What would the length of wire have to be increased so it was everywhere 1 meter?

Mathematics
Tutor: None Selected Time limit: 1 Day

Suppso that a wire is stretched tightly around the Earth along the equator. (Assume that the Earth is a circle along the equator with a circumference of 40,000 km) Approximately how much would the length of the wire have to be increased so that it was everywhere 1 meter above the surface?

Apr 29th, 2015

Length of wire = 40000 km

Circumference of circle = 2πr

Circumference of circle = Length of wire

2πr = 40000

r = 40000/2π

r = 40000/(2*3.14)

r = 6369.427 km


The wire has to be 1 m above the surface.

1 m = 10^-3 km = 0.001 km

So new radius, R = r + 1 = 6369.427 + 0.001 = 6369.428 km


Length of wire required = 2πR = 2*3.14*6369.428 = 40000.00784 km


Increase in length = 40000.00784 - 40000 = 0.00784 km = 0.00784 * 1000 m = 7.84 m


So the wire has to be increased by 7.84 m .

 

Apr 29th, 2015

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