Paliadon said:
Wow, so much to digest. lol I thought there was going to be a lot of stuff. Okay, so for arguments sake, let's say the rope is a static line with no stretch (sudden stop) what sort of force would be applied then? The second part to it would be what if that rope had the ability to stretch 18%?
Your safety gear probably has specifications how much it can take.
I have to admit that I have never taken a look at such specifications, but perhaps you have those specifications?
Either way, I'm going to make an educated guess.
The safety gear would not so much take a force, but an impulse.
The impulse taken, is the difference between the momentum of your body before and after your fall.
When you fall a certain distance, your body has a certain speed.
Your momentum is the mass of your body multiplied by your speed.
In this case the momentum is given by the formula:
p = m v = m \sqrt(20 h)
where p is the momentum, m is the mass of your body, v is the speed of your body, and h is the height from which you are falling.
In your example we would have:
p = 95 kg \cdot \sqrt( 20 \frac m {s^2} \cdot 3 m ) = 736 \frac {kg \cdot m} {s}
Your safety gear would be designed to take this momentum and reduce it to zero.
To do this it exerts a force over a period of time.
The longer the time is to do this, the less force is needed to break your fall.
This is the heart of all safety gear, including seat belts, airbags and such.
They are designed to spread the time of impact over as large a period of time as possible.
The relation is given by the formula:
F_{average} = \frac p t
where F is the exerted force, p is again the momentum of your body, and t is the time during which your fall is broken.
If this time is for instance 1 second, this would mean the average force on your body is 736 N, which corresponds to the weight of a mass of 73.6 kg.
Since the real weight of your body is also carried, the total average force would be 950 N + 736 N = 1686 N, or the equivalent of 168.6 kg.
To get back to your question, a static line with no stretch (sudden stop) would give you a time t that is very, very short. This would imply that the force on your body becomes very great indeed, and might break your back.
I wouldn't be able to say how much force a line that would stretch 18% would give. For that I would need more information.
The best thing would be a specification of your safety gear that says for instance how much impulse or momentum it can take, or perhaps it gives some other set of parameters?
