(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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3.63 • Leaping the River II. A physics professor did daredevil stunts in his spare time. His last stunt was an attempt to jump across a river on a motorcycle (Fig. P3.63). The takeoff ramp was inclined at 53.0°, the river was 40.0 m wide, and the far bank was 15.0 m lower than the top of the ramp. The river itself was 100 m below the ramp. Ignore air resistance. (a) What should his speed have been at the top of the ramp to have just made it to the edge of the far bank? (b) If his speed was only half the value found in part (a), where did he land? Figure P3.63 53.0° 100 m 40.0 m→ 15.0 m

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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