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Artificial Gravity

  1. Oct 29, 2009 #1

    jacksonpeeble

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    1. The problem statement, all variables and given/known data
    To create artificial gravity, the space station shown in the drawing is rotating at a rate of 1.10 rpm. The radii of the cylindrically shaped chambers have the ratio rA/rB = 3.85. Each chamber A simulates an acceleration due to gravity of 10.0 m/s2.

    05_36.gif

    (a) Find rA.
    (b) Find rB.
    (c) Find the acceleration due to gravity that is simulated in chamber B.

    2. Relevant equations
    aA=vA2/rA
    rA=aAT2/(4pi2)
    aB=4pirB/T2

    3. The attempt at a solution
    Obviously, we have the information that the problem statement gave. Also, t=60. When problem (a) is found, that would just have to be divided by 3.85 to get the next answer, as well. However, I do not understand how to apply the formulas that I have been given to yield answers.

    Thank you in advance for any help!
     
  2. jcsd
  3. Oct 29, 2009 #2
    You can either find the period of rotation or the linear velocity at rA. Use those in the equations you gave with aA being the acceleration.
     
  4. Oct 29, 2009 #3

    jacksonpeeble

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    I do not understand how to apply the equations. Detailed help would be greatly appreciated.

    I do need to turn these answers into my online class (online math classes are awful in my opinion, it's so hard to learn from them) by midnight, but I would also like to understand.
     
  5. Oct 29, 2009 #4
    From what it sounds like, your problem is the actual understanding of what each equation means.

    aA=VA2/rA

    This gives the acceleration (aA) from the linear velocity (VA) and the radius of rotation (rA).

    rA=aAT2/(4pi2)

    This gives the radius of rotation (rA) from the acceleration (aA) and the period of rotation (T).

    aB=4pi (rB/T2)

    This gives the acceleration (aB) from the radius of rotation (rB) and the period of rotation (T).
     
  6. Oct 29, 2009 #5

    jacksonpeeble

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    For the first equation, what are the values that go along with the variables?

    For example, as mentioned, T=60.

    aA=? (shouldn't it be equal to 10)
    VA=?
    rA=?
     
  7. Oct 29, 2009 #6
    I don't see how you are getting T=60.

    Yes. But don't forget your units.

    This is something that you would need to find.

    This is what the problem is asking for.

    One thing to note, you don't have to use the equations in the order they are given, nor do they have to be in the form they are given. You can algebraically manipulate them to find the terms you need.
     
  8. Oct 29, 2009 #7

    jacksonpeeble

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    Thanks for all of your help! I was able to solve all parts of the question because you pointed out that I was incorrect. I was accidentally using the value for 1 rpm, which would be 60.

    T=60*1.1=66

    This messed up the combined equation that I was attempting to use, and all of the others, leading me to believe that I misunderstood the variables.
     
  9. Oct 29, 2009 #8
    Double check your units, you have T = (1.1 rev/min) * (60 sec/min) = 66 rev*sec/min2.

    What it should be is Freq = (1.1 rev/min) * (1 min/60sec) = 1.1 rev/60 sec with T = 1/Freq, making T = 60 sec/1.1 rev.
     
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