posted by Taylor on .
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.
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.