Gravitational Field Strength of Space Station w/ N Astronauts

In summary, the problem involves a space station with two living modules attached to a central hub by long corridors. At the beginning of the day, the station is rotating so that the astronauts feel a gravitational field of strength g. When two astronauts climb into the central hub, the remaining astronauts feel a gravitational field of strength g'. The question is asking for the ratio g/g' in terms of the number of astronauts, N. To solve this problem, conservation of rotational kinetic energy can be used, as well as the formula for rotational kinetic energy. The angular momentum of the system is also conserved because the space station is isolated.
  • #1
fizics
21
0

Homework Statement


A space station consists of two living modules attached to a central hub on opposite sides of the hub by long corridors of equal length. Each living module contains N astronauts of equal mass. The mass of the space station is negligible compared to the mass of the astronauts, and the size of the central hub and living modules is negligible compared to the length of the corridors. At the beginning of the day, the space station is rotating so that the astronauts feel as if they are in a gravitational field of strength g. Two astronauts, one from each module, climb into the central hub, and the remaining astronauts now feel a gravitational field of strength g′. What is the ratio g/g′ in terms of N?

Homework Equations


mrw^2=mg

The Attempt at a Solution


I can go no further after calculating the new rotational inertia.I don't know how the angular velocity would change.
 
Last edited:
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  • #2
Welcome to PF.

How do you think you should approach the problem(s).
 
  • #3
I can go no further after calculating the new rotational inertia.I don't know how the angular velocity would change.
 
  • #4
A lot of problems involve conservation of physical quantities. What might be conserved here?
 
  • #5
kinetic energy?
 
  • #6
What is the formula for rotational kinetic energy?

You have the new moment of inertia. So ... don't you have a way to figure the new kinetic energy and hence the new force g'?
 
  • #7
Thank you.But I would like to know what is unchanged in the problem.Is the angular velocity unchanged?
 
  • #8
fizics said:
Thank you.But I would like to know what is unchanged in the problem.Is the angular velocity unchanged?

The rotational kinetic energy is unchanged isn't it?

KE = ½Iω² = ½Iv²/r

If you change I and KE is constant ...

v² = 2*KE*r/I

and new g = v²/r = 2*KE*/I
 
  • #9
OK,thx,and is angular momentum conserved here?Because the system of the station of astronauts is isolated.
 
  • #10
fizics said:
OK,thx,and is angular momentum conserved here?Because the system of the station of astronauts is isolated.
What's your gut feeling? Do you think it would be conserved, or wouldn't be conserved?
 
  • #11
I think the angular momentum of the system(people and station) is conserved.
 

1. What is the gravitational field strength of a space station with N astronauts?

The gravitational field strength of a space station with N astronauts is dependent on the mass and distance of the astronauts from the center of the station. It can be calculated using the formula g = GM/r^2, where G is the universal gravitational constant, M is the total mass of the astronauts, and r is the distance from the center of the station.

2. How does the number of astronauts affect the gravitational field strength of a space station?

The number of astronauts does not have a direct impact on the gravitational field strength of a space station. However, as the number of astronauts increases, so does the total mass of the station, which can lead to a higher gravitational field strength.

3. Is the gravitational field strength of a space station constant?

No, the gravitational field strength of a space station is not constant. It can vary based on the position of the astronauts and their distance from the center of the station. It can also vary over time as the mass of the station changes due to supplies being brought in or taken out.

4. How does the gravitational field strength of a space station compare to that of Earth?

The gravitational field strength of a space station is significantly weaker than that of Earth. On average, the gravitational field strength on the surface of Earth is about 9.8 m/s^2, while the field strength on a space station in low Earth orbit is around 9 m/s^2.

5. Can the gravitational field strength of a space station be manipulated?

Yes, the gravitational field strength of a space station can be manipulated by changing the mass and/or distance of the astronauts. This can be done by adjusting the amount of supplies on board or by using thrusters to change the station's position in orbit.

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