Analytical Mech Homework Solutions 20

Analytical Mech Homework Solutions 20 - Integrating 11A = t...

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Integrating 11 A t uu m α −= D and substituting v eu = (a) 1 ln 1 v A e t m vv  =− +   D D (b) tT @ 0 v == ln 1 v A ve m T =+ D D 1 A ee m αα T DD 1 v m Te A D (c) v dv A e dx m v vdv A dx em again, let u v e = du udv = or du dv u = 1 ln vu = 1 ln du u A u dx um Integrating and solving () 2 v m xv A + D D e 2.20 dm v Fm v v m dt + = m g but 3 4 3 mr ρ π = D 2 1 ρπ = v so (1) 32 2 2 1 44 33 rv rg πρ += = 3 4 3 Now 3 1 10 D so, second term is negligible-small hence v and g vg t speed t but or 22 1 4 r D ±± r v 1 1 4 D ± Hence 1 1 4 r D g t and rate of g r o w t h t The exact differential equation from (1) above is:
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This note was uploaded on 01/06/2012 for the course PHYSICS 4360C taught by Professor Johnanderson during the Fall '11 term at UNF.

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