Two astronauts in free space each have mass M and are connected by a rope of neg
ID: 2245654 • Letter: T
Question
Two astronauts in free space each have mass M and are connected by a rope of negligible mass and length d. See Figure. They each have a tangential speed of v and are orbiting their center of mass. Calculate: The magnitude of their total angular momentum. Their total energy. By pulling on the rope, one of the astronauts shortens the active rope between them to d/2. Now calculate: The new magnitude of their angular momentum. What are the astronauts? new tangential speeds? Incorrect: Your answer is incorrect. Their total energy. Incorrect: Your answer is incorrect. How much work was done by the astronaut who shortened the rope?Explanation / Answer
a)their total angular momentum. = mvd/2 + mvd/2 = mvd
b) total energy = (0.5*m*v^2)* 2 = mv^2
c) angular momentum remain conserve-
so,
new magnitude of their angular momentum. = mvd
so.
d) as angular momentum = mvd
=> m(v1)d/4 + m(v1)d/4 = mvd
=>astronauts? new tangential speeds = 2v
e)
total energy = (0.5*m*(2v)^2)* 2 = 4mv^2
f) work done by the astronaut =
change in energy = 4mv^2 - mv^2 = 3mv^2