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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