399_Physics ProblemsTechnical Physics

399_Physics ProblemsTechnical Physics - Chapter 13 e1.25 10...

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Chapter 13 401 P13.51 (a) a v r c = 2 a c = × × = 125 10 153 10 10 2 6 2 11 . . . ms m 2 ej (b) diff m s 2 =−= = 10 2 9 90 0 312 2 .. . GM r M = × ×⋅ 0312 667 10 110 10 11 2 11 32 . . ±ms ±m Nm kg kg 2 22 e j FIG. P13.51 P13.52 (a) The free-fall acceleration produced by the Earth is g GM r GM r E E == 2 2 (directed downward) Its rate of change is dg dr GM r GM r EE =− = −− 33 af . The minus sign indicates that g decreases with increasing height. At the Earth’s surface, dg dr GM R E E 2 3 . (b) For small differences, g r g h GM R E E 2 3 Thus, g GM h R E E = 2 3 (c) g = × × 2 6 67 10 5 98 10 6 00 637 10 185 10 11 2 24 6 3 5 . . . kg m m 2 2 e j *P13.53 (a) Each bit of mass dm in the ring is at the same distance from the object at A. The separate contributions Gmdm r to the system energy add up to GmM r ring . When the object is at A,
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