Artificial Gravity in a space station

[jacksonpeeble]

Homework Statement

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.

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

Homework Equations

a_A=v_A²/r_A
r_A=a_AT²/(4pi²)
a_B=4pir_B/T²

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!

 

[Jasso]

You can either find the period of rotation or the linear velocity at r_A. Use those in the equations you gave with a_A being the acceleration.

 

[jacksonpeeble]

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.

 

[Jasso]

From what it sounds like, your problem is the actual understanding of what each equation means.

a_A=V_A²/r_A

This gives the acceleration (a_A) from the linear velocity (V_A) and the radius of rotation (r_A).

r_A=a_AT²/(4pi²)

This gives the radius of rotation (r_A) from the acceleration (a_A) and the period of rotation (T).

a_B=4pi (r_B/T²)

This gives the acceleration (a_B) from the radius of rotation (r_B) and the period of rotation (T).

 

[jacksonpeeble]

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=?

 

[Jasso]

For example, as mentioned, T=60.

I don't see how you are getting T=60.

aA=? (shouldn't it be equal to 10)

Yes. But don't forget your units.

VA=?

This is something that you would need to find.

rA=?

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.

 

[jacksonpeeble]

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.

 

[Jasso]

T=60*1.1=66

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.