Chapter 14.4, Problem 28E

BuyFind*arrow_forward*

11th Edition

Ron Larson + 1 other

ISBN: 9781337275347

Textbook Problem

Finding the Center of Mass Using Technology

In Exercises 25–28, use a computer algebra system to find the mass and center of mass of the lamina bounded by the graphs of the equations for the given density.

To determine

**To Calculate:** The mass and center of mass of the lamina bounded by the graphs of the given equations.

Explanation

**Given:**

**Calculation:**

First, sketch the graph as shown below,

Draw the reference axis in xy coordinates.

Then. plot the provided equations:

0 | ||||||

R |
2 | 1.5 | 1 | 0 | -1.5 | 2 |

Further, mark the points on the plot and connect them.

Shade the region inside the graph as the area of interest is the area inscribed by the equations.

The final plot is shown below as:

Therefore, the mass of the lamina is:

Now, to find the center of the mass calculate the moment of inertia about both the axes.

The moment of inertia about *x-axis* is:

The moment of inertia about y-*axis* is:

Sect-14.1 P-1ESect-14.1 P-2ESect-14.1 P-3ESect-14.1 P-4ESect-14.1 P-5ESect-14.1 P-6ESect-14.1 P-7ESect-14.1 P-8ESect-14.1 P-9ESect-14.1 P-10E

