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Center of gravity

Center of gravity. For n particles fixed within a region of space Weights of particles comprise system of parallel forces Can be replaced by a single resultant weight (W R = ∑ W) at a defined point of application, G (the center of gravity) Determination of SHOW

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Center of gravity

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  1. Center of gravity • For n particles fixed within a region of space • Weights of particles comprise system of parallel forces • Can be replaced by a single resultant weight (WR = ∑ W) at a defined point of application, G (the center of gravity) • Determination of SHOW • For a system of particles composing a body • Each particle located at has a differential weight, dW • Integration is required rather than a discrete summation of terms • Substituting dW = γ dV into previous equations • γ = specific weight of body (weight per unit volume)

  2. Centroid • Centroid is the geometric center of an object • If material composing body is uniform (homogenous), then γis constant throughout body → it can be factored out of the integrals shown on previous slide • for volume • for area (thickness is constant) • for line (area is constant) • EXAMPLES (pg 466)

  3. Composite bodies • Composite bodies consist of a series of connected “simpler” shaped bodies (rectangular, triangular, semicircular, …) • The body can be sectioned into its composite parts, knowing the density or specific weight and center of gravity of each composite part, the center of gravity of the body can be determined • Centroid for composite volumes, areas, and lines can be found using relations similar to the above • EXAMPLES (pg 480)

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