390_Physics ProblemsTechnical Physics

390_Physics ProblemsTechnical Physics - 392 Universal...

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392 Universal Gravitation P13.29 (a) ρ π == × × M r S E 4 3 2 30 6 3 9 3 1 99 10 4 6 37 10 184 10 . . . kg m kg m 3 ej (b) g GM r S E ×⋅ × × 2 11 30 6 2 6 6 67 10 1 99 10 637 10 327 10 .. . . Nm kg kg m ms 22 2 e j (c) U GM m r g S E =− × × × 6 67 10 1 99 10 1 00 208 10 11 30 6 13 . . . N m kg kg kg m J e j bg P13.30 WU Gm m r F H G I K J 12 0 W = × × × 6 67 10 7 36 10 1 00 10 174 10 282 10 11 22 3 6 9 . . . N m kg kg kg m J e j e j P13.31 (a) UU U U U Gm m r Tot =++= = F H G I K J 12 13 23 12 12 33 U Tot m J × × −− 3 6 67 10 5 00 10 0300 167 10 11 3 2 14 . . e j (b) At the center of the equilateral triangle *P13.32 (a) Energy conservation of the object-Earth system from release to radius r : KU GM m Rh mv GM m r vG M rR h dr dt g h g r E E E E E += + + + F H G I K J F H G I K J altitude radius 0 1 2 2 11 2 (b) dt dr v dr v i f i f f i zz z =− = . The time of fall is tG M dr t r dr E E R E E + F H G I K J F H G I K J × × × × F H G I K J L N M O Q P + × × z z 2 2 6 67 10 5 98 10 687 10 11 24 6 6 . . m m 6.87 10 m 6 We can enter this expression directly into a mathematical calculation program. Alternatively, to save typing we can change variables to
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