5 - 2 Our notation is as follows x1 = 0 and y1 = 0 are the...

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2. Our notation is as follows: x 1 = 0 and y 1 = 0 are the coordinates of the m 1 = 3.0 kg particle; x 2 = 2.0 m and y 2 = 1.0 m are the coordinates of the m 2 = 4.0 kg particle; and, x 3 = 1.0 m and y 3 = 2.0 m are the coordinates of the m 3 = 8.0 kg particle. (a) The x coordinate of the center of mass is () ( ) ( ) 11 2 2 33 com 123 0 4.0 kg 2.0 m 8.0 kg 1.0 m 1.1 m. 3.0 kg 4.0 kg 8.0 kg mx x mmm ++ == = + + (b) The y coordinate of the center of mass is ( ) ( ) com 0 4.0 kg 1.0 m 8.0 kg 2.0 m 1.3m. 3.0 kg 4.0 kg 8.0 kg my my my y = + + (c) As the mass of m 3 , the topmost particle, is increased, the center of mass shifts toward that particle. As we approach the limit where m 3 is infinitely more massive than the others, the center of mass becomes infinitesimally close to the position of m 3 .
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3. Since the plate is uniform, we can split it up into three rectangular pieces, with the mass of each piece being proportional to its area and its center of mass being at its geometric center. We’ll refer to the large 35 cm × 10 cm piece (shown to the left of the y axis in Fig. 9-38) as section 1; it has 63.6% of the total area and its center of mass is at ( x 1 ,y 1 ) = ( 5.0 cm, 2.5 cm). The top 20 cm × 5 cm piece (section 2, in the first quadrant) has 18.2% of the total area; its center of mass is at ( x 2 , y 2 ) = (10 cm, 12.5 cm). The bottom 10 cm x 10 cm piece (section 3) also has 18.2% of the total area; its center of mass is at ( x 3 , y 3 ) = (5 cm, 15 cm). (a) The x coordinate of the center of mass for the plate is x com = (0.636) x 1 + (0.182) x 2 + (0.182) x 3 = – 0.45 cm . (b) The y coordinate of the center of mass for the plate is y com = (0.636) y 1 + (0.182) y 2 + (0.182) y 3 = – 2.0 cm .
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10. Since the center of mass of the two-skater system does not move, both skaters will end up at the center of mass of the system. Let the center of mass be a distance x from the 40-kg skater, then 65 10 40 6 2 kg m kg m bg b g −= ¡ = xx x ..
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5 - 2 Our notation is as follows x1 = 0 and y1 = 0 are the...

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