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. A danger of the space station is if an entity (whatever that may be) decides to increase the rotational speed while humans are inside.

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 *2720kg/m^3

= 1.88E10 kg.

The mass is almost concentrated in the rim, so we can use the linear acceleration at the rim, which is

a = 5.155E5 N / 1.88E10 kg

= 2.75E-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 / 2.76E-5 m/s^2

= 1.52E7 s

= 1.52E7 / 3600*24

= 176 days approx.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.