Explanation Calculation: Sketch the machine element as shown in Figure 1. Refer to Figure 1. Consider the sections I, II, III, IV, and V. The radius of half cylinder IV is R = 1.5 in . . The radius of the half cylinder III and cylinder V is r = 0.95 in . . Calculate the sum of the volume and centroid as shown below. Reducing the volume ( V ) of the half cylinder (section III) and cylinder (section V) from the summation of remaining sections. Sum = Volume of ( I + II − III + IV − V ) . Calculate the volume and centroid of the each section as shown below. Section Shape Volume ( in 3 ) y ¯ , in . y ¯ V , in 4 I Rectangular plate 5.25 × 3 × 0.5 = 7.875 − 0.5 2 = − 0.25 − 1.96875 II Rectangular plate 3 × 1.5 × 0.75 = 3.375 1.5 2 = 0.75 2.53125 III Half cylinder π × 0.95 2 × 0.75 2 = 1.063 1.5 − 4 × 0.95 3 π = 1.0968 1.1659 IV Half cylinder π × 1.5 2 × 0.5 2 = 1.767 − 0.5 2 = − 0.25 − 0.44175 V Cylinder π × 0.95 2 × 0.5 = 1

Vector Mechanics for Engineers: Statics, 11th Edition

11th Edition

ISBN: 9780077687304

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek

Publisher: McGraw-Hill Education

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Chapter 5.4, Problem 5.102P

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Find the location of the y coordinate of the center of gravity.

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Chapter 5.4, Problem 5.101P

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