It's not that simple to model, but we can make a rough guess.
Let's model the cable as being made up of 100 individual pieces. Each piece starts in a motion around the Earth, but with the same angular velocity as the Earth. (So, not in orbit.) In an actual space elevator cable, there would be some tension forces between pieces. But just for simplicity, in the model each piece will only have the gravitational force from the interaction with the Earth.
Now I can just model the motion of these individual 100 parts of the cable to see what happens...
Posts: 3400 From: Belfast, United Kingdom Registered: Feb 2002
posted 01-27-2022 11:02 AM
This was described in great detail in a sci-fi novel by, I think, Ben Bova. Suffice it to say the structure caused considerable damage around equatorial lands.