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e2A_fall05a - Exam 2A Phys 111 Section Fall 2006 Name A The...

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Exam 2A Phys 111 Section_____ _ Fall 2006 Name____________________________________________ A The exam is closed book and closed notes. Make sure you put your name on the SCANTRON form. Use pencil #2. 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 = A x î + A y ĵ A + B = C C x = A x + B x , C y = A y + B y ; y y x x B A B A cos | B || A | B A + = θ = ; One-dimensional motion : x = v avr t ; x = x 0 + 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 + = ; Free-fall: y =y 0 + v o t - 2 1 gt 2 , v = v o - gt, g 2 v v y 2 o 2 - - = ; g 2 v y 2 0 max = g 2 v t y 0 tot = Two-dimensional motion: r = r 0 + (v ox t + 1 2 a x t 2 ) î + (v oy t + 1 2 a y t 2 ) ĵ v = (v ox + a x t) î + (v oy + a y t) ĵ; Projectile motion : x = v ox t ; y = v 0y t - 1 2 gt 2 ; v y = v oy - gt; v ox = v o cos θ ; v oy = v o sin θ ; g 2 v v y 2 oy 2 y - - = ; Range = ; g 2 sin v 2 o θ 2 0 2 ) cos v ( 2 gx x ) (tan y θ - θ = g 2 v y 2 oy max = g 2 v 2 t oy tot = Circular motion: a c = R v 2 ; period T = v R 2 π ; Dynamic: F net = ma; F netx = ma x ; F nety = ma y ; |F g | = mg, ; g = 9.8 m/s 2 ; F net = r mv 2 ; Incline: F gx (along an incline) = mgsinθ F gy (perpendicular to an incline) = mgcosθ work: W = F d = Fdcos φ ; W mg = mg(y 0 - y) , F spring = -kx ; W spring = 1 / 2 k(x 0 2 -x 2 ) W fr = -F k d; F k = μ k N; W tot = K f - K i ; P avg = t W P = F 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; P i = P f ; m 1 v i1 + m 2 v i2 = m 1 v f1 + m 2 v f2 ; F net
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