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 4.00 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 35.0°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. (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? (c) Explain how your answers to (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 4.00 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 35.0°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. (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? (c) Explain how your answers to (a) and (b) would change if the Golden Gate Bridge were twice as long.

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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Concept explainers

Energy transfer

The flow of energy from one region to another region is referred to as energy transfer. Since energy is quantitative; it must be transferred to a body or a material to work or to heat the system.

Molar Specific Heat

Heat capacity is the amount of heat energy absorbed or released by a chemical substance per the change in temperature of that substance. The change in heat is also called enthalpy. The SI unit of heat capacity is Joules per Kelvin, which is (J K-1)

Thermal Properties of Matter

Thermal energy is described as one of the form of heat energy which flows from one body of higher temperature to the other with the lower temperature when these two bodies are placed in contact to each other. Heat is described as the form of energy which is transferred between the two systems or in between the systems and their surrounding by the virtue of difference in temperature. Calorimetry is that branch of science which helps in measuring the changes which are taking place in the heat energy of a given body.

Question

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
4.00 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 35.0°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. (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? (c) Explain how your answers to (a) and (b)
would change if the Golden Gate Bridge were twice as long.

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Step 4: Determine the tension and temperature when length is twice

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