1. Question Details A space station is constructed in the shape of a hollow ring
ID: 1403631 • Letter: 1
Question
1. Question Details A space station is constructed in the shape of a hollow ring of mass 4.00 X 10^4 kg and radius 130m. The station has 150 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 s Initially not rotatlng 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 It there are 2 rockets, and each exerts e thrust of 100 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) If the centripetal acceleration is g, v^2/r = g, and the tangential velocity is v = (gr). The total angular momentum is v*r*m = (gr)rm = (9.8*115)*115*(5.4 x 10^4 + 150*70) = 2.49 x 10^8 J•s.
(b) The amount of work done is equal to the station's kinetic energy, which is equal to mv2/2 (since the entire ship is traveling the same speed) = mgr/2 = 64500*9.8*115/2 = 3.63 x 10^7 J.
(c) The rockets are the same radius as the mass, so Ft = vm, and t =vm/F = (gr)m/F = (9.8*115)*64500/1200 = 1,800 s, half an hour.
(d) To conserve angular momentum, m1v1 = m2v2, and v2= v1m1/m2, (the astronauts do not contribute to the angular momentum in the center)so(v22/r)/(v12/r) = m12/m22 , and thus a = g*(64500/54000)2 = 14 m/s2.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.