Questions 16-20: Two astronauts (m = 90 kg each) hold onto a rope under tension.
ID: 2152735 • Letter: Q
Question
Questions 16-20: Two astronauts (m = 90 kg each) hold onto a rope under tension. The length of the rope is initially d = 4.0 m. Initially, the astronauts are at rest. One of the astronauts fires a booster rocket at a right angle to the rope, which sets the astronauts in rotation around their common center-of-mass. The thrust in the booster rocket is F = 9000 N and it is turned on for only 0.3 s (assume this time is so short that it is almost instantaneous).http://www.webassign.net/pse/p11-59.gif
16.) After the booster rocket is turned off, what is the velocity of the center-of-mass through space?
A.) 7.5 m/s
B.) 15 m/s
C.) 30 m/s
D.) 45 m/s
E.) 60 m/s
AB.) 0 (center-of-mass does not move)
17.) After the booster rocket is turned off, what is the angular speed of the astronauts around their
common center-of-mass?
A.) 7.5 rad/s
B.) 15 rad/s
C.) 30 rad/s
D.) 45 rad/s
E.) 60 rad/s
18.) The astronauts pull on the rope, shortening the distance between them to only 1.0 m. What is
the ratio of the final angular momentum to initial angular momentum, Lf/Lo?
A.) 1/16 E.) 16
B.) 1/4 AB.) 4
C.) 1/2 AC.) 2
D.) 1
19.) After the astronauts shorten the rope, what is the ratio of the final kinetic energy to initial kinetic
energy, Kf/Ko?
A.) 1/16 E.) 16
B.) 1/4 AB.) 4
C.) 1/2 AC.) 2
D.) 1
20.) After the astronauts shorten the rope, what is the ratio of the final angular speed to initial angular
speed, (angular speed)final /(angular speed)initial?
A.) 1/16 E.) 16
B.) 1/4 AB.) 4
C.) 1/2 AC.) 2
D. 1
Please explain and show work
Explanation / Answer
momentum gained = 900*0.3 = 2700 kgm/s vcm = 2700/(90+90) = 15m/s 16) B 17) A 18) D 19) B 20) AC
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