205_final_spring10

# 205_final_spring10 - Dr Gundersen Signature Idnumber Phy...

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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 0 + v 0 t + 1 2 at 2 , v 2 = v 2 0 + 2 a ( x - x 0 ) , x = x 0 + 1 2 ( v 0 + v ) t, x = x 0 + vt - 1 2 at 2 v = v 0 + at, v av = 1 2 ( v 0 + v ) = v 0 + 1 2 at 2 , vector r ( t ) = vector r 0 + vector v 0 t + 1 2 vector a t 2 , vector v ( t ) = vector v 0 + vector a t ω = ω 0 + αt, θ = θ 0 + ω 0 t + 1 2 αt 2 , ω 2 = ω 2 0 + 2 α ( θ - θ 0 ) vector v = dvector r dt , vector v av = vector r 1 - vector r 0 t 1 - t 0 , x 1 - x 0 = integraldisplay t 1 t 0 v x ( t ) dt, vector a = dvector v dt , vector a av = vector v 1 - vector v 0 t 1 - t 0 , v x 1 - v x 0 = integraldisplay t 1 t 0 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, 0 ≤ | vector f s | ≤ μ s F N , | vector f k | = μ k F N vector F = - mv 2 r ˆ r = - 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

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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 0 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 = 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 = dt = d 2 θ dt 2 , α avg = Δ ω Δ t K = 1 2 mv 2 + 1 2 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 0 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 + Δ E int U ( r ) = - GMm r , E tot = 1 2 mv 2 - GMm r = 1 2 mv 2 + 1 2 kx 2 = 1 2 mv 2 + mgy, v esc = radicalbigg 2 GM R v 1 f = m 1 - m 2 m 1 + m 2 v 1 i + 2 m 2 m 1 + m 2 v 2 i , v 2 f = 2 m 1 m 1 + m 2 v 1 i + m 2 - m 1 m 1 + m 2 v 2 i , v 1 i - v 2 i = - ( v 1 f - v 2 f ) M = Σ i m i , vector r com = Σ i m i vector r i M = x com ˆ i + y com ˆ j + z com ˆ k , vector v com = Σ i m i vector v i M x com = Σ i m i x i M , y com = Σ i m i y i M , z com = Σ i m i z i M , I = Σ i m i R 2 i , I = I com + Mh 2 vector τ net = Ivectorα = d vector L dt = vector r × vector F , | vector τ | = | rF sin φ | , vector L = Ivectorω = vector r × vector p , | vector L | = | rp sin φ | , vector L i = vector L f Ω = Mgr
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