The golden gate bridge in San Francisco has a main span of length 1.28km, one of

Question

The golden gate bridge in San Francisco has a main span of length 1.28km, one of the longest in the world. Imagine that a steel wire with this length, and a cross sectional area A=4.00 x 10^-6m2 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 degrees C. When winter arrives, the temperature drops to -10.0 degrees C. (a) what would be the change in the length of a wire with this length? (b) If the wire were not allowed to contract, what would be the tension, and the tension per meter^2? How does this compare to the elastic limit of steel?

Explanation / Answer

a) change in length = l**

l = 1.28 km, = 12*10^(-6) /0C , = 35-(-10) = 450 C

so l = 0.0576 m

b) to find tension we have to find out stress produced.

Young's modulus Y = stress/strain.

strain = l/l = 0.0576/1.28*10^3 = 4.5*10^(-5)

Y of steel = 1.9*10^(11) N/m^2

stress = 8.55*10^6 N/m^2

tension = stress * area = 8.55*10^6*4*10^(-6) = 34.2 N

tension per m^2 = stress *1 = 8.55*10^6 N

elastic limit of steel is around 400 M N/m^2

so the stress is around 0.021 times elastic limit

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