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, 21m away. The rope must sag sufficiently so it won't break. Assume the rope can provide a tension force of up to 26kN before breaking, and use a "safety factor" of 10 (that is, the rope should only be required to undergo a tension force of 2.6kN ) at the center of the Tyrolean traverse.

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 .

Express your answer using two significant figures.

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. (Figure 1)

Express your answer using two significant figures.

Will the rope break?

Explanation / Answer

1.

Christian's mass is 73.0 kg
Christian's weight = 73 x 9.81 N

Christian's weight will be igual to 2 times the tension times the sin ?

So 73 X 9.81 N = 2(2.6KN)sin ?
?= sin-1 [(73X 9.81N)/(2X2.6KN)]
?=7.9157

the distance between the two trees is 21m, and the x will be the half the distance times the tan?,

So x = 21/2 m ( tan?) = 1.4599 m

2.

if x = 1.4599/4 m
tan?= (1.4599/4) / (21/2)
?= tan-1 [(1.4599/4) / (21/2)] =1.99077

Make the tension force in the rope = T

So 73 X 9.81 N = 2Tsin ?
T = (73X9.81)/(2sin ?)
T = 10307.439 N = 10.307 KN aprox.

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