Chapter 9, Problem 79GP

In a mountain-climbing technique called the Tyrolean traverse,” a rope is anchored on both ends (to rocks or strong trees) across a deep chasm, and then a climber traverses the rope while attached by a sling as in Fig. 9-91.This technique generates tremendous forces in the rope and anchors, so a basic understanding of physics is crucial for safety A typical climbing rope can undergo a tension force of perhaps 29 KN before breaking, and a “safety factor” of 10 is usually recommended The length of rope used in the Tyrolean traverse must allow for some “sag” to remain in the recommended safety range Consider a 75-kg climber at the center of a Tyrolean traverse, spanning a 25-m chasm (a) To be within its recommended safety range, what minimum distance x must the rope sag? (b) If the Tyrolean traverse is set up incorrectly so that the rope sags by only one-fourth the distance found in (a), determine the tension in the rope Ignore stretching of the rope. Will the rope break?

Figure 9-91