(a) Explanation Given info: The mass of the block is m , the initial speed of the block is v 1 and the initial radius of the circle is r 1 and the final radius is r 2 . Formula to calculate the initial moment of inertia is, I i = m r 1 2 (I) I i is the initial moment of inertia m is the mass of the block r 1 is the initial radius of the block Formula to calculate initial angular momentum is, L i = I i ω i (II) L i is the initial angular momentum ω i is the initial angular velocity Substitute equation (I) in equation (II). L i = m r 1 2 ω i Substitute v 1 / r 1 for ω i . L i = m r 1 2 ( v 1 r 1 ) = m v 1 r 1 v 1 is the initial speed r 1 is the initial radius From the Conservation of angular momentum, m v 1 r 1 = m v 2 r 2 r 2 is the final radius Rearrange equation for v 2 (b) To determine The work done by the tension to change the radius from r 1 to r 2 . (c) To determine The change in the kinetic energy of the string.

14th Edition

ISBN: 9780133969290

Author: Hugh D. Young, Roger A. Freedman

Publisher: PEARSON

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Question

Chapter 10, Problem 10.91CP

(a)

To determine

The tension in the string as a function of r .

(b)

To determine

The work done by the tension to change the radius from r1 to r2.

(c)

To determine

The change in the kinetic energy of the string.

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Chapter 10, Problem 10.90P

Chapter 10, Problem 10.92CP

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The tension in the string as a function of r .

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The tension in the string as a function of r .

The work done by the tension to change the radius from r1 to r2.

The change in the kinetic energy of the string.

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Chapter 10 Solutions