It has been argued that power plants should make use of

University Physics | 13th Edition | ISBN: 9780321675460 | Authors: Hugh D. Young, Roger A. Freedman

Problem 75P Chapter 9

University Physics | 13th Edition

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University Physics | 13th Edition | ISBN: 9780321675460 | Authors: Hugh D. Young, Roger A. Freedman

University Physics | 13th Edition

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Problem 75P

It has been argued that power plants should make use of off-peak hours (such as late at night) to generate mechanical energy and store it until it is needed during peak load times, such as the middle of the day. One suggestion has been to store the energy in large flywheels spinning on nearly frictionless ball bearings. Consider a flywheel made of iron (density 7800 kg/m3) in the shape of a 10.0-cm-thick uniform disk. (a) What would the diameter of such a disk need to be if it is to store 10.0 megajoules of kinetic energy when spinning at 90.0 rpm about an axis perpendicular to the disk at its center? (b) What would be the centripetal acceleration of a point on its rim when spinning at this rate?

Step-by-Step Solution:

Solution 75P Step 1: The kinetic energy of a rotating disk is K.E = 1/2 Iw2 Where K.E = kinetic energy in joules 2 I = moment of inertia in kg/m w = angular velocity in rad/s The moment of inertia of rotating disk is 2 I = Mr /2 2 Mass of disk M = dr Here d is density,r is radius and h is thickness. So 2 2 2 K.E = 1/4 * * r * *r *w 4 2 K.E = 1/4 * * r * *w 2 1/4 r = (4K.E/(d*hw ) Step 2: w = 90.0 rpm *(2 rad/rev)/(60 s/1 min)] = 9.424 rad/s K.E = 10 × 10 J6 2 h = 11 × 10 m 3 d = 7800 kg/m Then r = [4(10 × 10 J)/(7800 kg/m 3 × 11 × 10 2(9.424 rad/s) ]1/4 * r = 3.595 m Then diameter d = 2r = 2(3.595 m) = 7.190 m

Step 3 of 3

Chapter 9, Problem 75P is Solved
Textbook: University Physics
Edition: 13
Author: Hugh D. Young, Roger A. Freedman
ISBN: 9780321675460

This textbook survival guide was created for the textbook: University Physics, edition: 13. This full solution covers the following key subjects: disk, such, store, spinning, Energy. This expansive textbook survival guide covers 26 chapters, and 2929 solutions. The full step-by-step solution to problem: 75P from chapter: 9 was answered by Patricia, our top Physics solution expert on 05/06/17, 06:07PM. The answer to “It has been argued that power plants should make use of off-peak hours (such as late at night) to generate mechanical energy and store it until it is needed during peak load times, such as the middle of the day. One suggestion has been to store the energy in large flywheels spinning on nearly frictionless ball bearings. Consider a flywheel made of iron (density 7800 kg/m3) in the shape of a 10.0-cm-thick uniform disk. (a) What would the diameter of such a disk need to be if it is to store 10.0 megajoules of kinetic energy when spinning at 90.0 rpm about an axis perpendicular to the disk at its center? (b) What would be the centripetal acceleration of a point on its rim when spinning at this rate?” is broken down into a number of easy to follow steps, and 129 words. University Physics was written by Patricia and is associated to the ISBN: 9780321675460. Since the solution to 75P from 9 chapter was answered, more than 499 students have viewed the full step-by-step answer.

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