Map Sapling Learning Artifical gravity is a must for any space station if humans

Question

Map Sapling Learning Artifical gravity is a must for any space station if humans are to live there for any extended length of time. Without artificial gravity, human growth is stunted and biological functions break down The most effective way to create artificial gravity is through the use of a rotating enclosed cylinder, as shown in the figure Humans walk on the inside edge of the cylinder, which is sufficiently large that its curvature is not a factor. The space station rotates at a speed designed to apply a radial force on its inhabitants that mimics the normal force they would experience on Earth 1.26 km 1.25 km A danger of the space station is if an entity (whatever that may be) decides to increase the rotational s inside while humans are Humans typically can withstand accelerations up to 40.0g. Suppose alien creatures install a rocket possessing 592910 N of thrust to the outside of the rotating space station, as s take (in days) for the artificial gravity to exceed 40.0g? Assume that the artificial gravity was g before the rocket was installed, and that the inside and outside diameters of the space station are 1.25 km and 1.26 km (respectively), its height is 35.0 m, and that the station is largely aluminum alloy of density 2.66 g/cm3. n. How long wouldt Number days

Explanation / Answer

let d1 = 1.25 km
r1 = d1/2 = 1.25/2 = 0.625 km = 625 m
h = 30 m

d2 = 1.26 km
r2 = d2/2 = 1.26/2 = 0.63 m = 630 m

mass of the space station,

m = density*volume

= rho*pi*(r2^2 - r1^2)*h

= 2.66*10^3*pi*(630^2 - 625^2)*35

= 1.835*10^9 kg

moment of inertia of the cyllinder,

I = m*(r1^2 + r2^2)/2

= 1.835*10^9*(625^2 + 630^2)/2

= 7.22*10^14 kg.m^2

let w is the angular speed required to have acceleration 40*g

we know, a_rad = r*w^2

40*g = r1*w^2

==> w = sqrt(40*g/r1)

= sqrt(40*9.8/625)

= 0.792 rad/s

let alfa is the angular acceleraton of the space station.

use, Torque = I*alfa

F*r2 = I*alfa

==> alfa = F*r2/I

= 592910*630/(7.22*10^14)

= 5.17*10^-7 rad/s^2

now time taken, t = (wf - wi)/alfa

= (0.792 - 0)/(5.17*10^-7)

= 1531914 s

= 1531914/(24*60*60)

= 17.7 days <<<<<<<<<<--------------------Answer

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