Artifical gravity is a must for any space station if humans are to live there fo

Question

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 speed while humans are inside Humans typically can withstand accelerations up to 40.0g. Suppose alien creatures install a rocket possessing 283230 N of thrust to the outside of the rotating space station, as 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 knm and 1.26 km (respectively), its height is 35.0 m, and that the station How long would it is largely aluminum alloy of density 2.66 g/cm" Number days

Explanation / Answer

The centripetal acceleration is initially u^2/R = g and finally v^2/R = 40g.
The required increase in linear speed at the rim is
v-u = sqrt(40gR) - sqrt(gR)
= sqrt(40gR)*(1 - sqrt(1/40))
= sqrt(40*9.8*1250/2)*(1 - 0.158)
= 4.17E2 m/s.

The total mass of the space station is
2pi*((1250+1260)/4)m *(1260-1250)/2 *10m *35m *2660kg/m^3
= 1.84E10 kg.
The mass is almost concentrated in the rim, so we can use the linear acceleration at the rim, which is
a = 283230 N/ 1.84E10 kg
= 1.54E-5 m/s^2.
The time taken to increase the linear speed at the rim by 416.8 m/s is
t = 4.17E2 m/s / 1.54E-5 m/s^2
= 2.71E7 s
= 2.71E7 / 3600*24
= 313.7 days

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