Learning Goal: 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 = 1.50 ft, where a is the diameter of the semi-circle.b = 3.71 ft and c 2.35 ft. A hole with diameter d=0.750 ft is centered at (1.21, 0.750) Find the area of the body. (Figure 1) Express your answer numerically in feet squared to three significant figures. Find x, the x-coordinate of the body's centroid. (Figure 1) Express your answer numerically in feet to three significant figures. Find y, the y-coordinate of the body's centroid. (Figure 1) Express your answer numerically in feet to three significant figures. 4.00 in 1.25 in 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=1.64in 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 z centroid for the cone (the scoop of ice cream and the cone). Express your answer numerically in inches to three significant figures.
Learning Goal: 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 = 1.50 ft, where a is the diameter of the semi-circle.b = 3.71 ft and c 2.35 ft. A hole with diameter d=0.750 ft is centered at (1.21, 0.750) Find the area of the body. (Figure 1) Express your answer numerically in feet squared to three significant figures. Find x, the x-coordinate of the body's centroid. (Figure 1) Express your answer numerically in feet to three significant figures. Find y, the y-coordinate of the body's centroid. (Figure 1) Express your answer numerically in feet to three significant figures. 4.00 in 1.25 in 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=1.64in 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 z centroid for the cone (the scoop of ice cream and the cone). Express your answer numerically in inches to three significant figures.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Learning Goal:
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 = 1.50 ft, where a is the diameter of the semi-circle.b = 3.71 ft
and c 2.35 ft. A hole with diameter d=0.750 ft is centered at
(1.21, 0.750)
Find the area of the body. (Figure 1)
Express your answer numerically in feet squared to three significant figures.
Find x, the x-coordinate of the body's centroid. (Figure 1)
Express your answer numerically in feet to three significant figures.
Find y, the y-coordinate of the body's centroid. (Figure 1)
Express your answer numerically in feet to three significant figures.
4.00 in
1.25 in
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=1.64in 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 z centroid for the cone
(the scoop of ice cream and the cone).
Express your answer numerically in inches to three significant figures.
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