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sampfinexams - Sample Final Exam Phys 111 _ Vectors: Ax = A...

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Sample Final Exam Phys 111 ________________________________________________________________________________________________ Vectors: A x = A cos θ ; A y = A sin θ ; A = 2 y 2 x A A + ; θ = tan -1 x y A A ; A + B = C C x = A x + B x , C y = A y + B y ; y y x x B A B A cos AB B A + = θ = ; A x B = ABsin θ ; A x B = (A x B y - A y B x )k ; A = A x i + B x j One-dimensional motion: x = v o t + 1 2 at 2 , a 2 v v x 2 0 2 - = ; v = v o + at; t 2 v v x 2 1 + = ; y = v o t - 2 1 gt 2 , v = v o - gt, g 2 v v y 2 0 2 - - = g 2 v y 2 0 max = g v 2 t 0 tot = projectile motion: v ox = v o cos θ ; v oy = v o sin θ ; x = v ox t ; y = v oy t - 1 2 gt 2 ; v y = v oy - gt; 2 0 2 ) cos v ( 2 gx x ) (tan y θ - θ = R = v g o 2 2 sin ; θ g 2 v v y 2 oy 2 y - - = ; a c = v R 2 ; F net = ma; weight: W = mg, ; g = 9.8 m/s 2 ; incline: W x = mgsin θ , W y = mgcos θ , Friction: f s,max = μ s N; f k = μ k N; centripetal force: F = mv r 2 ; work: W = F d = Fdcos φ ; W mg = mg(y 0 - y) , F spring = -kx ; W spring = 1/2k(x 0 2 -x 2 ) W tot = K f - K i ; W fr = -F k d; P avg = t W Kinetic energy: K = m 2 1 v 2 ; U g = mg(y-y 0 ) U s = 1 / 2 kx 2 , U gi + U si + K I = U gf + U sf + K f U gi + U si + K I + W nc = U gf + U sf + K f momentum: p = mv; F net t = mv f - mv i P i = P f ; m 1 v i1 + m 2 v i2 = m 1 v f1 + m 2 v f2 ; rotational motion: θ = s r ; v = ϖ r; a t = α r;1 rev = 2 π rad; ϖ = ϖ 0 + α t; θ = ϖ 0 t + 1 2 2 2 2 0 2 α θ ϖ ϖ α t ; = - ; K= 2 I 2 1 ϖ τ = r x F; τ = rFsin φ ; Στ = I α ; work: W = τ θ ; W = 2 i 2 f I 2 1 I 2 1 ϖ - ϖ P avr = t W I point mass = mr 2 I disck = 2 mR 2 1 I hoop = mR 2 I rod = 2 mR 12 1 I rod(end) = 2 mR 3 1 I ball = 2 mR 5 2 I shell = 2 mR 3 2 I = I com + MD 2 Rolling: v com = R ϖ K = 2 I 2 1 ϖ + m 2 1 v com 2 τ = f s R Angular momentum: l point mass = m r x v l = mrvsin θ ; l =m ( r x v y - r y v x ) k L = I ϖ L I = L f G = 6.67x10 -11 Nm 2+ /kg 2 F net = m R v 2 , W = mg, 2 2 1 R m m G F = ; 2 p R M G g = ; R m M G U o E - = ; period T = v R 2 π ; R GM 2 v p esc = R GM v p sat = ; ; R GM 4 T 3 2 2 π = R E = 6.37x10 6 m , M E = 5.98x10 24 kg. Oscillations: x = x m cos( ϖ t) v = - ϖ x m sin( ϖ t) a = - ϖ 2 x m cos( ϖ t) ϖ = 2 π f = T 2 π F = -kx period: T spring = k m 2 π ; f = T 1 T pend = g l 2 π U spr = 2 1 kx 2 E tot = 1 /2 kx m 2 E tot =1/2kx 2 + 1/2mv 2 E tot = 1/2mv max 2 v max = x m ϖ a max = x m ϖ 2 ϖ = m k
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Sample Final Exam Phys 111 1. A cart with an initial velocity of 20 m/s to the right experiences a constant acceleration of a = 2 m/s 2 to the left. What is its velocity after traveling 64 m? A. 32
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This note was uploaded on 03/22/2011 for the course BME 111 taught by Professor Gokce during the Spring '11 term at NJIT.

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sampfinexams - Sample Final Exam Phys 111 _ Vectors: Ax = A...

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