(a) Explanation Given data: Mass of the child ( m ) is 20 kg. Height of the playground slide is 3.0 m. Speed of the child at the bottom is 2.0 m s . Formula used: Write the expression for kinetic energy. K = 1 2 m v 2 (1) Here, m is the mass of the object, and v is the velocity (speed) of the object. Write the expression for gravitational potential energy. U g = m g y (2) Here, g is the acceleration due to the gravity, which is 9.8 m s 2 , and y is the height. Explanation: The child has gravitational potential energy when she is at the top of the playground slide. The gravitational potential energy is transformed to the kinetic energy and thermal energy during the slide. The transformation of energy is explained with the following calculations. Consider the initial height (at the starting) of the child as 3.0 m, and the final height of the child (at the bottom) as 0 m. Calculation of initial gravitational potential energy: Modify the expression in equation (2) to find the initial gravitational potential energy of the child as follows. ( U g ) i = m g y i Substitute 20 kg for m , 9.8 m s 2 for g , and 3.0 m for y i . ( U g ) i = ( 20 kg ) ( 9.8 m s 2 ) ( 3.0 m ) ≃ 590 kg ⋅ m 2 s 2 ≃ 590 J ( ∵ 1 kg ⋅ m 2 s 2 = 1 J ) Calculation of final gravitational potential energy: Modify the expression in equation (2) to find the final gravitational potential energy of the child as follows. ( U g ) f = m g y f Substitute 20 kg for m , 9.8 m s 2 for g , and 0 m for y f . ( U g ) f = ( 20 kg ) ( 9.8 m s 2 ) ( 0 m ) = 0 kg ⋅ m 2 s 2 = 0 J From the given data, consider the initial velocity of the child at the top of the playground slide as 0 m s (b) To determine To find: The total change in the thermal energy of the slide and the seats of the child’s pants.

College Physics: A Strategic Approach Plus Mastering Physics with Pearson eText -- Access Card Package (4th Edition) (What's New in Astronomy & Physics)

4th Edition

ISBN: 9780134641492

Author: Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field

Publisher: PEARSON

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Instantaneous Power

Power is defined in physics as the amount of energy transmitted or transformed per unit time. The watt is the unit of electricity in the International System of Units, equivalent to one joule per second.

Question

Chapter 10, Problem 42P

(a)

To determine

To explain: The energy transfer and transformations during the slide.

(b)

To determine

To find: The total change in the thermal energy of the slide and the seats of the child’s pants.

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Chapter 10 Solutions

College Physics: A Strategic Approach Plus Mastering Physics with Pearson eText -- Access Card Package (4th Edition) (What's New in Astronomy & Physics)

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The energy transfer and transformations during the slide.

Solution Summary: The author explains how the child's gravitational potential energy is transformed to kinetic energy and thermal energy during the slide.

Concept explainers

To explain: The energy transfer and transformations during the slide.

To find: The total change in the thermal energy of the slide and the seats of the child’s pants.

Chapter 10 Solutions