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

`l=12916.5m`

Step-by-step 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=(F)/(A)`

`S=(\rho Alg)/(A)`

Therefore

`l=(s)/(\rhog)`

`l=( 1*10^9)/(7900kg/m^3*9.8)`

`l=12916.5m`