   Chapter 15.6, Problem 47E

Chapter
Section
Textbook Problem

Set up, but do not evaluate, integral expressions for (a) the mass, (b) the center of mass, and (c) the moment of inertia about the z-axis.47. The solid of Exercise 21;  ρ   ( x ,   y ,   z )   =   x 2 + y 2 21. The solid enclosed by the cylinder y = x2 and the planes z = 0 and y + z = 1

(a)

To determine

To find: The integral expression for the mass and not to evaluate the value.

Explanation

Given:

From exercise 21 notice that, the solid enclose by the cylinder y=x2 and the planes z=0 , y+z=1 and the density is given by ρ(x,y,z)=x2+y2 .

Calculation:

Mass of the solid, mass(m)=density×volume . Here the density is given by ρ(x,y,z)=x2+y2 .

The mass of the solid is, m=liml,m,ni=1lj=1mk=1nρ(xij*,yij*,zij*)ΔA=Eρ(x,y,z)dA

(b)

To determine

To find: The integral expression for the center of mass and not to evaluate the value.

(c)

To determine

To find: The integral expression for the moment of inertia about the z-axis and not to evaluate the value.

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