Two weekends ago I went out sport climbing at Thatcher Park in Albany, NY. Unlike top rope climbing, where the rope is always taught against you so even if you fell off the wall you would be caught immediately by your belayer, sport climbing involves you clipping into the wall as you make your way up the wall. Top rope climbing the rope goes all the way up to the top of the climb and then back down, whereas sport climbing your bing the rope up from the bottom of the climb.This means that while you are climbing to your next clipping point (known as a bolt) there is slack that is paid out into the system.
So as I was climbing up to the top, the first thing that went through my mind was: if I cant do this, whats is the first thing that is going to break? Would it be me? My rope? My Carabiner? My harness? Wow. Many more things that could break than I realized. Well. In order to find out I decided to do some quick thinking physics while I was in the middle to decide whether or not I should have fallen from that height.
My known mass was about 72kg, and on this specific climb there were about 6 bolts spaced out over 60 feet. So my best guess was that there was about a ten foot gap between one bolt and the next, and I was about to be clipping in. So after doing some quick conversion in my head, I realized that my height was 3.0m. Therefore, the amount of slack that was in my rope was 6.0m, but since I like to have extra slack in my rope because I am ~nuts~ I had an extra meter, so I had 7.0m of total falling to do -- if I were to fall. So. We could find my final velocity via the change in energy. My initial potential energy was m*g*h, however my mass cancels out with the kinetic energy equation 1/2*m*v^2, so as a result my final velocity when I reached the length of the slack in the rope would be 12m/s. Wow. thats fast. We could then find what the force of the fall would be on my rope, my carabiner, and my harness, along with me, with the impulse equation, where force=p/t, and I would stop in about 0.01 seconds, if I were using a static rope. Therefore the force that I would experience would be on the scale of 84,000N! Wow. I would most definitely be dead, since the carabiner I was falling on could hold 22,000N of force, and the rope cant hold even close to that, and my harness couldn't have held that either since it can hold only 16,000N o force. My body definitely can't hold that much. My legs may have stayed on the wall and my torso would probably be down on the ground.
That made me pretty scared to fall. Like really scared. But then I realized that my rope was not static! It was dynamic! So instead of stopping over .01 seconds, I am really stopping in 1-2 seconds. Because of that I would only experience between 840N-420N, safely in the range where i wouldnt break anything.
So I realized that I could fall without being worried. And so, I continued climbing without falling getting to the top and looking out over Albany.
video of someone taking a whipper: https://www.youtube.com/watch?v=_0XuntyZg74
The moment when I did math-->
The moment that I looked out over Albany-->