Concept explainers
(a)
Centroid of the volume generated by revolving the area shown about x axis
Answer to Problem 8.73P
The centroid
Explanation of Solution
Given information:
The centroid of the volume is defined as:
Calculation:
Consider a thin shell element generated by rotating the shaded area about x axis.
The differentiate volume
The centroidal coordinate
The volume V of the element
The first moment
Apply Simpson's rule to evaluate above integrals.
x (in) | y (in) | | |
0 | 0 | 0 | 0 |
2 | 4.9 | 24 | 48 |
4 | 6.93 | 48 | 192 |
6 | 8.49 | 72 | 432.5 |
8 | 9.8 | 96 | 768.5 |
10 | 10.95 | 120 | 1199 |
12 | 12 | 144 | 1728 |
The volume V of the element
The first moment
The point of action
Due to symmetry
Conclusion:
The centroid
(b)
Assume curve OB is a parabola and verify the result found on part a
Answer to Problem 8.73P
The results obtained at sub part 'a' is equal to the results in sub part 'b'.
Explanation of Solution
Given information:
According to table 8.3
Paraboloid of revolution:
Calculation:
The volume V
Substitute and solve
The point of action
The results obtained at sub part 'a' is equal to the results in sub part 'b'.
Conclusion:
The results obtained at sub part 'a' is equal to the results in sub part 'b'.
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Chapter 8 Solutions
International Edition---engineering Mechanics: Statics, 4th Edition
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- International Edition---engineering Mechanics: St...Mechanical EngineeringISBN:9781305501607Author:Andrew Pytel And Jaan KiusalaasPublisher:CENGAGE L