6.2.2 To be able to find the center of gravity, the center of mass, and the centroid of a composite body. A centroid is an object's geometric center. For an object of uniform composition, its centroid is also its center of mass. Often the centroid of a complex composite body is found by, first, cutting the body into regular shaped segments, and then by calculating the weighted average of the segments" centroids. An object is made from a uniform piece of sheet metal. The object has dimensions of a = 1.70 ftft, where a is the diameter of the semi-circle.b. = 2.81 ftft, and c = 1.95 ft. A hole with diameter d = 0.750 ftft is centered at (1.25,0.850)(1.25,0.850). L Part A k-d-* A = 4.00 in IT vec 3 -1.25 in Find the area of the body. (Figure 1) Express your answer numerically in feet squared to three significant figures. ▸ View Available Hint(s) ΠΫΠΙ ΑΣΦ EWO y ? ft² Part B Find , the x-coordinate of the body's centroid. (Eigure 1) Express your answer numerically in feet to three significant figures. ▸ View Available Hint(s) 195] ΑΣΦ | 11 | vec ← 7- Part C Find y, the y-coordinate of the body's centroid. (Eigure 1) Express your answer numerically in feet to three significant figures. ► View Available Hint(s) 195] ΑΣΦΗ y= Part D vec 3 ? ? ft ft A single-scoop ice cream cone is a composite body made from a single scoop of ice cream placed into a cone. (Figure 2) Assume that the scoop of ice cream is a sphere with radius r= 1.55in that is placed into a 4.00 in tall cone. The interior height of the cone is 3.60 in. The cone has an exterior radius of 1.25 in and an interior radius of 1.10 in. The scoop of ice cream sits on the cone's interior radius and extends into the cone some distance. Find the centroid for the cone (the scoop of ice cream and the cone). Express your answer numerically in inches to three significant figures. ▸ View Available Hint(s)
6.2.2 To be able to find the center of gravity, the center of mass, and the centroid of a composite body. A centroid is an object's geometric center. For an object of uniform composition, its centroid is also its center of mass. Often the centroid of a complex composite body is found by, first, cutting the body into regular shaped segments, and then by calculating the weighted average of the segments" centroids. An object is made from a uniform piece of sheet metal. The object has dimensions of a = 1.70 ftft, where a is the diameter of the semi-circle.b. = 2.81 ftft, and c = 1.95 ft. A hole with diameter d = 0.750 ftft is centered at (1.25,0.850)(1.25,0.850). L Part A k-d-* A = 4.00 in IT vec 3 -1.25 in Find the area of the body. (Figure 1) Express your answer numerically in feet squared to three significant figures. ▸ View Available Hint(s) ΠΫΠΙ ΑΣΦ EWO y ? ft² Part B Find , the x-coordinate of the body's centroid. (Eigure 1) Express your answer numerically in feet to three significant figures. ▸ View Available Hint(s) 195] ΑΣΦ | 11 | vec ← 7- Part C Find y, the y-coordinate of the body's centroid. (Eigure 1) Express your answer numerically in feet to three significant figures. ► View Available Hint(s) 195] ΑΣΦΗ y= Part D vec 3 ? ? ft ft A single-scoop ice cream cone is a composite body made from a single scoop of ice cream placed into a cone. (Figure 2) Assume that the scoop of ice cream is a sphere with radius r= 1.55in that is placed into a 4.00 in tall cone. The interior height of the cone is 3.60 in. The cone has an exterior radius of 1.25 in and an interior radius of 1.10 in. The scoop of ice cream sits on the cone's interior radius and extends into the cone some distance. Find the centroid for the cone (the scoop of ice cream and the cone). Express your answer numerically in inches to three significant figures. ▸ View Available Hint(s)
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
I have parts A and C correct, but can I get help with B and D. The answer for A is 3.21 ft^2 and answer for C is 0.778ft. Thank you
On part B, I keep getting 0.805 ft for the x coordinate
On part D, I keep getting 0.924 in for z-centroid
B and D are incorrect
![6.2.2
To be able to find the center of gravity, the center of mass, and the centroid of a composite body.
