205_final_spring10 - Dr Gundersen Phy 205DJ Final Exam 12...

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Unformatted text preview: Dr. Gundersen Phy 205DJ Final Exam 12 May 2010 Signature: Name: 1 2 3 4 5 6 Idnumber: DO ALL SIX PROBLEMS! TO GET PARTIAL CREDIT IN PROBLEMS 3 - 6 YOU MUST SHOW GOOD WORK. CHECK DISCUSSION SECTION ATTENDED: [ ] Dr. Gundersen 2O, 9:30 - 10:20 a.m. [ ] Dr. Nepomechie 2P, 11:00 - 11:50a.m. [ ] Dr. Alvarez 2Q, 12:30 - 1:20 p.m. [ ] Dr. Barnes 2R, 2:00 - 2:50 p.m. [ ] Mr. Perez-Veitia 2S, 3:30 - 4:20 p.m. vector a = a x ˆ i + a y ˆ j , a = | vector a | = radicalBig a 2 x + a 2 y , θ = tan- 1 a y a x , a x = a cos θ, a y = a sin θ vector b = b x ˆ i + b y ˆ j + b z ˆ k , b = | vector b | = radicalBig b 2 x + b 2 y + b 2 z , ˆ b = vector b /b, vector v AC = vector v AB + vector v BC vector a · vector b = | vector a || vector b | cos θ = a x b x + a y b y + a z b z vector a × vector b = ( a y b z- a z b y ) ˆ i + ( a z b x- a x b z ) ˆ j + ( a x b y- a y b x ) ˆ k , | vector a × vector b | = | vector a || vector b || sin θ | x = x + v t + 1 2 at 2 , v 2 = v 2 + 2 a ( x- x ) , x = x + 1 2 ( v + v ) t, x = x + vt- 1 2 at 2 v = v + at, v av = 1 2 ( v + v ) = v + 1 2 at 2 , vector r ( t ) = vector r + vector v t + 1 2 vector a t 2 , vector v ( t ) = vector v + vector a t ω = ω + αt, θ = θ + ω t + 1 2 αt 2 , ω 2 = ω 2 + 2 α ( θ- θ ) vector v = dvector r dt , vector v av = vector r 1- vector r t 1- t , x 1- x = integraldisplay t 1 t v x ( t ) dt, vector a = dvector v dt , vector a av = vector v 1- vector v t 1- t , v x 1- v x = integraldisplay t 1 t a x ( t ) dt vector F net = mvector a = dvector p dt = d ( mvector v ) dt , vector F BA =- vector F AB , | vector F g | = mg, ≤ | vector f s | ≤ μ s F N , | vector f k | = μ k F N vector F =- mv 2 r ˆ r =- mω 2 r ˆ r , vector F s =- k vector d , vector F =- dU dx ˆ i- dU dy ˆ j- dU dz ˆ k , vector F =- dU ( r ) dr ˆ r Physics 205DJ Final Exam 12 May 2010 Dr. Gundersen Phy 205DJ Final Exam 12 May 2010 vector F =- GMm r 2 ˆ r , vector p = mvector v , vector p 1 i + vector p 2 i = vector p 1 f + vector p 2 f , Δ vector p = vector p f- vector p i = integraldisplay t f t i vector F dt = vector F av Δ t vector r ( t ) = r (cos θ ˆ i + sin θ ˆ j ) = r ˆ r , vector v ( t ) = ωr (- sin θ ˆ i + cos θ ˆ j ) = ωr ˆ θ, θ = ωt + θ vector a ( t ) =- ω 2 r (cos θ ˆ i + sin θ ˆ j ) =- ω 2 r ˆ r =- v 2 r ˆ r , θ = s r , ω = dθ dt = 2 πf = 2 π/T = v/r T 2 = 4 π 2 GM r 3 , vector a tot = vector a r + vector a t =- v 2 r ˆ r + αr ˆ θ, α = dω dt = d 2 θ dt 2 , α avg = Δ ω Δ t K = 1 2 mv 2 + 1 2 Iω 2 = p 2 2 m + L 2 2 I = 1 2 I com ω 2 + 1 2 Mv 2 com , P = dW dt = vector F · vector v = vector τ · vectorω W = F x Δ x + F y Δ y + F z Δ z = vector F · vector d = | vector F || vector d | cos φ = integraldisplay vector r B vector r A vector F · dvector r = integraldisplay θ θ τdθ = Δ K Δ U =- integraldisplay x f x i F ( x ) dx =- W =- Δ K, U ( y ) = mgy, U ( x ) = 1 2 kx 2 , Δ E th = f k d P = dE dt , E mech = K + U, W = Δ E mech + Δ E th...
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This note was uploaded on 01/08/2012 for the course PHYSICS 205 taught by Professor Galeazzi during the Fall '11 term at University of Miami.

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205_final_spring10 - Dr Gundersen Phy 205DJ Final Exam 12...

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