3. A large celebratory ride is being planned to open in the year 2100, on the 50

Question

3. A large celebratory ride is being planned to open in the year 2100, on the 50th anniversary of establishing the Moon Colony. The ride will give the visitors an extended view of the Colony from the capsule while it soars in orbit overhead. One of the early sketches shows the cylindrical capsule in which the visitors wi ride. The capsule leaves the platform, rolls without slipping down a slope, and enters a low altitude circular lunar orbit at the bottom. The eventual capture and return of the capsule is yet in the planning stages. The exact mass distribution of the outer capsule is as yet a matter of design. For the following questions, assume the moment of inertia of the capsule is I K. I where k represents the h.c., relative distribution of mass and I s the moment of inertial for a hollow cylindrical shell. a. (5 pts.) Find a relationship for the minimum height H necessary to ensure that the speed of the capsule is sufficient to enter orbit once it reaches the surface. Your answer should only include the variables given above (i.e. R, d or K) or other universal constants b. (5 pts.) The financiers ofthe new ride want the capsule to be a hollow cylindrical shell, such that the sides can remain open for a maximum viewing experience. Given your solution to part (a), why is this a problem?

Explanation / Answer

2/5mr^2=mgh

To reach the maximum height the kinetic energy will be converted to the potential energy

the inertia is given by the above formula now

1/2 IW^2=mgh

this will give the maximum height that will be attained

now the problem that will arise is the rotation of the earth. The locus point will constantantly change whne the object reaches the maximum height because earth is also rotating simultaneously and frame of refrence is not stationary

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