help with physics problem please! 4. 016 points Previous Answers My Notos Ask Yo
ID: 1794722 • Letter: H
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help with physics problem please!
4. 016 points Previous Answers My Notos Ask Your A space station is constructed in the shape of a hollow ring of mass 4.85 x 10" kg and radius 135 m. The station has 300 crew members (each with average mass 70 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 thet the entire mass of the space stetion is concentrated in the outer ring. Also assume that the crew is initielly 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? Your response differs from the correct answer by more than 10%. Double check your calculations. (b) How much work is done to get the space station spinning? (c) How long must the rockets be fired if there are 6 rockets, and each exerts a thrust of 175 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?Explanation / Answer
(A) a_c = w^2 r = g
w = sqrt(9.8 / 135) = 0.269 rad/s
I = (4.85 x 10^4 + (300 x 70)) 135^2 { I = m r^2 }
I = 1.267 x 10^9 kg m^2
L = I w = 3.414 x 10^8 kg m^2 /s
(B) work done = change in KE = I w^2 / 2 = 4.58x 10^7 J
(C) torque = dL/dt
6 x (175 x 135) = (3.414 x 10^8) / t
t = 2408.5 sec Or 40.1 min
(d) If = (4.85 x 10^4) (135)^2 = 0.884 x 10^9 kg m^2
Applying angular momentum conservation,
3.414 x 10^8 = (0.884 x 10^9) w
w = 0.386 rad/s
a = w^2 r = 20.1 m/s^2
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