At the instant I slip, the rope starts to stretch-but without at first exerting much stopping force on me. So for a fraction of a second I am falling and gaining speed. Then, as the rope stretches more and you hang on without letting any rope slip through your hand, the stopping force slows me down as it increases to some maximum-as much as double my weight if I am on vertical rock-and then goes back down to just my weight as I come to a stop and hang there motionless, held up by the rope. This all takes place in a second or less.

Suppose that by merely gripping the rope, you can resist a pull of about 40 pounds of force before the rope starts to slip through your grasp. But you've run the rope around your hips, adding the friction of the rope against your body. You will therefore be able to resist a pull of about 250 to 350 pounds of force. You may not actually exert that much force when I fall-only what's necessary to stop me without the rope slipping.Suppose I climb up faster than you can take in rope.

With slack in the rope, if I fall, I will gain more speed before the rope begins to stop me, and the peak force, assuming you don't let the rope slip, will be greater than before.What if the force becomes too great and the rope starts to slip through your hand?

Does this mean I will fall to the bottom of the climb while you lose a lot of skin off your hand?

No. A surprising but important fact is that, even as the rope runs through your hand, as long as the stopping force that you are exerting by continuing to grip the rope is greater than my weight, I will eventually slow to a stop and end up hanging motionless as before. Though not necessarily a disaster, this may not be an ideal result either. The farther I fall, the more risk there is of hitting something and being injured-and even if I'm not injured, I'll get more excitement than I wanted.