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A size-5 soccer ball of diameter 22.6 cm and mass 426 g

University Physics | 13th Edition | ISBN: 9780321675460 | Authors: Hugh D. Young, Roger A. Freedman ISBN: 9780321675460 31

Solution for problem 29E Chapter 10

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 29E

A size-5 soccer ball of diameter 22.6 cm and mass 426 g rolls up a hill without slipping, reaching a maximum height of 5.00 m above the base of the hill. We can model this ball as a thin-walled hollow sphere. (a) At what rate was it rotating at the base of the hill? (b) How much rotational kinetic energy did it have then?

Step-by-Step Solution:

Solution 29E Introduction We have to first calculate the initial kinetic energy of the ball using the rotational motion. So we have to calculate the moment of inertia of the ball. No at maximum height, the potential energy of the ball will be equal to the initial kinetic energy of the ball. So equating the initial kinetic energy and maximum potential energy we can calculate the rotational speed and then rotational kinetic energy. Step 1 The mass of the ball is m = 426 g = 0.426 kg And the diameter of the ball is d = 22.6 cm = 0.226 m Hence the radius of the ball is r = d/2 = 0.113 m The moment of inertia of hollow sphere is given by I = mr 2 2 3 2 3 Hence the moment of inertia of the ball is I = (0.326 kg)(0.113 m) = 3.626 × 10 kg.m 2 Step 2 Suppose the angular velocity of the ball is Since the ball is rotating without sleeping, the translational velocity of the ball is v = r Hence the kinetic energy of the ball is 1 2 1 2 1 2 1 2 2 K = I2+ mv = 2 + m 2 2 = (3.626 × 10 3 kg.m ) + (0.426 kg)(0.113 m) 2 2 2 2 = (3.626 × 10 3 kg.m ) + (5.439 × 10 3 kg.m ) 2 2 2 = (4.532 × 10 3 kg.m ) 2 Step 3 The maximum height of the ball is h = 5.00 m Hence the potential energy of the ball at maximum height is U = mgh = (0.426 kg)(9.8 m/s )(5.00 m) = 20.87 J

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Chapter 10, Problem 29E is Solved
Step 5 of 5

Textbook: University Physics
Edition: 13
Author: Hugh D. Young, Roger A. Freedman
ISBN: 9780321675460

The full step-by-step solution to problem: 29E from chapter: 10 was answered by , our top Physics solution expert on 05/06/17, 06:07PM. Since the solution to 29E from 10 chapter was answered, more than 757 students have viewed the full step-by-step answer. University Physics was written by and is associated to the ISBN: 9780321675460. This full solution covers the following key subjects: Hill, base, ball, much, Energy. This expansive textbook survival guide covers 26 chapters, and 2929 solutions. The answer to “A size-5 soccer ball of diameter 22.6 cm and mass 426 g rolls up a hill without slipping, reaching a maximum height of 5.00 m above the base of the hill. We can model this ball as a thin-walled hollow sphere. (a) At what rate was it rotating at the base of the hill? (b) How much rotational kinetic energy did it have then?” is broken down into a number of easy to follow steps, and 64 words. This textbook survival guide was created for the textbook: University Physics, edition: 13.

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