Two astronauts (Fig. P11.51), each having a mass of 79.0 kg, are connected by a
ID: 1608018 • Letter: T
Question
Two astronauts (Fig. P11.51), each having a mass of 79.0 kg, are connected by a 11.0 m rope of negligible mass. They are isolated in space, orbiting their center of mass at speeds of 4.60 m/s.
(a) Treating the astronauts as particles, calculate the magnitude of the angular momentum.
__________kg·m2/s
(b) Calculate the rotational energy of the system.
__________J
(c) By pulling on the rope, one of the astronauts shortens the distance between them to 5.00 m. What is the new angular momentum of the system?
__________kg·m2/s
(d) What are the astronauts' new speeds?
__________m/s
(e) What is the new rotational energy of the system?
__________J
(f) How much work does the astronaut do in shortening the rope?
__________kJ
Explanation / Answer
(a) L = mvr = 2 * 79kg * 4.6m/s * 5.5m = 3910.5 kg·m²/s
(b) KErot = ½I² = ½(mr²)(v/r)² = ½mv² = ½ * 2 * 79kg * (4.6m/s)² = 1671.64 J
(c) conserve momentum: still L = 3910.5 kg·m²/s
(d) 3910.5 kg·m²/s = 2 * 79kg * v * 2.5m v = 9.9 m/s
(e) new KErot = ½ * 2 * 79kg * (9.9m/s)² = 7742.79 J
(f) 7742.79J - 1671.64J = 6071.15 J