Concept explainers
Centroid of the surface generated by revolving the parabola about y axis
Answer to Problem 8.74P
The centroid
Explanation of Solution
Given information:
The centroid of the surface is defined as:
Calculation:
Consider the surface element, a ring obtained by rotating the line of length
We know that
Differentiate
The differential area
The centroidal coordinate
The area A of the element
The first moment
Apply Simpson's rule to evaluate above integrals.
x (m) | y (m) | | |
0 | 0 | 0 | 0 |
1 | 0.1875 | 1.068 | 0.20025 |
2 | 0.75 | 2.5 | 1.875 |
3 | 1.6875 | 4.5155 | 7.62 |
4 | 3.0 | 7.211 | 21.633 |
The Area A of the element
The first moment
The point of action
Due to symmetry
Conclusion:
The centroid
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Chapter 8 Solutions
International Edition---engineering Mechanics: Statics, 4th Edition
- Determine the centroidal z-coordinate of the curved surface of the half cone by integration.arrow_forwardUse numerical integration to find the centroid of the volume generated by revolving the area shown about the x-axis.arrow_forwardLocate the centroid of the volume generated by revolving the area shown about the line AB. Use numerical integration.arrow_forward
- Using the method of composite areas, find the dimension h that maximizes the centroid coordinate y of the plane region shown.arrow_forwardUse integration to compute the z-coordinate of the centroid of the half cone.arrow_forwardThe picture board and its triangular supporting bracket form a composite surface. Calculate the height h of the support that minimizes the centroidal z-coordinate of the assembly.arrow_forward
- International Edition---engineering Mechanics: St...Mechanical EngineeringISBN:9781305501607Author:Andrew Pytel And Jaan KiusalaasPublisher:CENGAGE L