Four very thin rods, each 9.0 m long, are joined to form asquare, as part (a) of

Question

Four very thin rods, each 9.0 m long, are joined to form asquare, as part (a) of the drawing shows. The center of mass of thesquare is located at the coordinate origin. The rod on the right isthen removed, as shown in part (b) of the drawing. What are the x-and y-coordinates of the center of mass of the remaining three-rodsystem? Give your answer to two significant figures and include aminus sign if the answer is negative, e.g., 1.3 or -0.65. I have no clue where I'm supposed to start. Any helpwould be greatly appreciated!

Explanation / Answer

Let     mass of each rod , m = M     length of each rod , L = 9 m Case(a): ( with all four rods )     Total mass, m1 = 4 M     X-coordinate of center of mass , X1 =0     Y-coordinate of center of mass , Y1 =0 Case (b) : ( for the removed rod )     mass, m2 = M     X-coordinate of center of mass , X2 =L / 2 = 9 /2 = 4.5 m     Y-coordinate of center of mass , Y2 =0 Center of mass of the removed part:     X-coordinate of center of mass , Xcm = (m1 X1 - m2 X2 ) / ( m1- m2 )                                                                = ( 4 M * 0 - M * 4.5 ) / ( 4 M - M )                                                                = - 1.5 m     Y-coordinate of center of mass , Ycm = (m1 Y1 - m2 Y2 ) / ( m1- m2 )                                                                = ( 4 M * 0 - M * 0 ) / ( 4 M - M )                                                                = 0 m

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