If it was possible to attach a carbon nanotube rope between the Earth and the Moon, how could it be used to collect energy? Assume that someone made a 400,000+ km long rope and managed to attach it to the Moon. The rope is strong, but not unrealistically strong (carbon nanotube?). Now, Earth and Moon have kinetic and potential energy.Hhow would you use the rope to collect this energy for human use, up to the point when the Moon will be very close and the Earth will tidal lock to it? And how much power and total energy it would theoretically be possible to harvest in such way? What would be the most noticeable short-term and long-term effects on Earth? Would the Earth get tidally locked to the Moon much before the Moon comes really close (about the geostationary orbit) to the Earth?
Edit: as suggested in one of the comments, the rope should be really strong and light in order not to break just because of its own weight. Any conventional material would probably break, though there are indications CTNs (carbon nanotubes) might be fit for the job ( https://en.wikipedia.org/wiki/Space_elevator ). However, unlike a Space Elevator here the rope would not necessarily stand vertical to the earth surface. If the rope is instead kept horizontal (for example keeping its end around a point on Earth where the Moon appears at the horizon), would then the stress on the rope's material be significantly less than the Space Elevator case?
 A: Make a large wind turbine with wings and pull it gliding around the Earth through the atmosphere (somewhere above the weather stuff but low enough to get some air there).
There are something like 40 megameters around the Earth and the spins around every day (it takes 24h50m to make a rotation with respect to Moon). If my calculations are correct, the rope will be pulled at around 17 m/s 447m/s at the surface of Earth.
I'll include the numbers, maybe they will be useful for someone. Distance around the Earth
$$
d = 2\pi R = 2 \pi \cdot 6371km = 40.0Mm
$$
Average speed the Earth-end of the rope should travel at:
$$
v = \frac{d}{T} = \frac{40\cdot 10^{6}}{1\ \rm{ day\ w.r.t. Moon}} = \frac{40}{(24\cdot60+50)\cdot60}\cdot 10^{6} = 447m/s
$$
A: It is probably more likely that somehow changing the orbit of the moon would actually cost energy, as you are changing the direction of something already in motion.  Even if we ignore the cost of building and attaching this metal rope. 
Think of it as though the Moon and Earth traveled in a straight line rather than in circular orbit. How do you harvest the energy of something with a higher relative velocity? If you had a way, the most energy you could get is using the following equation for Kenetic Energy, where v is the relative speed of the Moon to Earth. 
E = 0.5mv^2
Then you could convert the entire mass of the Moon to energy:
E = mc^2
