. - Component B occupies the region outside the sphere r=2 cos (p) and inside the sphere r=2 with € [0, π/2]. Assume B has a uniform density of PB.. Component C is a curved wedge that lies inside the region enclosed by the cylinder (x-2)²+y²=4 and the planes z=0 and z = -y. Assume C has a uniform density of ec " ii. Sketch B and C.
. - Component B occupies the region outside the sphere r=2 cos (p) and inside the sphere r=2 with € [0, π/2]. Assume B has a uniform density of PB.. Component C is a curved wedge that lies inside the region enclosed by the cylinder (x-2)²+y²=4 and the planes z=0 and z = -y. Assume C has a uniform density of ec " ii. Sketch B and C.
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
Please hand sketch Component B and C

Transcribed Image Text:MAST20029 Engineering Mathematics Formulae Sheet
1. Change of Variable of Integration in 2D
JJ₁ f(x, y) dxdy = [[ f(x(u, v), y(u, v))|J(u, v)| dudv
R
2. Transformation to Polar Coordinates
x = r cos 0,
3. Change of Variable of Integration in 3D
[[[ f(x, y, z) dadydz
4. Transformation to Cylindrical Coordinates
x = r cos 0, y = r sin 0,
5. Transformation to Spherical Coordinates
7. Work Integrals
y = r sin 0,
LFG
8. Surface Integrals
x = r cos sin o, y = r sin sin o, z = r cos o,
=
= [[[_ F(u, v), w)|J(u, v, w) dudvdw
[[₁, g(x, y, z) ds =
S
J(r,0) =
6. Line Integrals
Jo
f(x, y, 2) ds = ["* f(x(t), y(t), z(t)) √x'(t)² + y(t)}² + 2'(t)² dt
F(x, y, z). dr =
J(r, 0, z) = r
= r
cb dx
- [² R² +F="/
F₁ F₂
dt
a
F. ÂdS =
J(r, 0, 0) = r² sin o
9. Flux Integrals For a surface with upward unit normal,
11. F
+ F3
dz
= [[ g(x, y, f (x, y)) √[f² + f² +1dxdy
dt
= SS₁₂ - ²
-F₁fx - F2fy + F3 dydx
![Component A is bounded by the planes x=0, x=2, z=-y and z=
i. Sketch A and find its volume.
بوعان
Components B and C have different geometries and density but must be designed to have equal mass.
• Component B occupies the region outside the sphere r = 2 cos(p) and inside the sphere r=2 with = [0, π/2]. Assume B has a
uniform density of
PB.
· Component C is a curved wedge that lies inside the region enclosed by the cylinder (x-2)² + y²=4 and the planes z=0 and z = −y.
Assume C has a uniform density of Pe
ii. Sketch B and C.
Find the volume of B and C, and the ratio PB / PC to achieve equal mass.
iv. Find the flux of F across S, the surface of C, given that
F(x₁412) = [2x + cosh (Sy²)] i + [zxe*_6z]; +[1 + xy² ] K
V. What is the flux of F across the surface of a spherical body if F2,4₁2) = Ak
, where A is a real and negative constant?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F12fdac56-4b52-4434-8b00-5772085cd8ad%2F98eb042c-15f3-4314-ac9f-28d0afd8e821%2F85sqn4t_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Component A is bounded by the planes x=0, x=2, z=-y and z=
i. Sketch A and find its volume.
بوعان
Components B and C have different geometries and density but must be designed to have equal mass.
• Component B occupies the region outside the sphere r = 2 cos(p) and inside the sphere r=2 with = [0, π/2]. Assume B has a
uniform density of
PB.
· Component C is a curved wedge that lies inside the region enclosed by the cylinder (x-2)² + y²=4 and the planes z=0 and z = −y.
Assume C has a uniform density of Pe
ii. Sketch B and C.
Find the volume of B and C, and the ratio PB / PC to achieve equal mass.
iv. Find the flux of F across S, the surface of C, given that
F(x₁412) = [2x + cosh (Sy²)] i + [zxe*_6z]; +[1 + xy² ] K
V. What is the flux of F across the surface of a spherical body if F2,4₁2) = Ak
, where A is a real and negative constant?
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