   Chapter 14, Problem 37RE

Chapter
Section
Textbook Problem

Finding the Center of MassIn Exercises 37–40, find the mass and center of mass of the lamina bounded by the graphs of the equations for the given density. y = x 3 ,     y = 0 ,     x = 2 ,     ρ = k x

To determine

To calculate: The center of mass of given lamina is bounded by y=x3, y=0 and x=2.

Explanation

Given:

The lamina is bounded by y=x3, y=0 and x=2.

The density is ρ(x,y)=kx.

Formula used:

x¯=MYm,y¯=MXm

MY=Qxρ(x,y)dA is the moment of mass with respect to Y axis.

MX=Qyρ(x,y)dA is the moment of mass with respect to X axis.

m=Qρ(x,y)dA is the mass of the lamina, where ρ(x,y) is the density of the solid.

Calculation:

Plot the graph of equations y=x3, y=0 and x=2.

y=0 represents x- axis, x=2 represents vertical line parallel to y-axis intersecting x- axis at x=2.

y=x3 represents simple cubic curve,

For mass of lamina,

m=Qρ(x,y)dA=08y132kxdxdy=(k2)08[x2]y132dy=(k2)08(4y23)dy

Solve further,

m=(k2)[4y3y535]08=(325)k

Now,

MY=Qxρ(x,y)dA<

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Are the following graphs of functions? Explain. a. b. c. d.

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

In problems 1-4, fnd the powers and roots,if they are real numbers. 4. (a) ...

Mathematical Applications for the Management, Life, and Social Sciences

Evaluate the integral. 28. 02t2sin2tdt

Single Variable Calculus: Early Transcendentals

Name the four components of a mathematical system.

Elementary Geometry For College Students, 7e 