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?
a vertical uniform beam of length Lthat is hinged at its lower end.A horizontal force F is applied to the beam at distance y from the lower end. The beam remainsvertical because of a cable attached at the upper end, at angle uwith the horizontal. gives the tension T in the cableas a function of the position of the applied force given as a fractiony/L of the beam length.The scale of the T axis is set by Ts= 600 N.Figure 12-49c gives the magnitude Fh of the horizontal force on thebeam from the hinge, also as a function of y/L. Evaluate (a) angle uand (b) the magnitude of .
In Fig. 12-31 show that, if the ball is to swing completely around the fixed peg, then d > 3L/5. (Hint: The ball must be moving at the top of its swing; otherwise the string will collapse.)
An elevator is suspended by a heavy steel cable. If this cable were replaced by two steel cables each having the same length as the original one but half its diameter, how would the amount of stretch in the pair of thin cables (st) compare with that of the original cable (so)?
Chapter 12 Solutions
Physics for Scientists and Engineers, Vol 1 (Chapters 1-20)
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