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# 物理問題 (力學)

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, 25 m away. The

rope must sag sufficiently so it won't break. Assume the rope can

provide a tension force of up to 25 kN before breaking, and use a

"safety factor" of 10 (that is, the rope should only be required to

undergo a tension force of 2.5 kN) at the center of the Tyrolean

traverse.

1. Determine the distance x that the rope must sag if it is to be within

its recommended safety range and Christian's mass is 71.0 kg.

2. 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.

### 2 Answers

- 1 decade agoFavorite Answer
1.

Christian's mass is 71.0 kg

Christian's weight = 71 x 9.81 N

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

So 71 X 9.81 N = 2(2.5KN)sin θ

θ= sin-1 [(71X 9.81N)/(2X2.5KN)]

θ= 8.897175577

the distance between the two trees is 25m, and the x will be the half the distance times the tanθ,

So x = 25/2 m ( tanθ) = 1.758419689 m

2.

if x = 1.758419689/4 m

tanθ= (1.758419689/4) / (25/2)

θ= tan-1 [(1.758419689/4) / (25/2)] = 2.237967137

Make the tension force in the rope = T

So 71 X 9.81 N = 2Tsin θ

T = (71X9.81)/(2sin θ)

T = 9908.621341 N = 9.9 KN aprox.