Space Elevator - Your take on an exam question

[Stevecgz]

I recently had an exam in my 2nd year dynamics course that included a question concerning a Space Elevator. My view on this question (or the answer to this question) seems to be different than my instructor's. I was hoping to get some of your thoughts so I could get a better understanding.

The question on the exam was exactly as follows:

"The 'Space Elevator'. Should you decide to poke around www.howstuffworks.com, you will eventually stumble across this masterpiece. The basic idea is to build a very large nanotube steel structure several kilometers straight up from the surface of the earth, and use conventional propulsion to accelerate the craft along the rail, while utilizing the rotation of the Earth to impart a rotational acceleration on the craft as well, thus increasing the total amount of available acceleration. Assuming that convention propellant moves it along the rail according to the equation r(t) = 3t^2 + 40*10^6 m, and that the Earth completes one rotation in 24 hours, determine the total acceleration on the craft imparted by the propulsion system after 60 seconds."


Thanks,
Steven

 

[OlderDan]

You can write the position of the craft in cartesian coordinates (messy) or in polar coordinates (much easier) and take the derivatives to find velocity and acceleration. But you have to be careful. In polar coordinates the unit vectors in the radial direction and the tangential direction are functions of time.