Two astronauts, each having a mass of 88.0 kg, are connected by a 10.0 m rope of

Question

Two astronauts, each having a mass of 88.0 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 4.30 m/s. Treating the astronauts as particles, calculate each of the following. (b) the rotational energy of the system By pulling on the rope, the astronauts shorten the distance between them to 5.00 m. (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

Explanation / Answer

I = mr^2 = 2200 kgm2 b) KE = 2x 0.5 x I w^2 = I w^2 = 1627.12 J where w = v/r = 4.3/5 d) I1w1 =I2w2 I1 = 2I = 4400 I2 = 2x88x2.5^2 =1100 w2 = 4w1 = 3.44 rad/s v2 = 17.2 m/s e) KE =I2(w2)^2 = 13016.96 J = 13.016 kJ f) work done = change in energy = 11389.84 J =11.39 kJ

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