- #1
ConstableZiM
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Homework Statement
Please read the WHOLE post before replying, because I don't want the answer, but how to obtain one of the equations.
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 (Intro 1 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 28 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 72-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?
Homework Equations
[tex]
2Tsin\vartheta-mg = \Sigma
[/tex]F
The Attempt at a Solution
I don't have a problem with the question itself, I have a problem with understanding one of the equations, 2TSin(Theta) = mg... Why is the TSin(Theta) multiplied by 2? I can't conceptually comprehend that... if the line can take only 2900 Newtons, then multiplying it by two means we are putting a load of 4800 Newtons on the whole line?...
The answer is 1.5 meters