Gravitational Field Strength of Space Station w/ N Astronauts

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Homework Help Overview

The problem involves a rotating space station with astronauts experiencing a gravitational field strength. It examines the effects on gravitational field strength when some astronauts move from living modules to a central hub, specifically focusing on the ratio of gravitational strengths before and after this change in configuration.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the conservation of physical quantities, such as angular momentum and kinetic energy, in relation to the changes in the system. Questions are raised about the implications of changing the moment of inertia and whether angular velocity remains constant.

Discussion Status

The discussion is ongoing, with participants exploring various aspects of the problem, including the conservation laws and their implications on the system's dynamics. Some guidance has been offered regarding the relationships between kinetic energy, moment of inertia, and angular momentum.

Contextual Notes

Participants are considering the assumptions regarding the isolation of the system and the negligible mass of the space station compared to the astronauts. There is uncertainty about the constancy of angular velocity and its effects on the gravitational field strength.

fizics
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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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Welcome to PF.

How do you think you should approach the problem(s).
 
I can go no further after calculating the new rotational inertia.I don't know how the angular velocity would change.
 
A lot of problems involve conservation of physical quantities. What might be conserved here?
 
kinetic energy?
 
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'?
 
Thank you.But I would like to know what is unchanged in the problem.Is the angular velocity unchanged?
 
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
 
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.
 

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