# ch09 - Engineering Mechanics: Statics Chapter 9: Center of...

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Unformatted text preview: Engineering Mechanics: Statics Chapter 9: Center of Gravity and Centroid Chapter Objectives To discuss the concept of the center of gravity, center of mass, and the centroid. To show how to determine the location of the center of gravity and centroid for a system of discrete particles and a body of arbitrary shape. To use the theorems of Pappus and Guldinus for finding the area and volume for a surface of revolution. To present a method for finding the resultant of a general distributed loading and show how it applies to finding the resultant of a fluid. Chapter Outline Center of Gravity and Center of Mass for a System of Particles Center of Gravity and Center of Mass and Centroid for a Body Composite Bodies Theorems of Pappus and Guldinus Resultant of a General Distributed Loading Fluid Pressure 9.1 Center of Gravity and Center of Mass for a System of Particles Center of Gravity Locates the resultant weight of a system of particles Consider system of n particles fixed within a region of space The weights of the particles comprise a system of parallel forces which can be replaced by a single (equivalent) resultant weight having defined point G of application 9.1 Center of Gravity and Center of Mass for a System of Particles Center of Gravity Resultant weight = total weight of n particles Sum of moments of weights of all the particles about x, y, z axes = moment of resultant weight about these axes Summing moments about the x axis, Summing moments about y axis, n n R n n R R W y W y W y W y W x W x W x W x W W ~ ... ~ ~ ~ ... ~ ~ 2 2 1 1 2 2 1 1 + + + = + + + = = 9.1 Center of Gravity and Center of Mass for a System of Particles Center of Gravity Although the weights do not produce a moment about z axis, by rotating the coordinate system 90 about x or y axis with the particles fixed in it and summing moments about the x axis, Generally, m m z z m m y y m m x x W z W z W z W z n n R = = = + + + = ~ , ~ ; ~ ~ ... ~ ~ 2 2 1 1 9.1 Center of Gravity and Center of Mass for a System of Particles Center of Gravity Where represent the coordinates of the center of gravity G of the system of particles, represent the coordinates of each particle in the system and represent the resultant sum of the weights of all the particles in the system....
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## ch09 - Engineering Mechanics: Statics Chapter 9: Center of...

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