Space station living quarters problem

In summary, an astronaut in chamber B is moved along a circular arc at the same time as an astronaut in chamber A. However, the arc-length is different due to the fact that the arc-angle is 1 radian.
  • #1
sweedeljoseph

Homework Statement


A space station consists of two doughnut shaped living chambers, A and B, that have the radii shown in the drawing. As the station rotates, an astronaut in chamber A is moved 2.40 x 102 m along a circular arc. How far along a circular arc is an astronaut in chamber B moved during the same time?

here is the picture for more reference:
http://img407.imageshack.us/img407/2496/picgr3.jpg

Homework Equations


i don't know if these will help we just got a lot today so here:
w=[tex]\theta[/tex]/Delta t
*v=vo+at ~ w=wo+[tex]\omega[/tex]t
*v2=vo2+2ax ~ w2=wo2+2[tex]\omega[/tex][tex]\theta[/tex]
*x=vot+(1/2)at2 ~ [tex]\theta[/tex]=wot+(1/2)at2

the ones with * means i changed it to what the problem is about. means the same thing just different letters so you won't get confused i guess.

The Attempt at a Solution


i have no idea what I am supposed to do. i know the arc length should be the same as the radius because its has something to do with radians? i have no clue what I am supposed to do. please help me.

thank you!
sweedeljoseph
 
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  • #2
sweedeljoseph said:
i know the arc length should be the same as the radius because its has something to do with radians?

Hi sweedeljoseph! :smile:

Arc-length = radius times angle (with angle measured in radians):

arc-length = rθ :wink:​

(so the arc-length equals the radius only if the arc-angle is 1 radian!)
 
  • #3
how would i know if the angle is 1 radian?
 
  • #4
sweedeljoseph said:
how would i know if the angle is 1 radian?

2π radians is 360º

so 1 radian = (180/π)º. :smile:
 
  • #5
i know that but how do you know from the problem what the angles are?
 
  • #6
sweedeljoseph said:
A space station consists of two doughnut shaped living chambers, A and B, that have the radii shown in the drawing. As the station rotates, an astronaut in chamber A is moved 2.40 x 102 m along a circular arc. How far along a circular arc is an astronaut in chamber B moved during the same time?

Hi sweedeljoseph! :smile:

This is a very simple symmetry problem (expansional symmetry :wink:) …

you don't need to know anything about angles or radians …

the space station is rigid, so if A goes 240m round a circle of radius 320m, then B goes … round a circle of radius 1100m? :smile:
 
  • #7
yea...
my teacher showed me how to do this today. i feel so stupid. haha.

thank you though!
sweedeljoseph
 

FAQ: Space station living quarters problem

What is the "Space station living quarters problem"?

The "Space station living quarters problem" is a hypothetical scenario where a space station is running low on living quarters for its inhabitants. This could be due to a variety of factors, such as an increase in crew size or a decrease in available space.

Why is the "Space station living quarters problem" important?

The "Space station living quarters problem" is important because it highlights the challenges and limitations of living in space for extended periods of time. It also raises questions about how to efficiently use space and resources in a confined environment.

What are some potential solutions to the "Space station living quarters problem"?

Potential solutions to the "Space station living quarters problem" include expanding the living quarters through construction or utilizing unused space on the station, implementing more efficient and compact living arrangements, or sending crew members back to Earth to make room for new ones.

How do astronauts currently live on the International Space Station?

Astronauts currently live on the International Space Station in small, compact living quarters that include sleeping quarters, a bathroom, and a small workspace. They also have access to a communal living area and exercise equipment.

What challenges do astronauts face while living on a space station?

Astronauts face many challenges while living on a space station, including dealing with microgravity, limited resources and living space, and potential psychological impacts of living in isolation for extended periods of time.

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