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The Golden Gate Bridge in San Francisco has a main span of length 1.28 km, one of the longest in the world. Imagine that a steel wire with this length and a cross-sectional area of 3.40 x 10-6 m2 is laid on the bridge deck with its ends attached to the towers of the bridge, on a summer day when the temperature of the wire is 43.0°C. (a) When winter arrives, the towers stay the same distance apart and the bridge deck keeps the same shape as its expansion joints open. When the temperature drops to -10.0°C, what is the tension in the wire? Take Young's modulus for steel to be 20.0 x 1010 N/m2. (Assume the coefficient of thermal expansion of steel is 11 x 10-6 (°C)-1.) Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. N (b). Permanent deformation occurs if the stress in the steel exceeds its elastic limit of 3.00 x 108 N/m2. At what temperature would the wire reach its elastic limit?

The Golden Gate Bridge in San Francisco has a main span of length 1.28 km, one of the longest in the world. Imagine that a steel wire with this length and a cross-sectional area of 3.40 x 10-6 m2 is laid on the bridge deck with its ends attached to the towers of the bridge, on a summer day when the temperature of the wire is 43.0°C. (a) When winter arrives, the towers stay the same distance apart and the bridge deck keeps the same shape as its expansion joints open. When the temperature drops to -10.0°C, what is the tension in the wire? Take Young's modulus for steel to be 20.0 x 1010 N/m2. (Assume the coefficient of thermal expansion of steel is 11 x 10-6 (°C)-1.) Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. N (b). Permanent deformation occurs if the stress in the steel exceeds its elastic limit of 3.00 x 108 N/m2. At what temperature would the wire reach its elastic limit?

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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The text describes a problem regarding the thermal expansion and tension of a steel wire laid on the Golden Gate Bridge. The main span of the bridge is 1.28 km, and the wire has a cross-sectional area of \(3.40 \times 10^{-6} \, \text{m}^2\). The scenario considers the bridge on a summer day when the temperature is \(43.0^\circ\text{C}\). **Problem (a):** - The wire must sustain the same length in winter when the temperature drops to \(-10.0^\circ\text{C}\). - The task is to find the tension in the wire under these conditions. - The Young's modulus for steel is \(20.0 \times 10^{10} \, \text{N/m}^2\). - The coefficient of thermal expansion for steel is \(11 \times 10^{-6} \, (\circ\text{C})^{-1}\). - A response box indicates a placeholder for the tension answer: (N) **Feedback:** - The text notes that the response given "differs significantly from the correct answer," advising to rework the solution. **Problem (b):** - Permanent deformation occurs if the stress in the steel exceeds its elastic limit of \(3.00 \times 10^{8} \, \text{N/m}^2\). - The question is to determine the temperature at which the wire reaches its elastic limit. A boxed area shows a place to enter a numerical answer for part (b), and the temperature in question is unknown.
Transcribed Image Text:The text describes a problem regarding the thermal expansion and tension of a steel wire laid on the Golden Gate Bridge. The main span of the bridge is 1.28 km, and the wire has a cross-sectional area of \(3.40 \times 10^{-6} \, \text{m}^2\). The scenario considers the bridge on a summer day when the temperature is \(43.0^\circ\text{C}\). **Problem (a):** - The wire must sustain the same length in winter when the temperature drops to \(-10.0^\circ\text{C}\). - The task is to find the tension in the wire under these conditions. - The Young's modulus for steel is \(20.0 \times 10^{10} \, \text{N/m}^2\). - The coefficient of thermal expansion for steel is \(11 \times 10^{-6} \, (\circ\text{C})^{-1}\). - A response box indicates a placeholder for the tension answer: (N) **Feedback:** - The text notes that the response given "differs significantly from the correct answer," advising to rework the solution. **Problem (b):** - Permanent deformation occurs if the stress in the steel exceeds its elastic limit of \(3.00 \times 10^{8} \, \text{N/m}^2\). - The question is to determine the temperature at which the wire reaches its elastic limit. A boxed area shows a place to enter a numerical answer for part (b), and the temperature in question is unknown.
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