Two astronauts of equal mass 86 kg are holding on to opposite ends of a straight
ID: 1467612 • Letter: T
Question
Two astronauts of equal mass 86 kg are holding on to opposite ends of a straight rope in space. The length of the rope between them is 18 meters. They are rotating about an axis that passes through the center of mass midway between the two astronauts with angular velocity 1 radian/sec. One of the astronauts pulls on the rope, decreasing the distance separating them to 18/2 meters. (In the following, take the rope to be massless.) Part A: What is the new angular velocity of the two astronauts? Part B: How much work did the astronaut who pulled on the rope do?
Explanation / Answer
conserving angular momentum around axis of rotation
initial angular momentum of the system= final angular momentum of the system
L=I
I=mr^2
r=9m initially and 4.5 m finally
2 * 86kg * (9m)² * 1rad/s = 2 * 86kg * (4.5m)² *
= 4 rad/s²
rorartional kinetic energy= ½ * I* ^2
I=mr^2
total mass of system = m = 2*86 kg=172 kg
initial KE = ½ * (2*86)kg * (9m)² * (1 rad/s)² = 6966 J
final KE = ½ * (2*86)kg * (4.5m)² * (4rad/s)² = 27864J
work done = (27864-6966)=20898 J