Two astronauts (Fig. P11.51), each having a mass of 78.0 kg, are connected by a

Question

Two astronauts (Fig. P11.51), each having a mass of 78.0 kg, are connected by a 10.5 m rope of negligible mass. They are isolated in space, orbiting their center of mass at speeds of 4.80 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

here,

mass of each astronauts , m = 78 kg

length of rod , L = 10.5 m

r = 5.25 m

speed , v = 4.8 m/s

(a)

the magnitude of the angular momentum , P = m * v * r

P = 78 * 4.8 * 5.25

P = 1965.6 kg.m^2/s

the magnitude of the angular momentum 1965.6 kg·m2/s

(b)

the rotational energy of the system , E = 2 * 0.5 * m * v^2

E = 78 * 4.8^2

E = 1797.12 J

the rotational energy of the system is 1797.12 J

(c)

new distance , L' = 5 m

r' = 2.5 m

as the momentum remains conserved

the new angular momentum is 1965.6 kg.m^2/s

(d)

let the new speed be v'

the new angular momentum = 2 * m * v' * r'

1965.6 = 2 * 78 * v' * 2.5

v' = 5.04 m/s

the astronauts' new speeds are 5.04 s

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