A centroid is an object's geometric center. For an object of uniform composition, its centroid is also its
center of mass. Often the centroid of a complex composite body is found by, first, cutting the body
into regular shaped segments, and then by calculating the weighted average of the segments'
centroids. An object is made from a uniform piece of sheet metal. The object has dimensions of a =
1.70 ftft where a is the diameter of the semi-circle.b. = 2.81 ftft, and c = 1.95 ftft. A hole with
diameter d = 0.750 ftft is centered at (1.25,0.8501(1.25,0.850).
Part A
k-d-
A =
X
4.00 in
Find the area of the body. (Figure 1)
Express your answer numerically in feet squared to three significant figures.
▸ View Available Hint(s)
[5] ΑΣΦ
↓↑ vec
-1.25 in
?
ft²
Part B
Find , the x-coordinate of the body's centroid. (Figure 1)
Express your answer numerically in feet to three significant figures.
► View Available Hint(s)
IVE] ΑΣΦ ↓↑ vec
z =
Part C
Find y, the y-coordinate of the body's centroid. (Figure 1)
Express your answer numerically in feet to three significant figures.
► View Available Hint(s)
VE ΑΣΦ
y =
Part D
↓↑ vec
AΣo↓ vec
C
www.
P ?
?
?
A single-scoop ice cream cone is a composite body made from a single scoop of ice cream placed into a cone
(Figure 2) Assume that the scoop of ice cream is a sphere with radius r = 1.55in that is placed into a 4.00 in
tall cone. The interior height of the cone is 3.60 in. The cone has an exterior radius of 1.25 in and an interior
radius of 1.10 in. The scoop of ice cream sits on the cone's interior radius and extends into the cone some
distance. Find the centroid for the cone (the scoop of ice cream and the cone).
Express your answer numerically in inches to three significant figures.
► View Available Hint(s)
in
ft
ft](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4b096e23-0624-436f-a8d4-1120c037fff2%2F9c969d31-8647-4466-a91d-fac7a7ac0455%2Fiiauqap_processed.png&w=3840&q=75)
Transcribed Image Text:6.2.2
To be able to find the center of gravity, the center of mass, and the centroid of a composite body.
A centroid is an object's geometric center. For an object of uniform composition, its centroid is also its
center of mass. Often the centroid of a complex composite body is found by, first, cutting the body
into regular shaped segments, and then by calculating the weighted average of the segments'
centroids. An object is made from a uniform piece of sheet metal. The object has dimensions of a =
1.70 ftft where a is the diameter of the semi-circle.b. = 2.81 ftft, and c = 1.95 ftft. A hole with
diameter d = 0.750 ftft is centered at (1.25,0.8501(1.25,0.850).
Part A
k-d-
A =
X
4.00 in
Find the area of the body. (Figure 1)
Express your answer numerically in feet squared to three significant figures.
▸ View Available Hint(s)
[5] ΑΣΦ
↓↑ vec
-1.25 in
?
ft²
Part B
Find , the x-coordinate of the body's centroid. (Figure 1)
Express your answer numerically in feet to three significant figures.
► View Available Hint(s)
IVE] ΑΣΦ ↓↑ vec
z =
Part C
Find y, the y-coordinate of the body's centroid. (Figure 1)
Express your answer numerically in feet to three significant figures.
► View Available Hint(s)
VE ΑΣΦ
y =
Part D
↓↑ vec
AΣo↓ vec
C
www.
P ?
?
?
A single-scoop ice cream cone is a composite body made from a single scoop of ice cream placed into a cone
(Figure 2) Assume that the scoop of ice cream is a sphere with radius r = 1.55in that is placed into a 4.00 in
tall cone. The interior height of the cone is 3.60 in. The cone has an exterior radius of 1.25 in and an interior
radius of 1.10 in. The scoop of ice cream sits on the cone's interior radius and extends into the cone some
distance. Find the centroid for the cone (the scoop of ice cream and the cone).
Express your answer numerically in inches to three significant figures.
► View Available Hint(s)
in
ft
ft
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