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Centre of Gravity for Composite Bodies | Engineering Mechanics - Civil Engineering (CE) PDF Download
Locate the center of gravity of the steel machine element. The diameter of each hole is 1 in.
Solution: Form the machine element from a rectangular parallelepiped and a quarter cylinder and then subtracting two 1-in. diameter cylinders.
| Volume,mm3 |  |  |  |  |  |  | |
| I | 70312.5 | 6.25 | -25 | 56.25 | 439,453 | -1,757,813 | 3,955,078 |
| II | 24,553.6 | 33.71 | -21.21 | 6.25 | 827,702 | -520,782 | 153,460 |
| III | -6138.4 | 6.25 | -25 | 87.5 | -38,365 | 153,460 | -537,110 |
| IV | -6138.4 | 6.25 | -25 | 37.5 | -38,365 | 153,460 | 230,190 |
| 82,589.3 | 1190,425 | -1,961,662 | 3,341,238 |
| Shape |  | Volume | |
| Cone |  | h/4 | 1/3 πa2h |
| Pyramid |  | h/4 | 1/3 abh |
| Shape | | Volume | |
| Hemisphere |  | 3a/8 | 2/3πa3 |
| Semiellipsoid of revolution |  | 3h/8 | 2/3πa2h |
| Paraboloid of revolution |  | h/3 | 1/2πa2h |
For the machine element shown, locate the z coordinate of the center of gravity.
| V, in3 |  |  | |
| I | 4*0.75*7=21 | 3.5 | 73.5 |
| II | π/2*22*0.75=4.7124 |  | 36.987 |
| III | -π*1.252*0.75=−3.68 | 7 | -25.76 |
| IV | 1*2*4=8 | 2 | 16 |
| V | −π1.252*1=−2.453 | 2 | -4.906 |
| ∑ | 27.579 | 95.821 |
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FAQs on Centre of Gravity for Composite Bodies - Engineering Mechanics - Civil Engineering (CE)
| 1. What is the concept of the center of gravity for composite bodies? |  |
Ans. The concept of the center of gravity for composite bodies is the calculation of the average position of the weight distribution in a complex object or system. It takes into account the individual center of gravity of each component and their respective masses to determine the overall center of gravity.
| 2. How is the center of gravity determined for composite bodies? | |
Ans. The center of gravity for composite bodies is determined by dividing the sum of the moments of each component's mass by the total mass of the system. The moment of a mass is calculated by multiplying its mass by the distance between its center of gravity and the reference point.
| 3. Can the center of gravity be outside the physical boundaries of a composite body? | |
Ans. Yes, the center of gravity can be outside the physical boundaries of a composite body. This occurs when the individual components have different masses and are positioned in such a way that the resultant center of gravity is located outside the body. It is important to consider this in order to ensure stability and balance in the system.
| 4. How does the center of gravity affect the stability of a composite body? | |
Ans. The center of gravity plays a crucial role in determining the stability of a composite body. If the center of gravity is located within the base of support, the body will be stable. However, if the center of gravity is outside the base of support, the body will be unstable and prone to tipping or toppling over.
| 5. What are the practical applications of understanding the center of gravity for composite bodies? | |
Ans. Understanding the center of gravity for composite bodies has various practical applications. It is essential in designing stable structures, such as buildings and bridges, to ensure they can withstand external forces without collapsing. It is also important in fields like engineering, sports, and transportation, where stability and balance are critical factors for performance and safety.
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