P22_011 - r cancels because both the electric and...

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11. (a) The magnitudes of the gravitational and electrical forces must be the same: 1 4 πε 0 q 2 r 2 = G mM r 2 where q isthechargeone itherbody , r is the center-to-center separation of Earth and Moon, G is the universal gravitational constant, M is the mass of Earth, and m is the mass of the Moon. We solve for q : q = p 4 πε 0 GmM . According to Appendix C of the text, M =5 . 98 × 10 24 kg, and m =7 . 36 × 10 22 kg, so (using 4 πε 0 =1 /k ) the charge is q = s (6 . 67 × 10 11 N · m 2 / kg 2 )(7 . 36 × 10 22 kg)(5 . 98 × 10 24 kg) 8 . 99 × 10 9 N · m 2 / C 2 =5 . 7 × 10 13 C
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Unformatted text preview: r cancels because both the electric and gravitational forces are propor-tional to 1 /r 2 . (b) The charge on a hydrogen ion is e = 1 . 60 10 19 C, so there must be q e = 5 . 7 10 13 C 1 . 6 10 19 C = 3 . 6 10 32 ions . Each ion has a mass of 1 . 67 10 27 kg, so the total mass needed is (3 . 6 10 32 )(1 . 67 10 27 kg) = 6 . 10 5 kg ....
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