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t3_equations_no_words

# t3_equations_no_words - MIME 2300 Test 3 Equations Revised...

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MIME 2300 - Test 3 Equations Revised July 18, 2007 12:53 P.M . g = 32.2 ft/s 2 or g = 9.81 m/s 2 12.1 12.2 dt ds v = 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 dt r d v = dt ds v = dt v d a = 12.5 k z j y i x r + + = k v j v i v dt r d v z y x + + = = z v y v x v z y x = = = 2 z 2 y 2 x v v v v + + = k a j a i a dt v d a z y x + + = = 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 + + = 12.6 ( 29 x o x v v = ( 29 t v x x x o o + = ( 29 gt v v y o y - = ( 29 2 y o o gt 2 1 t v y y - + = ( 29 ) y y ( g 2 v v o 2 y o 2 y - - = 12.7 t u v v = s v = t t u v u v v a + = = n n t t u a u a a + = vdv ds a or v a t t = = 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 + = 12.8 j ) sin( i ) cos( u r θ + θ = j ) cos( i ) sin( u θ + θ - = θ k u z = r u r r = θ r u θ u = θ θ u v u v v r r + = r v r = θ r v θ = ( 29 2 2 θ r r v + = r θ u θ u - = 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 + = Test 3 Equations Page 1

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13.1 2 2 1 r m m G F = ( 29 ( 29 2 s / m 81 . 9 g N mg W = = ( 29 ( 29 2 s / ft 2 . 32 g slug g W m = = 13.2 a m F = Σ 13.3 i i i a m F Σ Σ = G a m F = Σ 13.4 x x ma F = Σ y y ma F = Σ z z ma F = Σ N F N F s f k f μ = μ = ) x x ( k F 0 s - = 13.5 t t ma F = Σ n n ma F = Σ 0 F z = Σ dx dy ψ tan = 13.6 r r ma F = Σ θ θ ma F Σ = z z ma F = Σ θ d / dr r ψ tan = 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 3 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 i i v m Σ v m Σ = ( 29 ( 29 2 G 1 G V V = 15.4 ( 29 ( 29 ( 29 ( 29 2 B B 2 A A 1 B B 1 A A v m v m v m v m + = + ( 29 ( 29 ( 29 ( 29 1 B 1 A 2 A 2 B v v v v e - - = 15.5 ( 29 ( 29 ( 29 mv d H z O = v m r H O × = z y x z y x O mv mv mv r r r k j i H = 15.6 O O H M Σ = L F Σ = O O H M Σ = 15.7 ( 29 ( 29 2 O t t O 1 O H dt M H 2 1

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