Thermal expansion of steel pipe

[rwh]

The equatorial radius of the Earth is about 6370km. Consider a 40,000 km long steel pipe that forms a giant ring that fits snugly around the equator of the earth. Suppose the temp. of the pipe is increases 1 degree C. The pipe gets longer. it is also no longer snug. How high does the pipe stand off the ground?

Assume that D L = L o x 1/100,000 x D T

. I came up with .07 km. The radius of the pipe is actually 6369.42 km. When the temperature of the pipe is increased 1 degree Celsius it will expand .4 km making the pipe 40000.4 km. 40000.4 / 3.14 = 12738.98. 12738.98 / 2 = 6369.49 (radius) 6369.49- 6369.42 is .07km.

Am I right?

 

[Pseudopod]

yes, I believe so

 

[Gokul43201]

Simpler yet ... (with DT = 1)

$$\Delta L = \Delta 2 \pi R = 2 \pi \Delta R = \frac{L_o}{ 100,000} = \frac {2 \pi R}{100,000}$$

Canceling 2pi on both sides :

$$\Delta R = \frac {R}{100,000} = 0.06369 ~km$$

Your number is a little high because of round off error. If your first significant digit is in the second decimal place, you want to calculate with numbers written up to at least 3 decimal places.

 

[rwh]

Thank you!