Problem 5.155 y For the machine element shown, locate the z coordinate x 0.75 in z 1 in 2 in 3 in r = 1.25 in For the machine element shown, locate the z coordinate of the center of gravity.

X S V = S x V Y S V = S y V Z S V = S z V 0.75 in z 1 in 2 in 3 in r = 1.25 in Problem 5.155 Solving Problems on Your Own For the machine element shown, locate the z coordinate of the center of gravity. Determine the center of gravity of composite body. For a homogeneous body the center of gravity coincides with the centroid of its volume. For this case the center of gravity can be determined by X S V = S x V Y S V = S y V Z S V = S z V where X, Y, Z and x, y, z are the coordinates of the centroid of the body and the components, respectively.

Determine the center of gravity of composite body. x 0.75 in z 1 in 2 in 3 in r = 1.25 in Problem 5.155 Solution Determine the center of gravity of composite body. First assume that the machine element is homogeneous so that its center of gravity will coincide with the centroid of the corresponding volume. y x z I II III IV V Divide the body into five common shapes.

II (p/2)(2)2 (0.75) = 4.71 7+ [(4)(2)/(3p)] = 7.85 37.0 y x z I II III IV V y x 0.75 in z 1 in 2 in 3 in r = 1.25 in V, in3 z, in. z V, in4 I (4)(0.75)(7) = 21 3.5 73.5 II (p/2)(2)2 (0.75) = 4.71 7+ [(4)(2)/(3p)] = 7.85 37.0 III -p(1.25)2 (0.75)= -3.68 7 -25.8 IV (1)(2)(4) = 8 2 16 V -(p/2)(1.25)2 (1) = -2.45 2 -4.9 S 27.6 95.8 Z S V = S z V : Z (27.6 in3 ) = 95.8 in4 Z = 3.5 in