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 Fig. 12–102. 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 29 kN before breaking, and a “safely 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 75-kg climber at the center of a Tyrolean traverse, spanning a 25-m chasm. ( a ) To be within its recommended safety range, what minimum distance x must the rope sag? ( b ) If the Tyrolean traverse is set up incorrectly so that the rope sags by only one-fourth the distance found in ( a ), determine the tension in the rope. Will the rope break? FIGURE 12–102 Problem 96.
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 Fig. 12–102. 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 29 kN before breaking, and a “safely 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 75-kg climber at the center of a Tyrolean traverse, spanning a 25-m chasm. ( a ) To be within its recommended safety range, what minimum distance x must the rope sag? ( b ) If the Tyrolean traverse is set up incorrectly so that the rope sags by only one-fourth the distance found in ( a ), determine the tension in the rope. Will the rope break? FIGURE 12–102 Problem 96.
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 Fig. 12–102. 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 29 kN before breaking, and a “safely 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 75-kg climber at the center of a Tyrolean traverse, spanning a 25-m chasm. (a) To be within its recommended safety range, what minimum distance x must the rope sag? (b) If the Tyrolean traverse is set up incorrectly so that the rope sags by only one-fourth the distance found in (a), determine the tension in the rope. Will the rope break?
In a mountain-climbing technique called the "Tyrolean tra-
verse," 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 Fig. 9–91. 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 29 kN
before breaking, and a “safety factor" of 10 is usually recom-
mended. The length of rope used in the Tyrolean traverse
must allow for some “sag" to remain in the recommended
safety range. Consider a 75-kg climber at the center of a
Tyrolean traverse, spanning a 25-m chasm. (a) To be within its
recommended safety range, what minimum distance x must
the rope sag? (b) If the Tyrolean traverse is set up incorrectly
so that the rope sags by only one-fourth the distance found in
(a), determine the tension in the rope. Ignore stretching of
the rope. Will the rope break?
25 m…
(II) An iron bolt is used to connect two iron plates together. The bolt must withstand shear forces up to about 3300 N. Calculate the minimum diameter for the bolt, based on a safety factor of 7.0.
(II) A 15-cm-long tendon was found to stretch 3.7 mm bya force of 13.4 N. The tendon was approximately roundwith an average diameter of 8.5 mm. Calculate Young’smodulus of this tendon.
Chapter 12 Solutions
Physics for Scientists & Engineers with Modern Physics [With Access Code]
Sears And Zemansky's University Physics With Modern Physics
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