Center of Mass In Exercises 37-40, find the mass and the indicated coordinate of the center of mass of the solid region Q of density ρ bounded by the graphs of the equations. Find z ¯ using ρ ( x , y , z ) = k x Q : z = 4 − x , z = 0 , y = 0 , y = 4 , x = 0
Center of Mass In Exercises 37-40, find the mass and the indicated coordinate of the center of mass of the solid region Q of density ρ bounded by the graphs of the equations. Find z ¯ using ρ ( x , y , z ) = k x Q : z = 4 − x , z = 0 , y = 0 , y = 4 , x = 0
Solution Summary: The author explains how to calculate the mass and coordinate of the center of mass of a solid region.
Center of Mass In Exercises 37-40, find the mass and the indicated coordinate of the center of mass of the solid region Q of density
ρ
bounded by the graphs of the equations.
Express the mass of a solid tetrahedron T, with vertices (0,0,0), (3,0,0), (3,3,0) and (3,0,2) with density function ρ(x,y,z)=6xyz as a triple integral.
The motion of a solid object can be analyzed by thinking of the mass as concentrated at a single
point, the center of mass. If the object has density p(x, y, z) at the point (x, y, z) and occupies a region
W, then the coordinates (, y, z) of the center of mass are given by
1
1
1
zpdV
yp dV z
zpdV,
т
т
т
where m = Sw pdV is the total mass of the body.
Consider a solid is bounded below by the square z = 0,0 < x < 3,0 < y < 1 and above by the
surface z = x + y +3. Let the density of the solid be 1 g/cm, with x, y, z measured in cm. Find each
of the following:
The mass of the solid = 9 gm
a for the solid = 11/4 cm
y for the solid =
z for the solid =
(For each, include units.)
Chapter 14 Solutions
Student Solutions Manual For Larson/edwards? Multivariable Calculus, 11th
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