Answer:
a) 3750 kgm²/s
b) 1875 J
c) 3750 kgm²/s
d) 10 m/s
e) 7500 J
f) 5625 J
Explanation:
a)
d = distance between the two astronauts = 10 m
m = mass of each astronaut = 75 kg
v = speed of each astronaut = = 5 m/s
r = distance of each astronaut from center of mass = (0.5) d = (0.5) (10) = 5 m
= Angular momentum of the system
Angular momentum of the system is given as
= 2 m v r
= 2 (75) (5) (5)
= 3750 kgm²/s
b)
Rotational energy of the system is given as
= 2 (0.5) m v²
= 2 (0.5) (75) (5)² = 1875 J
c)
= Angular momentum of the system after pulling
Using conservation of angular momentum,
=
= 3750 kgm²/s
d)
r' = new distance of each astronaut from center of mass = (0.5) r = (0.5) (5) = 2.5 m
v' = new speed of each astronaut
Angular momentum of the system after pulling is given as
= 2 m v' r'
3750 = 2 (75) (2.5) v'
v' = 10 m/s
e)
Rotational energy of the system after pulling the rope is given as
= 2 (0.5) m v'²
= 2 (0.5) (75) (10)² = 7500 J
f)
W = work done by astronaut in pulling the rope
Work done is given as
W = -
W = 7500 - 1875
W = 5625 J
