Christian is making a Tyrolean traverse as shown in the figure. That is, he trav

Question

Christian is making a Tyrolean traverse as shown in the figure. That is, he traverses a chasm by stringing a rope between a tree on one side of the chasm and a tree on the opposite side, 23m away. The rope must sag sufficiently so it won't break. Assume the rope can provide a tension force of up to 25kN before breaking, and use a "safety factor" of 10 (that is, the rope should only be required to undergo a tension force of 2.5kN ) at the center of the Tyrolean traverse. a)Determine the distance x that the rope must sag if it is to be within its recommended safety range and Christian's mass is 73.0kg. b)If the Tyrolean traverse is incorrectly set up so that the rope sags by only one-fourth the distance found in part A, determine the tension force in the rope

Explanation / Answer

let x be the distance the rope must sag.

Let 2 be the angle the rope makes(2<180)

then 2Tcos=mg

cos=73*9.8/(2*2500)

=81.77 degrees

x=L/2*cos=1.645m

b) x=0.411m

=Cos-1(2x/l)

=87.95

2T cos=mg

T=10000N

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