Two astronauts, each having a mass of 78.5 kg, are connected by a 10.0-m rope of negligible mass. They are isolated in space, moving in circles around the point halfway between them at a speed of 5.50 m/s. Treating the astronauts as particles, calculate each of the following.

Question

(a) the magnitude of the angular momentum of the system
kg · m2/s

(b) the rotational energy of the system
kJ

By pulling on the rope, the astronauts shorten the distance between them to 5.00 m.
(c) What is the new angular momentum of the system?
kg · m2/s

(d) What are their new speeds?
m/s

(e) What is the new rotational energy of the system?
kJ

(f) How much work is done by the astronauts in shortening the rope?
kJ

Answer 1

Hints:

when they shorten the rope, there is no external moment on he system so the angular momentum CAN NOT change. Get the new (higher)speeds from conservation of angular momentum.

they did work shortening the rope so the energy goes up

the work done equals the change in kinetic energy of the system