Sect-14.1 P-11ESect-14.1 P-12ESect-14.1 P-13ESect-14.1 P-14ESect-14.1 P-15ESect-14.1 P-16ESect-14.1 P-17ESect-14.1 P-18ESect-14.1 P-19ESect-14.1 P-20ESect-14.1 P-21ESect-14.1 P-22ESect-14.1 P-23ESect-14.1 P-24ESect-14.1 P-25ESect-14.1 P-26ESect-14.1 P-27ESect-14.1 P-28ESect-14.1 P-29ESect-14.1 P-30ESect-14.1 P-31ESect-14.1 P-32ESect-14.1 P-33ESect-14.1 P-34ESect-14.1 P-35ESect-14.1 P-36ESect-14.1 P-37ESect-14.1 P-38ESect-14.1 P-39ESect-14.1 P-40ESect-14.1 P-41ESect-14.1 P-42ESect-14.1 P-43ESect-14.1 P-44ESect-14.1 P-45ESect-14.1 P-46ESect-14.1 P-47ESect-14.1 P-48ESect-14.1 P-49ESect-14.1 P-50ESect-14.1 P-51ESect-14.1 P-52ESect-14.1 P-53ESect-14.1 P-54ESect-14.1 P-55ESect-14.1 P-56ESect-14.1 P-57ESect-14.1 P-58ESect-14.1 P-59ESect-14.1 P-60ESect-14.1 P-61ESect-14.1 P-62ESect-14.1 P-63ESect-14.1 P-64ESect-14.1 P-65ESect-14.1 P-66ESect-14.1 P-67ESect-14.1 P-68ESect-14.1 P-69ESect-14.1 P-70ESect-14.1 P-71ESect-14.1 P-72ESect-14.1 P-73ESect-14.1 P-74ESect-14.1 P-75ESect-14.1 P-76ESect-14.1 P-77ESect-14.1 P-78ESect-14.1 P-79ESect-14.1 P-80ESect-14.2 P-1ESect-14.2 P-2ESect-14.2 P-3ESect-14.2 P-4ESect-14.2 P-5ESect-14.2 P-6ESect-14.2 P-7ESect-14.2 P-8ESect-14.2 P-9ESect-14.2 P-10ESect-14.2 P-11ESect-14.2 P-12ESect-14.2 P-13ESect-14.2 P-14ESect-14.2 P-15ESect-14.2 P-16ESect-14.2 P-17ESect-14.2 P-18ESect-14.2 P-19ESect-14.2 P-20ESect-14.2 P-21ESect-14.2 P-22ESect-14.2 P-23ESect-14.2 P-24ESect-14.2 P-25ESect-14.2 P-26ESect-14.2 P-27ESect-14.2 P-28ESect-14.2 P-29ESect-14.2 P-30ESect-14.2 P-31ESect-14.2 P-32ESect-14.2 P-33ESect-14.2 P-34ESect-14.2 P-35ESect-14.2 P-36ESect-14.2 P-37ESect-14.2 P-38ESect-14.2 P-39ESect-14.2 P-40ESect-14.2 P-41ESect-14.2 P-42ESect-14.2 P-43ESect-14.2 P-44ESect-14.2 P-45ESect-14.2 P-46ESect-14.2 P-47ESect-14.2 P-48ESect-14.2 P-49ESect-14.2 P-50ESect-14.2 P-51ESect-14.2 P-52ESect-14.2 P-53ESect-14.2 P-54ESect-14.2 P-55ESect-14.2 P-56ESect-14.2 P-57ESect-14.2 P-58ESect-14.2 P-59ESect-14.2 P-60ESect-14.2 P-61ESect-14.2 P-62ESect-14.2 P-63ESect-14.2 P-64ESect-14.2 P-65ESect-14.2 P-66ESect-14.2 P-67ESect-14.2 P-68ESect-14.2 P-69ESect-14.2 P-70ESect-14.2 P-71ESect-14.2 P-72ESect-14.2 P-73ESect-14.2 P-74ESect-14.2 P-75ESect-14.2 P-76ESect-14.3 P-1ESect-14.3 P-2ESect-14.3 P-3ESect-14.3 P-4ESect-14.3 P-5ESect-14.3 P-6ESect-14.3 P-7ESect-14.3 P-8ESect-14.3 P-9ESect-14.3 P-10ESect-14.3 P-11ESect-14.3 P-12ESect-14.3 P-13ESect-14.3 P-14ESect-14.3 P-15ESect-14.3 P-16ESect-14.3 P-17ESect-14.3 P-18ESect-14.3 P-19ESect-14.3 P-20ESect-14.3 P-21ESect-14.3 P-22ESect-14.3 P-23ESect-14.3 P-24ESect-14.3 P-25ESect-14.3 P-26ESect-14.3 P-27ESect-14.3 P-28ESect-14.3 P-29ESect-14.3 P-30ESect-14.3 P-31ESect-14.3 P-32ESect-14.3 P-33ESect-14.3 P-34ESect-14.3 P-35ESect-14.3 P-36ESect-14.3 P-37ESect-14.3 P-38ESect-14.3 P-39ESect-14.3 P-40ESect-14.3 P-41ESect-14.3 P-42ESect-14.3 P-43ESect-14.3 P-44ESect-14.3 P-45ESect-14.3 P-46ESect-14.3 P-47ESect-14.3 P-48ESect-14.3 P-49ESect-14.3 P-50ESect-14.3 P-51ESect-14.3 P-52ESect-14.3 P-53ESect-14.3 P-54ESect-14.3 P-55ESect-14.3 P-56ESect-14.3 P-57ESect-14.3 P-58ESect-14.3 P-59ESect-14.3 