Climbing with Rope: Shock Dynamics Explained

[billyboy]

Hello
I often go climbing. When I went with a guide recently he told me that you should be especially carefull when climbing when you only have a small length of rope paid out arguing that because the rope is so short at this point it must take a large shock under a fall. Conversley, if you have a lot of rope paid out, although you will fall further the shock on the rope will be less because the rope has a larger length over which to expand. I think I have solved the problem and just wanted to see if you guys come up with the same answer. Can anyone come up with a quantitative relation to prove the above?

 

[vincentchan]

let take the case to the extreme... if you have a loooooong rope about 1mile to extent and you fall... do you think the rope could save you after falling down a mile??

something using intuition is more important than using formulas to solve problemmmmm