Analytical Mech Homework Solutions 101

Analytical Mech Homework Solutions 101 - v V = m m dv m dv...

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mm d vm d v d m v m d tm d m d t d αα α −= = = = ± ±± ± d v m vV dm dv mvV = 0 1 mv m dm dv V = ∫∫ D 1 ln ln V mV  =   D 1 1 =− + D 1 1 m m    D 7.28 From eqn. 7.7.5, mg mv Vm −=− G GG ± ± V v since V is opposite in direction from G v G , mg mv Vm + mgdt mdv Vdm + dm dt = ± m so dm dt = m ± dm mg mdv Vdm m + ± gV dm + ± dv 0 ep m dv dm + D ± m p = payload mass () ln p m g m V + D D ± fp mmmm =− ≈ DD f m = fuel mass ln 1 f ef p m g V =+ + ± ln 1 f e p m vg m V += D ± m exp 1 f e p m m V m D ± 17
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