Question

Space Station Suppose a space-station is designed in s shape of a torus such as the one depicted in Stanley Kubrick's "2001: A space Odyssey". Suppose the space station has a diameter of 175 meters. At what rotational rate should the sta- tion be spun so that occupants standing on the inside surface of the outer wall (maximum distance from the center) experience earth-normal artificial gravity? Give your answer in terms of rotations per minute Suppose that inside the space station there is a transport cart for transport around the rim that can reach a maxumum speed of 25.0 meters per second. Using such a cart, how could you tell which way the space station from spinning from inside without looking out any windows? Be quite specific about what you experience when you drive around with the cart in one direction or the other

Answer 1

Answer:

w = 3.2 rev / min

Explanation:

For this exercise we will use the centrine acceleration equal to the acceleration of gravity

      a = v² / r

Angular and linear variables are related.

     v = w r

Let's replace

     a = w² r = g

     w = √ g / r

     r = d / 2

     r = 175/2 = 87.5 m

    w = √( 9.8 / 87.5)

    w = 0.3347 rad / s

Let's reduce to rotations per min

     w = 0.3347 rad / s (1 rov / 2pi rad) (60 s / 1 min)

     w = 3.2 rev / min

Suppose the space station rotates counterclockwise, we have two possibilities for the car

The first car turns counterclockwise (same direction of the station

     $v_{c}$ =  $w_{c}$ r

     [texwv_{c}[/tex] =  $v_{c}$ / r

     [texwv_{c}[/tex] = 25.0 / 87.5

     [texwv_{c}[/tex] = 0.286 rad / s

When the two rotate in the same direction their angular speeds are subtracted

     w total = w -[texwv_{c}[/tex]

     w total = 0.3347 - 0.286

    w  total= 0.487 rad / s

The car goes in the opposite direction of the station the speeds add up

    w = 0.3347 + 0.286

    w = 0.62 rad / s

From this values ​​we can see that the person feels a variation of the acceleration of gravity, feels that he has less weight when he goes in the same direction of the season and that his weight increases when he goes in the opposite direction to the season.