Two astronauts (see figure below), each having a mass M , are connected by a rop
ID: 1796057 • Letter: T
Question
Two astronauts (see figure below), each having a mass M, are connected by a rope of length d having negligible mass. They are isolated in space, moving in circles around the point halfway between them at a speed v. (Use any variable or symbol stated above as necessary.)
(a) Calculate the magnitude of the angular momentum of the system by treating the astronauts as particles.
Li =
(b) Calculate the rotational energy of the system.
KEi =
By pulling on the rope, the astronauts shorten the distance between them to d/2.
(c) What is the new angular momentum of the system?
Lf =
(d) What are their new speeds?
vf =
(e) What is the new rotational energy of the system?
KEf =
(f) How much work is done by the astronauts in shortening the rope?
Wnet =
Explanation / Answer
a)
Intial angular momentum
Li=mvr+mvr =2mvr
L=2*m*v*(d/2)=mvd
b.
rotational energy of the system
Ki=(1/2)mV2+(1/2)mV2
Ki=mV2
c.
By Conservation of angular momentum
Li =Lf
Lf=mvd
d.
Vf=2Lf/md =2*mvd/md
Vf=2V
e.
Kf=(1/2)m(2V)2+(1/2)m(2V)2=4mV2
f.
Wnet =Kf-Ki =4mV2-mV2
Wnet =3mV2