What Happens to Apparent Gravity in a Rotating Cylindrical Space Station?

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Homework Help Overview

The discussion revolves around a cylindrical space station that rotates in deep space, focusing on the apparent gravity experienced by an astronaut as they climb a spoke towards the center. The problem includes two main questions: the fractional change in apparent gravity on the surface of the cylinder and the distance the astronaut would fall if they let go halfway up the spoke.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the conservation of angular momentum versus total energy as the astronaut climbs down the spoke, questioning which is conserved and why. There are attempts to apply conservation principles to the astronaut's motion and the effects of climbing on apparent gravity.

Discussion Status

The discussion is ongoing, with participants exploring different aspects of the problem. Some guidance has been provided regarding the conservation of angular momentum, but there is still uncertainty about the implications for energy conservation and the astronaut's fall. Multiple interpretations of the astronaut's experience of gravity are being considered.

Contextual Notes

Participants are grappling with the implications of friction, heat, and the structural integrity of the space station, which may affect energy conservation. There is also a lack of clarity regarding the astronaut's experience of gravity when not in contact with the cylinder's surface.

bon
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1. Homework Statement

cylindrical space station - large diameter, thin walled - radius r, mass M rotating in deep space, no gravity

1)radial spokes of negligible mass connect the cylinder ti the centre of motion. Astronaut mass m climbs a spoke to the centre. What is the fractional change in apparent gravity on the surface of the cylinder?

2)if the astronaut climbs halfway up a spoke and let's go, how far form the base of the spoke will he hit the cylinder? Assume the astronaut is point like..

2. Homework Equations



3. The Attempt at a Solution

1) Got the answer to be 1+m/M for ratio after/before..

is this right? I applied conservation of energy rather than angular momentum...why is angular momentum not conserved?

2) How do i do this one? Consv of energy again?
 
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what is conserved as the astronaut climbs down a spoke - angular momentum or total energy, and why?
 
bon said:
what is conserved as the astronaut climbs down a spoke - angular momentum or total energy, and why?
What do you think? (and why?)
 
My hunch is that angular momentum is conserved but not energy...because as he goes down the spoke there is no torque wrt centre of the cylinder..

but can't see why energy wouldn't be conserved..
 
Friction? Heat? Flexing of the space station? (not to mention the motion of the astronaut's body)

Your hunch is correct.
 
diazona said:
Friction? Heat? Flexing of the space station? (not to mention the motion of the astronaut's body)

Your hunch is correct.

Thanks okay so how do I solve part 2?

My attempt:

When he's half way up a spoke, I = Mr^2 + 1/4 mr^2

After he let's go I = Mr^2

angular mom is conserved again so Mr^2 w2 = (Mr^2 + 1/4mr^2)w1...

don't see how i can use this to work out how far from the base of the spoke he hits the cylinder!
 
I don't think I even understand why he'd fall! I thought you only experienced the "apparent" gravity when you were on the inner surface of this rotating cylinder..
 
so...?
 
  • #10
diazona said:
Friction? Heat? Flexing of the space station? (not to mention the motion of the astronaut's body)

Your hunch is correct.

Sorry just thought I'd quote you to see if you can help with my next question... thanks
 
  • #11
?
 

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