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Unformatted text preview: Thevalingam, Donald Homework 22 Due: Mar 19 2007, midnight Inst: Eslami 1 This printout should have 4 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points A uniform flat plate of metal with a circular hole is situated in the reference frame shown in the figure below. 10 8 6 4 2 2 4 6 8 10 10 8 6 4 2 2 4 6 8 10 Calculate the xcoordinate of the center of mass x cm of the metal plate. Correct answer: 1 . 53215 . Explanation: Basic Concept: The center of mass coor dinate is x cm x i m i m i Z xdm M , (1) where M Z dm, dm = y dx, and is the areal density mass area of the plate. Solution: Let : y = 8 , y = 2 y = 2 (8) = 16 , x 1 = 5 , x 2 = 8 , A r = [ x 2 x 1 ] ( y ) = [(8) ( 5)] (16) = 208 x r = [ x 2 + x 1 ] 2 = [(8) + ( 5)] 2 = 1 . 5 A c = r 2 = (2) 2 = 12 . 5664 x c = 1 , and r = 2 , Since the plate is symmetry about the x axis, the ycoordinate of the center of mass must fall on the xaxis, y cm = 0 . Using the definition of x cm from Eq. 1, we have x cm = A r x r A c x c A r A c = (208) (1 . 5) + (12 . 5664) (1) (208) (12 . 5664) = 1 . 53215 ....
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