Falling objects

JBP

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

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

pmb_phy

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

JBP

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 don´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)

Nenad

doesnt the rope act as a spring, it decelerates the faller. Dont you need the ropes spring coefficient?

JBP

Nenad,

I see Your point - do You know how to find/calculate the spring effect?

Nenad

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.