   Chapter 8, Problem 81AP

Chapter
Section
Textbook Problem

S This is a symbolic version of problem 80. Two astronauts (Fig. P8.80), 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. (a) Calculate the magnitude of the angular momentum of the system by treating the astronauts as particles. (b) Calculate the rotational energy of the system. 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? (d) What are their new speeds? (c) What is the new rotational energy of the system? (f) How much work is done by the astronauts in shortening the rope?

(a)

To determine
The angular momentum of the system.

Explanation

Given Info:

The mass of the astronauts is M, the speed of the astronauts is v, and the distance between them is d

System consists of two astronauts moving in circles around the point halfway between them.

Formula to calculate the angular momentum of the system is,

Li=Mviri+Mviri=2Mviri

• Li is the initial angular momentum of the system

(b)

To determine
The rotational energy of the system.

(c)

To determine
The angular momentum of the system for the shortened distance

(d)

To determine
The speed of the astronauts.

(e)

To determine
The new rotational energy of the system.

(f)

To determine
The work done by the astronauts.

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