The distance between the towers of the main span of the Golden Gate Bridge is ab

Question

The distance between the towers of the main span of the Golden Gate Bridge is about 1280 m; the sag of the cable halfway between the towers on a cold winter day is about 143 m. See Figure 8.112.

(a)   How long is the cable, assuming it has an approximately parabolic shape? (Represent the cable as a parabola of the form y = kx2 and determine k to at least 1 decimal place.) (b)   On a hot summer day the cable is about 0.05% longer, due to thermal expansion. By how much does the sag increase? Assume no movement of the towers The distance between the towers of the main span of the Golden Gate Bridge is about 1280 m; the sag of the cable halfway between the towers on a cold winter day is about 143 m. See Figure 8.112. How long is the cable, assuming it has an approximately parabolic shape? (Represent the cable as a parabola of the form y = kx2 and determine k to at least 1 decimal place.) On a hot summer day the cable is about 0.05% longer, due to thermal expansion. By how much does the sag increase? Assume no movement of the towers

Explanation / Answer

You get K by knowing that the parabola is centered in the middle of the span (where the sag is lowest). So

k= y/x^2 = 143/640^2 = 3.5x10^-4

From there use the path length equation to get the length of the cable. When you have that, multiply by 1.05 and work backwards for (b)

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