Question

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 the figure (Figure 1). 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 27 kN before breaking, and a "safety factor" of 12 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. To be within its recommended safety range, what minimum distance x must the rope sag?

Express your answer using two significant figures.

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.

Express your answer using two significant figures.

Will the rope break?

Answer 1