P-60ESect-14.3 P-61ESect-14.3 P-62ESect-14.3 P-63ESect-14.3 P-64ESect-14.3 P-65ESect-14.3 P-66ESect-14.3 P-67ESect-14.3 P-68ESect-14.4 P-1ESect-14.4 P-2ESect-14.4 P-3ESect-14.4 P-4ESect-14.4 P-5ESect-14.4 P-6ESect-14.4 P-7ESect-14.4 P-8ESect-14.4 P-9ESect-14.4 P-10ESect-14.4 P-11ESect-14.4 P-12ESect-14.4 P-13ESect-14.4 P-14ESect-14.4 P-15ESect-14.4 P-16ESect-14.4 P-17ESect-14.4 P-18ESect-14.4 P-19ESect-14.4 P-20ESect-14.4 P-21ESect-14.4 P-22ESect-14.4 P-23ESect-14.4 P-24ESect-14.4 P-25ESect-14.4 P-26ESect-14.4 P-27ESect-14.4 P-28ESect-14.4 P-29ESect-14.4 P-30ESect-14.4 P-31ESect-14.4 P-32ESect-14.4 P-33ESect-14.4 P-34ESect-14.4 P-35ESect-14.4 P-36ESect-14.4 P-37ESect-14.4 P-38ESect-14.4 P-39ESect-14.4 P-40ESect-14.4 P-41ESect-14.4 P-42ESect-14.4 P-43ESect-14.4 P-44ESect-14.4 P-45ESect-14.4 P-46ESect-14.4 P-47ESect-14.4 P-48ESect-14.4 P-49ESect-14.5 P-1ESect-14.5 P-2ESect-14.5 P-3ESect-14.5 P-4ESect-14.5 P-5ESect-14.5 P-6ESect-14.5 P-7ESect-14.5 P-8ESect-14.5 P-9ESect-14.5 P-10ESect-14.5 P-11ESect-14.5 P-12ESect-14.5 P-13ESect-14.5 P-14ESect-14.5 P-15ESect-14.5 P-16ESect-14.5 P-17ESect-14.5 P-18ESect-14.5 P-19ESect-14.5 P-20ESect-14.5 P-21ESect-14.5 P-22ESect-14.5 P-23ESect-14.5 P-24ESect-14.5 P-25ESect-14.5 P-26ESect-14.5 P-27ESect-14.5 P-28ESect-14.5 P-29ESect-14.5 P-30ESect-14.5 P-31ESect-14.5 P-32ESect-14.5 P-33ESect-14.5 P-34ESect-14.5 P-35ESect-14.5 P-36ESect-14.5 P-37ESect-14.5 P-38ESect-14.6 P-1ESect-14.6 P-2ESect-14.6 P-3ESect-14.6 P-4ESect-14.6 P-5ESect-14.6 P-6ESect-14.6 P-7ESect-14.6 P-8ESect-14.6 P-9ESect-14.6 P-10ESect-14.6 P-11ESect-14.6 P-12ESect-14.6 P-13ESect-14.6 P-14ESect-14.6 P-15ESect-14.6 P-16ESect-14.6 P-17ESect-14.6 P-18ESect-14.6 P-19ESect-14.6 P-20ESect-14.6 P-21ESect-14.6 P-22ESect-14.6 P-23ESect-14.6 P-24ESect-14.6 P-25ESect-14.6 P-26ESect-14.6 P-27ESect-14.6 P-28ESect-14.6 P-29ESect-14.6 P-30ESect-14.6 P-31ESect-14.6 P-32ESect-14.6 P-33ESect-14.6 P-34ESect-14.6 P-35ESect-14.6 P-36ESect-14.6 P-37ESect-14.6 P-38ESect-14.6 P-39ESect-14.6 P-40ESect-14.6 P-41ESect-14.6 P-42ESect-14.6 P-43ESect-14.6 P-44ESect-14.6 P-45ESect-14.6 P-46ESect-14.6 P-47ESect-14.6 P-48ESect-14.6 P-49ESect-14.6 P-50ESect-14.6 P-51ESect-14.6 P-52ESect-14.6 P-53ESect-14.6 P-54ESect-14.6 P-55ESect-14.6 P-56ESect-14.6 P-57ESect-14.6 P-58ESect-14.6 P-59ESect-14.6 P-60ESect-14.6 P-61ESect-14.6 P-62ESect-14.6 P-63ESect-14.6 P-64ESect-14.6 P-65ESect-14.6 P-66ESect-14.6 P-67ESect-14.6 P-68ESect-14.6 P-69ESect-14.6 P-70ESect-14.6 P-71ESect-14.6 P-72ESect-14.6 P-73ESect-14.7 P-1ESect-14.7 P-2ESect-14.7 P-3ESect-14.7 P-4ESect-14.7 P-5ESect-14.7 P-6ESect-14.7 P-7ESect-14.7 P-8ESect-14.7 P-9ESect-14.7 P-10ESect-14.7 P-11ESect-14.7 P-12ESect-14.7 P-13ESect-14.7 P-14ESect-14.7 P-15ESect-14.7 P-16ESect-14.7 P-17ESect-14.7 P-18ESect-14.7 P-19ESect-14.7 P-20ESect-14.7 P-21ESect-14.7 P-22ESect-14.7 P-23ESect-14.7 P-24ESect-14.7 P-27ESect-14.7 P-29ESect-14.7 P-31ESect-14.7 P-32ESect-14.7 P-33ESect-14.7 P-34ESect-14.7 P-35ESect-14.7 P-36ESect-14.7 P-37ESect-14.7 P-38ESect-14.7 P-39ESect-14.7 P-40ESect-14.7 P-41ESect-14.7 P-43ESect-14.7 