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 . 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 75kg climber at the center of a Tyrolean traverse, spanning a 25m chasm. To be within its recommended safety range, what minimum distance x in meters must the rope sag?


If the Tyrolean traverse is set up incorrectly so that the rope sags by only one-fourth the distance found in Part A, determine the tension in the rope in Newtons.


Will the rope break?


Please, someone help me understand this problem.

Answer 1

Take the angle of sag. if Then x/12.5 =tan Sagangle.

But look at force. The downward force is 1/2 75g (each side holds half the weight)
so 37.5g/Tension=Sin Sagangle

But the tension cannot be greater than 27kN/12
so you can then determine the sag angle. Put that back in to the tangent equation, and find x.

Answer 2

Physics 201