lesson 3.4 Center of Mass

Lesson 3.4 Center - Center of Mass 1 A car of mass m 0 x1 cm 1 is at position x The center of mass of these cars is at position x cm The where the

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Center of Mass A car of mass m 1 is at position x 1 The center of mass of these cars is at position x cm where the combined mass of the two objects can be considered to be placed. The motion of the two objects can be summarized by considering the motion of their center of mass. x cm can be measured as: 1 1 2 2 1 2 cm m x m x x m m + = + x 1 x cm 0 1
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If there are n objects on the x-axis the position of their center of mass is given by: Similarly if there are n objects on the y-axis the position of their center of mass is given by: 1 1 n i i i cm n i i m y y m = = = http://www.kettering.edu/~drussell/Demos/COM/com-a.html 2
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Find the center of mass of a system composed of three spherical objects with masses of 3.0 kg, 2.0 kg and 4.0 kg and centers located at (-6.0 m, 0), (1.0 m, 0) and (3.0 m, 0). 1 1 2 2 3 3 1 2 3 cm m x m x m x x m m m + + = + + 4 ,0 9 cm = - 0 (-6, 0) (1, 0) (3, 0) 3 kg 2 kg 3( 6) 2(1) 4(3) 3 2 4 - + + = + + 4 9 - = x cm 4 kg 3
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Find the center of mass of a system composed of three spherical objects with masses of 3.0 kg, 2.0 kg and 4.0 kg and centers located at (0, 5 m), (0,0) and (0, -4 m). 1 1 2 2 3 3 1 2 3 cm m y m y m y y m m m + + = + + 1 0, 9 cm - = (0, 5) (0, 0) (0, -4) 3 kg 2 kg 3(5) 2(0) 4( 4) 3 2 4 + + - = + + 1 m 9 - = 4 kg y c m = -1/9 m 4
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Three balls A, B and C of masses 3 kg, 2 kg and 1 kg are placed as shown in the figure below. Find the position of their center of mass. 1
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This note was uploaded on 05/01/2011 for the course PHY 2048 taught by Professor George during the Fall '10 term at Edison State College.

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Lesson 3.4 Center - Center of Mass 1 A car of mass m 0 x1 cm 1 is at position x The center of mass of these cars is at position x cm The where the

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