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October 24 Solutions - 8.49 IDENTIFY The location of the...

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8.49. I DENTIFY : The location of the center of mass is given by Eq. 8.48. The mass can be expressed in terms of the diameter. Each object can be replaced by a point mass at its center. S ET U P : Use coordinates with the origin at the center of Pluto and the + x direction toward Charon, so P 0 x C 19,700 km x . 3 3 4 1 3 6 m V r d . E XECUTE : 3 3 1 C P P C C C C 6 cm C C C 3 3 3 3 1 1 P C P C P C P C 6 6 d m x m x m d x x x x m m m m d d d d . 3 3 cm 3 3 [1250 km] (19,700 km) 2.52 10 km [2370 km] [1250 km] x . The center of mass of the system is 3 2.52 10 km from the center of Pluto. E VALUATE : The center of mass is closer to Pluto because Pluto has more mass than Charon. 8.54. (a) I DENTIFY and S ET U P : Apply Eq. 8.28 and solve for 1 m and 2 . m E XECUTE : 1 1 2 2 cm 1 2 m y m y y m m 1 1 2 2 1 1 2 cm (0) (0.50 kg)(6.0 m) 1.25 kg 2.4 m m y m y m m m y and 1 0.75 kg. m E VALUATE : cm y is closer to 1 m since 1 2 . m m (b) I DENTIFY and S ET U P : Apply / d dt a v 5 for the cm motion. E XECUTE : 3 cm cm ˆ 1.5 m/s .
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