Center of Mass In Exercises 59 and 60, find the mass and the indicated coordinate of the center of mass of the solid region Q of density bounded by the graphs of the equations.
Find using .
To calculate: The mass and the indicated coordinate of center of mass of solid region with density given as . The solid region is bounded by the graph of the equation .
The density of solid region is and the solid is bounded by the graph of equation,
Mass of a solid region having density is,
First moment about plane is,
Coordinate of center of mass of a solid region is,
A 3-D plot is made with the help of maple software,
The limits of and can be calculated with the help of this 3-D plot.
Take the provided equation of the solid into consideration.
The upper limit of can be calculated from the above equation as follows:
If value of and are zero, then,
Thus, the upper limit of is and bounds of is .
Take the plane into consideration.
In this case, since the value of , the equation of the line will be given as,
Also, as depends on both and , the equation of contain both and
On subtracting from both sides, we get,
The lower limit of is provided in the question, i.e.,
On applying the formula for the mass of solid body , we get,
Next, on integrating with respect to , we get,
Further, on integrating with respect to , we get,
Therefore, mass of the solid body is calculated to be
Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!Get Started
Calculus: An Applied Approach (MindTap Course List)
Calculus: Early Transcendental Functions
Calculus: Early Transcendentals
Finite Mathematics and Applied Calculus (MindTap Course List)
Single Variable Calculus: Early Transcendentals, Volume I
Precalculus: Mathematics for Calculus (Standalone Book)
Essentials Of Statistics
Essentials of Statistics for The Behavioral Sciences (MindTap Course List)
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
Calculus (MindTap Course List)
Understanding Basic Statistics
Statistics for The Behavioral Sciences (MindTap Course List)
Single Variable Calculus
Mathematical Excursions (MindTap Course List)
Mathematical Applications for the Management, Life, and Social Sciences
Probability and Statistics for Engineering and the Sciences
Single Variable Calculus: Early Transcendentals
Contemporary Mathematics for Business & Consumers
Elementary Technical Mathematics
Elementary Geometry For College Students, 7e
Elements Of Modern Algebra
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