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?
(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.
17-45. The drop gate at the end of the trailer has a mass
of 1.25 Mg and mass center at G. If it is supported by the
cable AB and hinge at C, determine the tension in the cable
when the truck begins to accelerate at 5 m/s?. Also, what
are the horizontal and vertical components of reaction at
the hinge C?
30
1.5 m
45°
The figure shows an overhead view of a 0.025 kg lemon half and two of the three horizontal forces that act on it as it is on a frictionless
table. Force F has a magnitude of 7 N and is at 0, = 29°. Force F, has a magnitude of 9 N and is at e, = 26". In unit-vector
(12 – 16) m/s, and (c) has the
notation, what is the third force if the lemon half (a) is stationary, (b) has the constant velocity
= (14i – 13fj) m/s², where t is time?
(a) Number
i+
jUnits
(b) Number
i+
jUnits
(c) Number
i+
jUnits
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