Stretchable ropes are used to safely arrest the fall of rock climbers. Suppose one end of a rope with unstretched length l is anchored to a cliff and a climber of mass m is attached to the other end. When the climber is a height l above the anchor point, he slips and falls under the influence of gravity for a distance 2l, after which the rope becomes taut and stretches a distance as it stops the climber (see the figure). Assume a stretchy rope behaves as a spring with spring constant .
Applying the work-energy principle, find x.
Assuming = 86 kg , = 8.6 m and = 870 N/m , determine x/l (the fractional stretch of the rope) at the moment the climbers fall has been stopped.
Assuming = 86 kg , = 8.6 m and = 870 N/m , determine kx/mg (the force that the rope exerts on the climber compared to his own weight) at the moment the climbers fall has been stopped.