- #1
Fibo112
- 149
- 3
Homework Statement
The following task causes me problems:
The science fiction writer R.A. Heinlein describes in the novel "Friday" a satellite ("space elevator"), which consists of a long rope, placed directly above the equator. The rope is aligned along the Earth's radius. It moves so that it appears to the Earth observer that it is suspended at a fixed point above the equator. The lower end of the rope hangs just above the Earth's surface. Suppose that the linear mass density of the rope ρl is constant. The radius of the Earth is R 6370 km and the Earth mass ME = 5.97 x 1024 kg.
a) How long should such a rope be?
Homework Equations
Fg=Gm1m2/r^2, Fcentripedal=mv^2/r
The Attempt at a Solution
My only idea would be to set the Zentripedal force equal to the gravitational force. Then I would have a length of 144'000km. Would the rope actually behave as described? But then the tension in the rope would have to be exactly right at every point. What do you think? How would you solve the task?