Period of Rotation for Artificial Gravity on Earth

[astrololo]

Homework Statement

What must be the period of rotation of a spatial station so that artificial gravity in a cabin that is 45 m of radius from the axis of ration corresponds to gravitational field at the surface of Earth ?

Homework Equations

T=(2(pi)r)/v
Sum of forces r prime = (mv^2)/r

The Attempt at a Solution

I think that I have the following two forces : normal and gravitational force.

so :

n+mg=(mv^2)/r

After that I don't know what to do. The situation is btw a circle.

 

[haruspex]

In what environment is there both a gravitational force and a required centripetal force? (Or, if you prefer, a gravitational force and a centrifugal force.)

 

[astrololo]

In what environment is there both a gravitational force and a required centripetal force? (Or, if you prefer, a gravitational force and a centrifugal force.)

I'm not sure of understanding the question...

 

[haruspex]

I'm not sure of understanding the question...

You posted this equation:

n+mg=(mv^2)/r

You have both gravitational force and centripetal force in there, and a normal force. Did you draw any free body diagrams? Did you find all three of those forces acting in one diagram?

 

[astrololo]

You posted this equation:

You have both gravitational force and centripetal force in there, and a normal force. Did you draw any free body diagrams? Did you find all three of those forces acting in one diagram?

That's the problem, I'm not even sure what forces there are supposed to be. I don't even think there needs to be "mg" maybe only the normal force.

 

[haruspex]

That's the problem, I'm not even sure what forces there are supposed to be. I don't even think there needs to be "mg" maybe only the normal force.

You need to compare two scenarios, on board the space station versus standing on Earth. It is to feel the same to the person in each case. Since we are dealing with matters from the observers point of view, it makes sense to treat the space station case using centrifugal force.
Is there gravity in the space station case?
Is there centrifugal force in the surface case (ignoring the spin of the Earth)?
So what forces are there in each case?

 

[astrololo]

You need to compare two scenarios, on board the space station versus standing on Earth. It is to feel the same to the person in each case. Since we are dealing with matters from the observers point of view, it makes sense to treat the space station case using centrifugal force.
Is there gravity in the space station case?
Is there centrifugal force in the surface case (ignoring the spin of the Earth)?
So what forces are there in each case?

Since we want to imitate the gravity of earth, then I assume we're going to consider that mg exists. So yeah, there's gravity. There's for sure a normal also.

 

[haruspex]

Since we want to imitate the gravity of earth, then I assume we're going to consider that mg exists. So yeah, there's gravity. There's for sure a normal also.

Why would we need to imitate gravity if it exists?

 

[astrololo]

Why would we need to imitate gravity if it exists?

Sorry, but I forgot to specify that this station turn on itself (Around its axis) I think that by doing this, we create an artificial gravity and the questions asks for one that is the same as the one on earth. So we must have 9.8

 

[haruspex]

Sorry, but I forgot to specify that this station turn on itself (Around its axis) I think that by doing this, we create an artificial gravity and the questions asks for one that is the same as the one on earth. So we must have 9.8

Yes, we are creating an artificial gravity, but it is not gravity. The astronaut is to feel a force that is like gravity. But what actually is that force?

 

[astrololo]

Yes, we are creating an artificial gravity, but it is not gravity. The astronaut is to feel a force that is like gravity. But what actually is that force?

Mmmmh... i don't know tbh.

 

[berkeman]

Have a look at the wikipedia page on Artificial Gravity. That should help to clear up your confusion.

https://en.wikipedia.org/wiki/Artificial_gravity

 

[haruspex]

Mmmmh... i don't know tbh.

I need you to answer another question: have you been taught only to use inertial reference frames, or are you comfortable dealing with the concept of fictitious forces, such as centrifugal?