problem14_49

University Physics with Modern Physics with Mastering Physics (11th Edition)

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14.49: a) At , 0 = r the model predicts 3 m kg 700 , 12 = = A ρ and at , R r = the model predicts . m kg 10 3.15 m) 10 37 . 6 )( m kg 10 50 . 1 ( m kg 700 , 12 3 3 6 4 3 3 × = × × - = - = - BR A ρ b), c) - = - = - = = R BR A πR BR AR π dr r Br A π dm M 0 3 4 3 2 4 3 3 4 4 3 4 ] [ 4 × × - × = - 4 m) 10 37 . 6 )( m kg 10 50 . 1 ( 3 m kg 700 , 12 3 m) 10 37 . 6 ( 4 6 4 3 3 3 6 π kg, 10 99 . 5 24 × = which is within 0.36% of the earth’s mass. d) If m ) ( r is used to denote the mass contained in a sphere of radius , r then . ) ( 2 r r Gm g = Using the same integration as that in part (b), with an upper limit of r instead of R gives the result. e) ) kg m N 10 673 . 6 ( ) ( , at and , 0 at 0 2 2 11 2 × = = = = = - R R Gm g R r g r g . s m 85 . 9 m) 10 (6.37 kg) 10 99 . 5 ( 2 2 6 24 = × × f) ; 2 3 3 4 4 3 3 4 2 -
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