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.
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
4.00 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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