Physics with Calc - Please use the appropriate units and round to the .000 if ne
ID: 1409045 • Letter: P
Question
Physics with Calc - Please use the appropriate units and round to the .000 if needed.
Two astronauts, each having a mass of 77.0 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 5.40 m/s.
(a) Treating the astronauts as particles, calculate the magnitude of the angular momentum.
(b) Calculate the rotational energy of the system.
(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?
(d) What are the astronauts' new speeds?
(e) What is the new rotational energy of the system?
(f) How much work does the astronaut do in shortening the rope?
Explanation / Answer
a)
Angular momentum is given by,
L = I*
L = I*v/r
where I = 2*(M*r^2)
So,
L = 2*M*v*r
L = 2*77.0*5.40*(9.5)/2
L = 3950.1 kg-m^2/s
b)
Rotational energy of the system is given by,
K.Erot = 1/2*I*^2
K.Erot = 1/2*(2*M*r^2)*v^2/r^2
K.Erot = M*v^2 = 77.0*(5.40)^2
K.Erot = 2245.32 J
c)
Angular momentum of the system will remain conserved as there is no outside torque on the system !!
Therefore,
L = 3950.1 kg-m^2/s
d)
L = 2*M*v*r
3950.1 = 2*77.0*v*(5.0/2)
v = 10.26 m/s
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