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# A certain solid uniform ball reaches a maximum height h0 ISBN: 9780321675460 31

## Solution for problem 15DQ Chapter 10

University Physics | 13th Edition

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Problem 15DQ

A certain solid uniform ball reaches a maximum height h0 when it rolls up a hill without slipping. What maximum height (in terms of h0) will it reach if you (a) double its diameter, (b) double its mass, (c) double both its diameter and mass, (d) double its angular speed at the bottom of the hill?

Step-by-Step Solution:

Solution 15DQ Step 1: Mass of the solid ball m Maximum height reached by the ball h o Let the angular speed of the ball up the hill be By using law of conservation of energy KE = PE 2 2 We have KE = (1/2 ) × I + (1/2) × mv PE = mgh 0 Using this we can write 2 2 (1/2 ) × I + (1/2) × mv = mgh 0 (1/2 ) × ((2/5)mr ) × + (1/2) × mv = mgh 0 2 2 2 2 (1/5)mr + (1/2) m(r ) = mgh 0 7/10 r = gh 0 2 2 h 0 (7r )/10g h 0 (7v )/10g Step 2: When the diameter is doubled we have 2 2 Using h 0 (7r )/10g When r = 2r We have h 0 (7(2r) )/10g h = (7(4r )/10g 0 2 2 h 0 4 (7r )/10g Hence when the diameter doubled the height reached will be h = 4 (7r )/10g2 2 0

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##### ISBN: 9780321675460

Since the solution to 15DQ from 10 chapter was answered, more than 571 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: University Physics, edition: 13. University Physics was written by and is associated to the ISBN: 9780321675460. The full step-by-step solution to problem: 15DQ from chapter: 10 was answered by , our top Physics solution expert on 05/06/17, 06:07PM. The answer to “A certain solid uniform ball reaches a maximum height h0 when it rolls up a hill without slipping. What maximum height (in terms of h0) will it reach if you (a) double its diameter, (b) double its mass, (c) double both its diameter and mass, (d) double its angular speed at the bottom of the hill?” is broken down into a number of easy to follow steps, and 56 words. This full solution covers the following key subjects: its, Double, Hill, mass, diameter. This expansive textbook survival guide covers 26 chapters, and 2929 solutions.

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