How far along circular arch is an astronaut

In summary, the conversation discusses how to calculate the distance an astronaut in chamber B is moved along a circular arc as the space station rotates, given the distance an astronaut in chamber A is moved and the radii of the two chambers. The formula used is s = θ x r, and both chambers have the same value for θ. The conversation also mentions using a proportion to solve the problem, and how this approach also works using the arc length formula.
  • #1
sweetwilliam
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0

Homework Statement


a space station consists of two donut shaped living chambers A and B, that have radii r(A)= 3.2x10^2m and r(B)=1.10x10^3m. As the station rotates, the astronaut in chamber A is moved 2.40x10^2 m along a circular arc. how far along a circular arc is an astronaut in chamber B moved during the same time?


Homework Equations





The Attempt at a Solution


i used a proportion r(A)/ circular arc = r(B)/ x and solved for x i got the correct answer but my
but i was wondering if there was a different way to solve this using formulas...my physics prof. would not be happy if i didnt use correct formulas. thanks!
 
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  • #2
Do you remember the formula for arc length? Find θ, it will be the same for both living chambers. Do you see why your approach also works using the arc length formula?
 
  • #3
s=theta x r i see now how that works...thanks so much, i didnt think of that at first. thanks
 

1. How far along the circular arch is an astronaut?

An astronaut floating in space is technically not on a circular arch, as they are in a microgravity environment where there is no specific point of support or curvature. However, if we were to consider the orbit of the astronaut around the Earth, they would be approximately 400 kilometers above the surface.

2. How does the distance of an astronaut from Earth affect their position on the circular arch?

The distance of an astronaut from Earth does not directly affect their position on the circular arch, as they are in a weightless environment. However, the farther an astronaut is from Earth, the greater the curvature of their orbit will be, resulting in a larger circular arch.

3. Can an astronaut move along the circular arch?

An astronaut's movement along the circular arch is dependent on their propulsion and speed. If they are in a spacecraft with propulsion systems, they can maneuver and change their position on the circular arch. However, if they are floating in space without any external forces acting on them, they will continue to move along their orbit without changing position on the circular arch.

4. How does an astronaut's speed affect their position on the circular arch?

An astronaut's speed directly affects their position on the circular arch, as it determines the size and shape of their orbit. For example, a faster speed will result in a larger orbit with a greater curvature, while a slower speed will result in a smaller orbit with less curvature.

5. Can an astronaut's position on the circular arch change over time?

An astronaut's position on the circular arch can change over time if they have the means to maneuver and change their orbit. However, in a weightless environment, they will continue to move along their orbit without any external forces acting on them.

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