Falling Objects: Calculating Climbers' Force of Impact

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In summary: Thanks for asking!In summary, Pete has spent some time trying to create a simulator that calculates the forces involved in a climber's fall. The variables available for the simulation are length of the rope, fall factor, height of the fall, dynamics of the rope (percentage), and weight of the climber. Pete was not able to find the formulas for creating the simulator online, so he asked for help. The variables that need to be known for the simulation are Young's modulus of the rope, spring constant, and the amount of stretch in the rope. Pete was able to calculate the forces the rope would exert on a person when they fall using the equation E = 1/2kx^2. He also mentioned
  • #1
JBP
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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 [Broken]) 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
 
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  • #2
JBP said:
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 [Broken]) 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

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
 
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  • #3
pmb_phy said:
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

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 let's 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)
 
  • #4
doesnt the rope act as a spring, it decelerates the faller. Dont you need the ropes spring coefficient?
 
  • #5
Nenad said:
doesnt the rope act as a spring, it decelerates the faller. Dont you need the ropes spring coefficient?

Nenad,

I see Your point - do You know how to find/calculate the spring effect?
 
  • #6
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.
 

What is the force of impact for a falling object?

The force of impact for a falling object can be calculated using the formula F = m x a, where F is the force of impact, m is the mass of the object, and a is the acceleration due to gravity (9.8 m/s²). This means that the force of impact will increase as the mass and speed of the object increases.

How does the height of the fall affect the force of impact?

The height of the fall directly affects the force of impact. As the height increases, the object will gain more speed due to the acceleration of gravity, resulting in a higher force of impact upon impact with the ground.

What is the relationship between force of impact and surface area?

The force of impact and surface area have an inverse relationship. This means that as the surface area of the falling object increases, the force of impact will decrease. This is because a larger surface area allows for more air resistance, slowing down the object and reducing the force of impact.

How can we reduce the force of impact for a falling object?

There are a few ways to reduce the force of impact for a falling object. One way is to increase the surface area of the object, as mentioned before. Another way is to decrease the mass of the object, which will result in a lower force of impact. Additionally, cushioning materials or structures can also help absorb some of the force upon impact.

What are some real-life applications of calculating force of impact for falling objects?

Calculating force of impact for falling objects is important in many real-life situations. For example, engineers use this calculation to design safety features for amusement park rides, and safety equipment for sports. It is also used in the construction of buildings and bridges to ensure they can withstand potential impact forces from falling objects. In the medical field, calculating force of impact is crucial for understanding the severity of injuries from falls and other accidents.

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