4. 116 points My Notes Ask Your Teacher A space station is constructed in the sh

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4. 116 points My Notes Ask Your Teacher A space station is constructed in the shape of a hollow ring of mass 4.85 x 104 kg and radius 100 m. The station has 300 crew members (each with average mass 80 kg) who can walk on a deck formed by the inner surface of the outer cylindrical wall of the ring. Artificial gravity is produced when the ring rotates (that is, the crew members experience a normal force from the floor pushing them inward) (a) Assume the station is initially not rotating, and assume that the entire mass of the space station is concentrated in the outer ring. Also assume that the crew is initially on the outer rim. Rockets on the outside of the outer rim are fired tangentially to get the station spinning up to a speed such that the crew experiences a centripetal acceleration equal to g. What is the total angular momentum of the space station (plus crew) when it is up to maximum speed? (b) How much work is done to get the space station spinning? (c) How long must the rockets be fired if there are 4 rockets, and each exerts a thrust of 125 N? (d) The rockets are no longer thrusting. The entire crew moves to the very center of the space station. What acceleration does an ant experience on the outer rim? Submit Answer Save Progress

Explanation / Answer

a)

a=g=9.8m/s^2

a=w^2r

Plugging values,

9.8=w^2*100

w=sqrt(a/r)

w=sqrt0.098

w=0.313rad/s

I=mr^2 = (mstation+mcrew)*r^2 = (4.85*10^4+300*80)*100^2 = 7.25*10^8 kg*m^2

L=Iw= 7.25*10^8*0.313 = 2.27*10^8 kg*m^2/s

b)

W=1/2Iw^2 = ½*(4.85*10^4+300*80)*100^2*0.313^2= 3.55*10^7 J

c)

T=F*r

I­­­­=Fr

=Fr/I

Pluggung values,

=(4*125*100)/( 7.25*10^8) = 6.9*10^-5 rad/s

t=(wf-wi)/=

t=(0.313-0)/(6.9*10^-5)

t=4536.23s

d)

By conservation of angular momentum,

Lf=Li

Ifwf=Iiwi

2.27*10^8=()*wf=[(4.85*10^4+ 0)*100^2]*wf

wf=0.468rad/s

a=wf^2*r=0.468*^2*100 = 4680 m/s^2

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