Halliday-cap 22-vol.3- Rar - P22 011

Transcript

11. (a) The magnitudes of the gravitational and electrical forces must be the same: mM 1 q2 =G 2 2 4πε0 r r where q is the charge on either body, 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 = 4πε0 GmM . According to Appendix C of the text, M = 5.98 × 1024 kg, and m = 7.36 × 1022 kg, so (using 4πε0 = 1/k) the charge is  2 (6.67 × 10−11 N · m2 /kg )(7.36 × 1022 kg)(5.98 × 1024 kg) q= = 5.7 × 1013 C . 2 8.99 × 109 N · m2 /C We note that the distance r cancels because both the electric and gravitational forces are proportional to 1/r2 . (b) The charge on a hydrogen ion is e = 1.60 × 10−19 C, so there must be q 5.7 × 1013 C = = 3.6 × 1032 ions . e 1.6 × 10−19 C Each ion has a mass of 1.67 × 10−27 kg, so the total mass needed is (3.6 × 1032 )(1.67 × 10−27 kg) = 6.0 × 105 kg .