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? Safari File Edit View History Bookmarks Window Help webassign.net ? Physics question | Chegg.com CH 19 11. 4/6 points Previous Answers SerPSET9 19.P.022 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 3.90 10-6 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 38.0°C My Notes Ask Your Teacher (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 10-5oc-1.) 411.84 108 N/m2. At what temperature would (b) Permanent deformation occurs if the stress in the steel exceeds its elastic limit of 3.00 the wire reach its elastic limit? 174.36 Your response differs from the correct answer by more than 10%. Double check your calculations.°C (c) Explain how your answers to parts (a) and (b) would change if the Golden Gate Bridge were twice as long as we can see both answers do not depend on length of wire so the answer will not change even if length is doubled Score: 2 out of 2 Comment:

Explanation / Answer

We know that Young's modulus is given by:

Y = Stress/Strain

Strain = dL/L0

dL = L0*alpha*dT

Using above values

Y = stress/(L0*alpha*dT/L0)

Y = Stress/(alpha*dT)

dT = Stress/(Y*alpha)

alpha = linear thermal expansion coefficient for steel = 11*10^-6 /C

Y = 2*10^11 N/m^2

Stress = 3*10^8 N/m^2

So,

dT = 3*10^8/(2*10^11*11*10^-6)

dT = 136.36 = Tf - Ti

Now to increase the stress temperature must decrease to, (here final temperature is 38 C)

Tf - Ti = 136.36

Ti = Tf - 136.36

Ti = 38 - 136.36 = -98.36 C

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