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On which of these hills does the ball roll down with

Conceptual Physics | 12th Edition | ISBN: 9780321909107 | Authors: Paul G. Hewitt ISBN: 9780321909107 29

Solution for problem 19E Chapter 3

Conceptual Physics | 12th Edition

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Conceptual Physics | 12th Edition | ISBN: 9780321909107 | Authors: Paul G. Hewitt

Conceptual Physics | 12th Edition

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Problem 19E

On which of these hills does the ball roll down with increasing speed and decreasing acceleration along the path? (Use this example if you wish to explain to someone the difference between speed and acceleration.)

Step-by-Step Solution:
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Solution 19E In the first hill, the slope of the hill through which the ball is coming down remains constant. So the component of the force along the slope also remains constant. Hence the acceleration of the ball will be constant throughout the motion will remains constant. In the second hill the slope of the surface, through which the ball is coming down, is decreasing. Which means the surface is becoming more horizontal. Now, since the gravitational force is vertical, the component of the force along the surface will decrease. So the acceleration of the ball will also decrease. But, since, the acceleration and velocity will still be in same direction, the speed will increase. In the third hill, the slope of the surface, through which the ball is rolling is increasing. Which means the force along the direction of motion will increase. So the acceleration will also increase. So in the second hill the acceleration is decreasing but the velocity is increasing. So we have seen that even if the acceleration is decreasing, the velocity can still increase. So we have seen that, while one quantity is decreasing, the other quantity is increasing. This is the example that the two quantity are different physical quantity.

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Chapter 3, Problem 19E is Solved
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Textbook: Conceptual Physics
Edition: 12
Author: Paul G. Hewitt
ISBN: 9780321909107

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On which of these hills does the ball roll down with