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In the film, 2001: A Space Odyssey, astronauts travel through space and experience artificial gravity created by a spinning, cylindrical space station. In order to generate the same gravitational acceleration felt on Earth's surface, a space station rotates so that an astronaut standing inside its outer rim moves tangentially at 30.9 m/s. What is the diameter of the space station?

Respuesta :

Artificial gravity is created by rotating the cylinder

So here we can say that the acceleration is due to centripetal acceleration

So here we know that the formula of centripetal acceleration is given by

[tex]a_c = \frac{v^2}{R}[/tex]

so here we know that

[tex]a_c = 9.8 m/s^2[/tex]

[tex]v = 30.9 m/s[/tex]

now we will plug in all values

[tex]9.8 = \frac{30.9^2}{R}[/tex]

[tex]R = \frac{30.9^2}{9.8}[/tex]

[tex]R = 97.43 m[/tex]

So above is the radius of the cylinder

Now to find the diameter

[tex]d = 2R[/tex]

[tex]d = 2*97.43[/tex]

[tex]d = 194.8 m[/tex]

so its diameter is 194.8 m

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