t2_equations_with_words

# t2_equations_with_words - Test 2 Equation Sheet Revised...

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Test 2 Equation Sheet Revised 6/26/2007 12.1 12.1 12.2 s(t) - t) Δ s(t s Δ + = 1 2 21 s s s Δ - = dt ds v = t Δ s Δ v avg = dt ds v v sp = = t s v T avg = t Δ v Δ a avg = 2 2 dt s d a = dt dv a = vdv ads = t a v v c o + = 2 c o o t a 2 1 t v s s + + = ) s s ( a 2 v v o c 2 o 2 - + = 12.3 12.4 ) t ( r ) t t ( r r - + = t Δ r Δ v avg = dt r d v = v v sp = dt r d v = t s v T avg = dt ds v = t Δ v Δ a avg = 2 2 dt r d a = dt v d a = v d v r d a = 12.5 ( 29 ( 29 ( 29 k t z j t y i t x r + + = ( 29 ( 29 ( 29 k t z j t y i t x dt r d v + + = = z v y v x v z y x = = = 2 z 2 y 2 x v v v v + + = ( 29 ( 29 ( 29 k t z j t y i t x dt v d dt r d a 2 2 + + = = = z v a y v a x v a z z y y x x = = = = = = 2 z 2 y 2 x a a a a + + = ( 29 ( 29 ( 29 dt dy y , x f dy d dt dx y , x f dx d y , x f dt d + = ( 29 ( 29 ( 29 y y , x f dy d x y , x f dx d y , x f dt d + = 12.6 t x x x 0 0 + = ( 29 θ cos v x 0 0 = 0 x = ( 29 2 0 0 t g 2 1 t y y y - + + = gt y y 0 - = ( 29 θ sin v y 0 0 = g y - = ( 29 0 2 0 2 y y g 2 y y - - = 2 2 y x v + = ( 29 0 y dt d y max = = 12.7 t u v v = dt ds v = = ψ - dx dy tan 1 n n t t u a u a a + = vdv ds a or v a t t = = Test 2 Equations Page 1

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ρ v a 2 n = 2 n 2 t a a a + = ( 29 [ ] 2 2 2 / 3 2 dx / y d dx / dy 1 ρ + = = φ - x y tan 1 ) cos( a a t φ ± ψ ± = ) sin( a a n φ ± ψ ± = 12.8 j ) sin( i ) cos( u r θ + θ = j ) cos( i ) sin( u θ + θ - = θ k u z = z r u z u r r + = θ r u θ u = z θ r u z u θ r u r v + + = r v r = θ r v θ = 2 2 2 2 z 2 θ 2 r z ) θ r ( r v v v v + + = + + = θ θ r r u a u a a + = 2 r θ r r a - = θ r 2 θ r a θ + = ( 29 ( 29 2 2 2 θ r 2 θ r θ r r a + + - = z r P u z u r r + = z θ r u z u θ r u r v + + = ( 29 ( 29 z θ r 2 u z u θ r 2 θ r u θ r r a + + + - = 12.9 12.10 A / B A B r r r + = A / B A B v v v + = A / B A B a a a + = 14.1 = = - 2 1 2 1 s s r r 2 1 ds ) θ cos( F r d F U ) s s ( ) θ cos( F U 1 2 c c 2 1 - = - ) y y ( W y Δ W U 1 2 2 1 - - = - = - ) s s ( k 2 1 U 2 1 2 2 2 1 - - = - 14.2 2 1 2 2 s s t mv 2 1 mv 2 1 ds F Σ 2 1 - = 2 - - = 1 2 2 2 1 mv 2 1 mv 2 1 U Σ 2 2 1 1 T U Σ T = + - 14.3 = + - 2 2 1 1 T U T 14.4 dt dU P = v F P = input power output power ε = input energy output energy ε = hp 1 s lbf ft 550 = hp 1 min lbf ft 33000 = hp 1 Watt 746 = s lbf ft 737 . 0 Watt 1 = 14.5 Wy V g = 2 e ks 2 1 V + = e g V V V + = 2 1 2 1 V V U - = Σ - Eqs. 14-17 to 14-19 not covered 14.6 ( 29 2 2 noncons 2 1 1 1 V T U Σ V T + = + + - 2 2 1 1 V T V T + = + 2 2 1 1 V Σ T Σ V Σ T Σ + = + Test 2 Equations Page 2
15.1 ( 29 v m dt d a m F Σ = = 1 2 t t v m v m dt F 2 1 - = Σ 2 t t 1 v m dt F v m 2 1 = Σ + = Σ + = Σ + = Σ + 2 1 2 1 2 1 t t 2 z z 1 z t t 2 y y 1 y t t 2 x x 1 x mv dt F mv mv dt F mv mv dt F mv 15.2 dt v d m Σ F Σ i i i = ( 29 ( 29 2 i i t t i 1 i i v m dt F v m 2 1 Σ = Σ + Σ 2 G t t 1 G mv dt F mv 2 1 = Σ + 15.3 ( 29 ( 29 2 i i 1

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## This note was uploaded on 05/04/2008 for the course MIME 2300 taught by Professor Gan during the Spring '08 term at Toledo.

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t2_equations_with_words - Test 2 Equation Sheet Revised...

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