Two astronauts, each having a mass of 79.0 kg, are connected by a 9.5 m rope of

Question

Two astronauts, each having a mass of 79.0 kg, are connected by a 9.5 m rope of negligible mass. They are isolated in space, orbiting their center of mass at speeds of 5.20 m/s CM (a) Treating the astronauts as particles, calculate the magnitude of the angular momentum 392 1.4 kg·mm2/ (b) Calculate the rotational energy of the system. 2156.75J (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? 392 1.4 kg·m ^2/ (d) What are the astronauts new speeds? 5.23 m/s Your response differs from the correct answer by more than 10%. Double check your calculations (e) What is the new rotational energy of the system? 2047.6 J × Your response differs from the correct answer by more than 10%. Double check your calculations (f) How much work does the astronaut do in shortening the rope? 09.163Jx Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully

Explanation / Answer

(d) But the angular momentum of the system is L2 =2*m*v*r = 3921.4 kg.m2/s2          
                                                                                             v = 3921.4 / 2*m*r
                                                                                                = 5.22 m/s ( where r = 4.75 m )
(e) The new rotational energy is K2 =(1/2)I2
         = (1/2)[ 2mr2 ][ v / r]2
         = mv2
         = 2136.1 J
( f ) work done W = change in kinetic energy
                       
                          = 2.13*10^4 -2156.75 = 1.91*10^4J

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