A cable hanging vertically under gravity must support its weight, w = mg, where m is the mass of the cable and g = 9.8 m/s2 is the acceleration due to gravity. If the cable has a cross sectional area A, length ℓ, and density ?, then the weight of the cable is w = ?Aℓg. The force per unit area at the top of the cable is then T = ?ℓg. Steel has a tensile strength 2 GPa and a density 7.8 x 103 kg/m. If the force per unit area at the top of a hanging cable exceeds the tensile strength, it will snap. Given this, estimate the maximum length of a hanging steel cable.
A cable hanging vertically under gravity must support its weight, w = mg, where m is the mass of the cable and g = 9.8 m/s2 is the acceleration due to gravity. If the cable has a cross sectional area A, length ℓ, and density ?, then the weight of the cable is w = ?Aℓg. The force per unit area at the top of the cable is then T = ?ℓg. Steel has a tensile strength 2 GPa and a density 7.8 x 103 kg/m. If the force per unit area at the top of a hanging cable exceeds the tensile strength, it will snap. Given this, estimate the maximum length of a hanging steel cable.
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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A cable hanging vertically under gravity must support its weight, w = mg, where m is the mass of the cable and g = 9.8 m/s2 is the acceleration due to gravity. If the cable has a cross sectional area A, length ℓ, and density ?, then the weight of the cable is w = ?Aℓg. The force per unit area at the top of the cable is then T = ?ℓg.
Steel has a tensile strength 2 GPa and a density 7.8 x 103 kg/m. If the force per unit area at the top of a hanging cable exceeds the tensile strength, it will snap. Given this, estimate the maximum length of a hanging steel cable.
Give your answer in kilometres to one significant figure.
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