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Space Station Design

  1. Jun 4, 2009 #1
    1. The problem statement, all variables and given/known data

    Part 1:

    You want to design a large, permanent space station so that no artificial gravity is necessary. You decide to shape it like a large coffee can of radius 322 m and rotate it about its central axis. The acceleration of gravity is 9.8 m/s2. What rotation speed would be required to simulate gravity?

    Part 2:

    If an astronaut jogged in the direction of the rotation at 5 m/s, what is the simulated gravitational acceleration the astronaut would feel?

    2. Relevant equations

    a = v^2/r

    ω = v/r

    a = vω

    3. The attempt at a solution

    For Part 1:
    9.8 = v^2/322 m
    v^2 = 3155.6
    v = 56.17472741 m/s

    vω = v^2/r
    ω = v/r
    ω = (56.17472741 m/s)/(322 m)
    ω = 0.174456 rad/s


    For Part 2:

    v = rω

    I don't really know where to begin for this part.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jun 4, 2009 #2

    LowlyPion

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    Homework Helper

    a = v2/r = ω2r = g

    ω = (g/r)1/2

    ... which yields your answer.

    In part 2 they want you to determine what happens when Kier Dullea (astronaut from 2001:Space Odyssey) is jogging, thereby increasing his speed (and the g force) by 5 m/s in the direction of rotation.
     
  4. Jun 4, 2009 #3
    Oh...okay, so:

    astronaut's speed: 56.17472741 m/s + 5 m/s

    a = v^2/r
    a = (61.17472741 m/s)^2/322 m = 11.62223624 m/s^2
     
  5. Jun 4, 2009 #4

    LowlyPion

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    Homework Helper

    Pretty much.

    Since 9.8 is the given precision of gravity, maybe the correct form of your answer would be 11.6, depending on your instructor.
     
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