[BuffaloJack]

what is the length of a steel cable that can hang vertically without breaking under its own weight
breaking strength for steel is 720MPa and density of steel 7800 kg/m^3
Call the cross sectional area of the wire A and the maximum length without breaking L.
density = mass / volume
leads to
mass = density * volume
Length at breaking L
volume=A*L
Weight of cable W=density*A*L*g
The volume of the maximum length of this wire is just (A * L)
we know the density so its mass will be:
mass = 7.8*10^3 * A*L
Strength S=density*A*L*g / A
areas drop out
S=density*L*g
L = S / (g*density)
L=720MPa/(9.81 m/s^2 * 7800 kg/m^3)
L=9413 m

[namvolunteer]

Brilliant!

[DUMBGRUNT]

I suspect this was a couple of guys having fun at a long lunch,friends liked it so they upgraded from the napkin drawings.
A though problem.
Nothing more.

https://www.technologyreview.com/s/614276/a-space-elevator-is-possible-with-todays-technology-researchers-say-we-just-need-to-dangle/