Lesson_3.4_Printable

Lesson_3.4_Printable - Center of Mass A car of mass m 1 is...

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Unformatted text preview: Center of Mass A car of mass m 1 is at position x 1 Another car of mass m 2 is at position x 2 . x 1 x 2 x cm m 1 m 2 0 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 + = + 1 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 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). m 1 = 3.0 kg, x 1 = -6 m 0 (-6, 0) (1, 0) (3, 0) 3 kg 2 kg x cm m 2 = 2 kg, x 2 = 1 m m 3 = 4 kg, x 3 = 3 m 4 kg y cm = 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 = - 3( 6) 2(1) 4(3) 3 2 4- + + = + + 4 9- = 3 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). m 1 = 3.0 kg, y 1 = 5 m y m y m y + (0, 5) (0, 0) 3 kg 2 kg m 2 = 2 kg, y 2 = 0 m 3 = 4 kg, y 3 = -4 m y c m = -1/9 m x cm = 0 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, -4) 3(5) 2(0) 4( 4) 3 2 4 + +- = + + 1 m 9- = 4 kg 4 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. m 1 = 3.0 kg, x 1 = 2 m, y 1 = 2 m m 2 = 2 kg, x 2 = 1 m, y 2 = 1 m m 3 = 1 kg, x 3 = 3, y 3 = 0 m 1 2 3 A B (1,1) (2,2) 1 1 2 2 3 3 cm m x m x m x x m m + + = + 11 4 , 6 3...
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Lesson_3.4_Printable - Center of Mass A car of mass m 1 is...

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