the object being stopped by the rope would be F = -kx. You can play around with there equations and find the right constant so the g-force on the person is not too high.
     
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