How high does it now stand above ground level?

Question

Consider a 40000 kilometer long long steel strip that forms a ring that fits snugly all around the Earth at the equator. Suppose people along its length breathe on it so as to raise its temperature 1 degree Celsius. How high does it now stand above ground level? How high does it now stand above ground level? (To simplify, consider only the expanded distance of the circular strips radius the distance from the earth center and apply the geometry formula that relates circumference and radius R, C equals. C=2pi R.

Answer 1

This problem is in Hewitt. The answer is 70 m for the appropriate coeff of expansion for steel.

 

Use the formula for the coefficient of expansion of a 1-d steel strip.

L = L0 + alpha L0 (Tf-Ti)

L0 = 40000 km

 

Find L

 

Then set L = 2 pi R

 

and solve for R.