Question

If you tethered a space station to the earth by a long cable, you could get to space in an elevator that rides up the cable much simpler and cheaper than riding to space on a rocket. There's one big problem, however: There is no way to create a cable that is long enough. The cable would need to reach 36,000 km upward, to the height where a satellite orbits at the same speed as the earth rotates; a cable this long made of ordinary materials couldn't even support its own weight. Consider a steel cable suspended from a point high above the earth. The stress in the cable is highest at the top; it must support the weight of cable below it.
What is the greatest length the cable could have without failing?

Answer 1

Answer:

$l=12916.5m$

Explanation:

Distance $d=3600km$

Since

Density of steel $\rho=7900kg/m^3$

Stress of steel $\mu= 1*10^9$

Generally the equation for Stress on Cable is mathematically given by

$S=\frac{F}{A}$

$S=\frac{\rho Alg}{A}$

Therefore

$l=\frac{s}{\rhog}$

$l=\frac{ 1*10^9}{7900kg/m^3*9.8}$

$l=12916.5m$