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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 4.10 x 10 m2 is laid in a straight line on the bridge deck with its ends attached to the towers of the bridge. On a summer day the temperature of the wire is 22.0°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°C, what is the tension in the wire? (Take Young's modulus for steel to be 2.00 x 1011 N/m2, and the average linear expansion coefficient for steel to be 1.1 x 10 5°c-1.) N (b) Permanent deformation occurs if the stress in the steel exceeds its elastic limit of 3.00 x 10° N/m2. At what temperature would the wire reach its elastic limit? °C (c) Explain how your answers to parts (a) and (b) would change if the Golden Gate Bridge were twice as long.

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 4.10 x 10 m2 is laid in a straight line on the bridge deck with its ends attached to the towers of the bridge. On a summer day the temperature of the wire is 22.0°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°C, what is the tension in the wire? (Take Young's modulus for steel to be 2.00 x 1011 N/m2, and the average linear expansion coefficient for steel to be 1.1 x 10 5°c-1.) N (b) Permanent deformation occurs if the stress in the steel exceeds its elastic limit of 3.00 x 10° N/m2. At what temperature would the wire reach its elastic limit? °C (c) Explain how your answers to parts (a) and (b) would change if the Golden Gate Bridge were twice as long.

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 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 4.10 x 106 m2 is laid in a straight line on the bridge deck with its ends attached to the towers of the bridge. On a summer day the temperature of the wire is 22.0°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°C, what is the tension in the wire? (Take Young's modulus for steel to be 2.00 x 1011 N/m2, and the average linear expansion coefficient for steel to be 1.1 x 10-Soc-1.) (b) Permanent deformation occurs if the stress in the steel exceeds its elastic limit of 3.00 x 10° N/m2. At what temperature would the wire reach its elastic limit? (c) Explain how your answers to parts (a) and (b) would change if the Golden Gate Bridge were twice as long.
Transcribed Image Text: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 4.10 x 106 m2 is laid in a straight line on the bridge deck with its ends attached to the towers of the bridge. On a summer day the temperature of the wire is 22.0°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°C, what is the tension in the wire? (Take Young's modulus for steel to be 2.00 x 1011 N/m2, and the average linear expansion coefficient for steel to be 1.1 x 10-Soc-1.) (b) Permanent deformation occurs if the stress in the steel exceeds its elastic limit of 3.00 x 10° N/m2. At what temperature would the wire reach its elastic limit? (c) Explain how your answers to parts (a) and (b) would change if the Golden Gate Bridge were twice as long.
Expert Solution
Step 1

Given data,

L = Length of the bridge = 1.28 Km = 1280 m

A = Cross-sectional area of the wire = 4.10 x10-6 m2 

Ts = Temperature of the wire in summer = 22 °C

Tw = Temperature in winter = -10 °C

E = Young's modulus of the wire = 2 x1011 N/m2 

α = Linear thermal expansion = 1.1 x10-5 /°C

σelas = Stress at elastic limit = 3 x108 N/m2 

to determine:-

a) Tension in the wire when winter arrives

b) Temperature of the winter at the elastic limit

c) If the length of the wire will doubled, the effects of answer in (a) and (b)

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