z-air-friction-not-requirediintcalc

z-air-friction-not-requirediintcalc - CA 2Not required. For...

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2 dv 1 a - v dt L == 2 - L v = 0 vt 2 v0 - L v = ∫∫ 2 CA Fm a - v 2 ρ 2m L = 0 t 11 - vv L −= 00 1 v 1t L = + dx 1 1 L = + xt 0 L L (t ) v = + 0 0 L ) v x ln[ ] L L () v + = 0 v x ln[(1 t )] L L =+ 0 v xL e( 1 t ) L 0 -x L v e v = ⇒⇒ Not required. For advanced students Air friction effect
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)] τ t ln[cosh( τ v x )] τ t ln[cosh( τ v x dt ) τ t tanh( dx v 1 ) τ t tanh( dt dx v 1 t t t 0 x 0 t t = = = = ) τ t tanh( v v ] e [e ] e - [e v v 1] [e 1] - [e v v e ] v v v v [ τ 1 L v τ t 2 L 2v t ] v v v v ln[ L t ] v v v v ln[ 2v 1 dt L 1 v - v dv b 1 L b g v dt b v - b g dv dt v b - g dv dt v b - g dv v b - g dt dv L v - g v b - g v m b - g a b 1 L ma v b - mg F t τ t - τ t τ t - τ t t τ 2t τ 2t t τ 2t t t t t t t t t t t 0 v 0 2 2 t 2 2 2 t t 0 2 v 0 2 2 t 0 v 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 = + = = + = = + = = = + = + = = = = = = = = = = = = = Frictional force proportional to v 2 with mg. Here the constant b 2 , has the units of Kg/m and the constant 1/ b
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z-air-friction-not-requirediintcalc - CA 2Not required. For...

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