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268_Physics ProblemsTechnical Physics

268_Physics ProblemsTechnical Physics - F M I = v lnF M I...

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270 Linear Momentum and Collisions P9.52 (a) From Equation 9.41, v v M M v M M e i f e f i = F H G I K J = − F H G I K J 0 ln ln Now, M M kt f i = , so v v M kt M v k M t e i i e i = − F H G I K J = − F H G I K J ln ln 1 With the definition, T M k p i , this becomes v t v t T e p a f = F H G I K J ln 1 (b) With v e = 1 500 m s, and T p = 144 s, v t = − F H G I K J 1 500 1 144 m s s b g ln t s v a f b g m s 0 0 20 224 40 488 60 808 80 1220 100 1780 120 2690 132 3730 v (m/s) 2500 0 20 40 60 80 100 120 140 2000 1500 1000 500 0 3000 3500 4000 t (s) FIG. P9.52(b) (c) a t dv dt d v dt v T v T e t T e t T p e p t T p p p a f = = F H I K L N M O Q P = − F H G G I K J J F H G I K J = F H G I K J F H G G I K J J ln 1 1 1 1 1 1
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