GIVEN: Constant a > 0 W is the solid cube with edge length, a. 0 ≤ x ≤ a • forma {(x, y, z)|0 ≤ y ≤ a 0 ≤ z ≤ a W = Q= Top face of W. The square face where z = a at every point on it. oriented with unit normal pointing away from the interior of W; note that n = 2 on 9. Xx n = 2 F = (x, y, z) FIND: The flux of F through with out - ward normal, n flux = F.dS Ω: = top surface Z = (0,0,1) W Y
GIVEN: Constant a > 0 W is the solid cube with edge length, a. 0 ≤ x ≤ a • forma {(x, y, z)|0 ≤ y ≤ a 0 ≤ z ≤ a W = Q= Top face of W. The square face where z = a at every point on it. oriented with unit normal pointing away from the interior of W; note that n = 2 on 9. Xx n = 2 F = (x, y, z) FIND: The flux of F through with out - ward normal, n flux = F.dS Ω: = top surface Z = (0,0,1) W Y
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
for the first image attach please do the calculations similar to the second image attach
please please answer everything correctly I would really appreciate if you would answer
this is not a graded question
![[10] (4)
GIVEN: Constant a > 0
W is the solid cube with edge length, a.
0 ≤ x ≤ a
W
=
(x, y, z)|0 ≤ y ≤ a
xelo
0 ≤ z ≤ a
= Top face of W.
The square face where z = a
at every point on it.
oriented with unit normal
pointing away from
the interior of W;
note that n =
on Q.
X
ñ = 2 A
F = (x,- y, z)
FIND: The flux of F through with out - ward normal, n
flux = SF•.dS
Z
|
Ω
n
Ω
= top surface
=
Z = (0,0,1)
W
Y](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe343d170-4423-4dcd-9c75-f5f0118e0ff9%2Fac12ac61-df6c-4542-88db-5a629c056d9d%2Faqw4lyb_processed.png&w=3840&q=75)
Transcribed Image Text:[10] (4)
GIVEN: Constant a > 0
W is the solid cube with edge length, a.
0 ≤ x ≤ a
W
=
(x, y, z)|0 ≤ y ≤ a
xelo
0 ≤ z ≤ a
= Top face of W.
The square face where z = a
at every point on it.
oriented with unit normal
pointing away from
the interior of W;
note that n =
on Q.
X
ñ = 2 A
F = (x,- y, z)
FIND: The flux of F through with out - ward normal, n
flux = SF•.dS
Z
|
Ω
n
Ω
= top surface
=
Z = (0,0,1)
W
Y
![[15] (3)
GIVEN: constants a > 0
W is the solid cube with edge length, a.
0 ≤ x ≤
≤ y ≤ a
0 ≤z≤ a
W has constant density, S, and total mass, M.
Let L be the axis of about which
we want to calculate
the moment of inertia.
GIVEN: L = z-axis.
FIND: The moment of inertia of W w.r.t, L, I₂
(Express I in terms of a and M)
NOTE: V(W) = a³
I₂ = [(x² + y²) S dv
W
=
(x, y, z) 0
=
= 28 √ √ x²dv
W
= 28
=
||
X
s [ x ² dv + S√√ y ² d
S
L = 2-axis
a
a
28 √ ² √ ² √ ªz ² d z dy dz
x
2
Ma²
a
a
2
=
28 (√² x ²4x) ([² 4 ) ( ["dz)
:) (6
25 ( 1 a ²)(a)(a)
5
2011 (10³)
M
a
a³
Z
|
|
|
Note: If W is a solid of revolution about L,
then the computation of I may benefit
from the Cylindrical Transformation.
W
Y](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe343d170-4423-4dcd-9c75-f5f0118e0ff9%2Fac12ac61-df6c-4542-88db-5a629c056d9d%2Fos3yia_processed.png&w=3840&q=75)
Transcribed Image Text:[15] (3)
GIVEN: constants a > 0
W is the solid cube with edge length, a.
0 ≤ x ≤
≤ y ≤ a
0 ≤z≤ a
W has constant density, S, and total mass, M.
Let L be the axis of about which
we want to calculate
the moment of inertia.
GIVEN: L = z-axis.
FIND: The moment of inertia of W w.r.t, L, I₂
(Express I in terms of a and M)
NOTE: V(W) = a³
I₂ = [(x² + y²) S dv
W
=
(x, y, z) 0
=
= 28 √ √ x²dv
W
= 28
=
||
X
s [ x ² dv + S√√ y ² d
S
L = 2-axis
a
a
28 √ ² √ ² √ ªz ² d z dy dz
x
2
Ma²
a
a
2
=
28 (√² x ²4x) ([² 4 ) ( ["dz)
:) (6
25 ( 1 a ²)(a)(a)
5
2011 (10³)
M
a
a³
Z
|
|
|
Note: If W is a solid of revolution about L,
then the computation of I may benefit
from the Cylindrical Transformation.
W
Y
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