P-44ESect-14.7 P-45ESect-14.7 P-46ESect-14.7 P-47ESect-14.8 P-1ESect-14.8 P-2ESect-14.8 P-3ESect-14.8 P-4ESect-14.8 P-5ESect-14.8 P-6ESect-14.8 P-7ESect-14.8 P-8ESect-14.8 P-9ESect-14.8 P-10ESect-14.8 P-11ESect-14.8 P-12ESect-14.8 P-13ESect-14.8 P-14ESect-14.8 P-15ESect-14.8 P-16ESect-14.8 P-17ESect-14.8 P-18ESect-14.8 P-19ESect-14.8 P-20ESect-14.8 P-21ESect-14.8 P-22ESect-14.8 P-23ESect-14.8 P-24ESect-14.8 P-25ESect-14.8 P-26ESect-14.8 P-27ESect-14.8 P-28ESect-14.8 P-29ESect-14.8 P-30ESect-14.8 P-31ESect-14.8 P-32ESect-14.8 P-33ESect-14.8 P-34ESect-14.8 P-35ESect-14.8 P-36ESect-14.8 P-37ESect-14.8 P-38ESect-14.8 P-39ESect-14.8 P-40ESect-14.8 P-41ECh-14 P-1RECh-14 P-2RECh-14 P-3RECh-14 P-4RECh-14 P-5RECh-14 P-6RECh-14 P-7RECh-14 P-8RECh-14 P-9RECh-14 P-10RECh-14 P-11RECh-14 P-12RECh-14 P-13RECh-14 P-14RECh-14 P-15RECh-14 P-16RECh-14 P-17RECh-14 P-18RECh-14 P-19RECh-14 P-20RECh-14 P-21RECh-14 P-22RECh-14 P-23RECh-14 P-24RECh-14 P-25RECh-14 P-26RECh-14 P-27RECh-14 P-28RECh-14 P-29RECh-14 P-30RECh-14 P-31RECh-14 P-32RECh-14 P-33RECh-14 P-34RECh-14 P-35RECh-14 P-36RECh-14 P-37RECh-14 P-38RECh-14 P-39RECh-14 P-40RECh-14 P-41RECh-14 P-42RECh-14 P-43RECh-14 P-44RECh-14 P-45RECh-14 P-46RECh-14 P-47RECh-14 P-48RECh-14 P-49RECh-14 P-50RECh-14 P-51RECh-14 P-52RECh-14 P-53RECh-14 P-54RECh-14 P-55RECh-14 P-56RECh-14 P-57RECh-14 P-59RECh-14 P-60RECh-14 P-61RECh-14 P-62RECh-14 P-63RECh-14 P-64RECh-14 P-65RECh-14 P-66RECh-14 P-67RECh-14 P-68RECh-14 P-69RECh-14 P-70RECh-14 P-71RECh-14 P-72RECh-14 P-73RECh-14 P-74RECh-14 P-75RECh-14 P-76RECh-14 P-77RECh-14 P-78RECh-14 P-1PSCh-14 P-2PSCh-14 P-3PSCh-14 P-4PSCh-14 P-5PSCh-14 P-6PSCh-14 P-7PSCh-14 P-8PSCh-14 P-9PSCh-14 P-10PSCh-14 P-11PSCh-14 P-12PSCh-14 P-14PSCh-14 P-15PSCh-14 P-16PSCh-14 P-18PS

Precalculus: Mathematics for Calculus (Standalone Book)

Finite Mathematics and Applied Calculus (MindTap Course List)

Single Variable Calculus: Early Transcendentals, Volume I

Calculus: Early Transcendentals

Calculus: An Applied Approach (MindTap Course List)

Applied Calculus

Calculus: Early Transcendental Functions

Multivariable Calculus

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Essentials Of Statistics

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Single Variable Calculus

Calculus (MindTap Course List)

Statistics for The Behavioral Sciences (MindTap Course List)

Understanding Basic Statistics

Finite Mathematics

Probability and Statistics for Engineering and the Sciences

Mathematical Excursions (MindTap Course List)

Intermediate Algebra

Mathematical Applications for the Management, Life, and Social Sciences

Single Variable Calculus: Early Transcendentals

Elements Of Modern Algebra

Elementary Technical Mathematics

Elementary Geometry For College Students, 7e

Contemporary Mathematics for Business & Consumers

Trigonometry (MindTap Course List)

Calculus: Early Transcendental Functions (MindTap Course List)

Calculus of a Single Variable

Finite Mathematics for the Managerial, Life, and Social Sciences

Elementary Geometry for College Students