Anika and Sam are astronauts floating in space outside their spaceship.They are tethered together by a rope of length 10.5 m.They both begin pulling on the rope at the same time.Anika has mass of 80 kg,and Sam 100 kg.Because her mass is less,Anika reaches the middle of the rope first.Assuming the center of the rope is at the origin and that Anika and Sam start at 5.25 m and -5.25 m,respectively,where is Sam when Anika reaches the middle?
A)1.05 m
B)0.53 m
C)9.45 m
D)4.20 m

Question

​Anika and Sam are astronauts floating in space outside their spaceship.They are tethered together by a rope of length 10.5 m.They both begin pulling on the rope at the same time.Anika has mass of 80 kg,and Sam 100 kg.Because her mass is less,Anika reaches the middle of the rope first.Assuming the center of the rope is at the origin and that Anika and Sam start at 5.25 m and -5.25 m,respectively,where is Sam when Anika reaches the middle?
A)​1.05 m
B)0.53 m
C)9.45 m
D)4.20 m

Quizplus · Accepted Answer

When Anika reaches the middle of the rope, the system of Anika and Sam must conserve momentum. Since they start from rest, their center of mass doesn't move. The center of mass is closer to Sam because he is more massive. When Anika moves 5.25 m to the center (origin), the ratio of their distances moved is inversely proportional to their masses. Thus, Sam moves less distance towards the center. Given the total length of the rope is 10.5 m, and they are initially 5.25 m apart, when Anika moves to the center, Sam must move a distance that keeps the center of mass stationary. Since Anika has a mass of 80 kg and Sam 100 kg, Sam moves less because of his greater mass. The calculation based on the conservation of momentum and the center of mass being stationary leads to Sam being 1.05 m from the center when Anika reaches it.

​Anika and Sam Are Astronauts Floating in Space Outside Their

Anika and Sam Are Astronauts Floating in Space Outside Their