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sheet_final - WATCH SQUARES x = x2 x1 t = t2 t1 average...

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WATCH SQUARES!!!!! Δx = x 2 – x 1 Δt = t 2 – t 1 average velocity = Δx / Δt average acceleration = Δv / Δt Motion at Constant Acceleration v = v o +at x = x o + v o t + 1/2at 2 v 2 = v o 2 + 2a(x – x o ) average velocity = (v + v o ) / 2 Falling Body a = g v o = 0 v f = √2gy t = √2y/g Freely Falling Objects g = 9.80 m/s 2 v = v o +gt y = y o + v o t + 1/2gt 2 v 2 = v o 2 + 2g(y – y o ) average velocity = (v + v o ) / 2 Vectors Magnitude = √(Dx 2 + Dy 2 ) Angle = tan θ =Dy / Dx Incline Plane mg x = mg sin θ mg y = mg cos θ a (down the plane) = g sin θ there is no acceleration in the y direction moving down plane: v bottom = √2ax or √2gxsin θ with friction u k = tan θ sliding down plane: a = g (sinθ - µ k cosθ) Constant Acceleration in 2 Dimensions x component (horizontal) v x = v xo +a x t x = x o + v xo t + 1/2a x t 2 v x 2 = v xo 2 + 2a x (x – x o ) y component (vertical) v y = v yo +a y t y = y o + v yo t + 1/2a y t 2 v y 2 = v yo 2 + 2a y (y – y o ) Chasing T catch = x / (v 1 – v 2 ) Projectile Motion Horizontal Motion (a x = 0, v x = constant) v xo = v o cos θ o v x = v xo x = x o + v xo t Vertical Motion (a y = -g = constant) v yo = v o sin θ o v y = v yo – gt y = y o + v yo t - 1/2gt 2 v y 2 = v yo 2 – 2g(y – y o ) t flight = t up + t down = 2v o sinθ / g y max = (v o sinθ) 2 / 2g horizontal range: R = v o 2 sin2θ / g Friction F fr = µ k F N F fr ≤ µ s F N (will oppose any smaller force) Skidding: x = v 2 / 2 µ k g or F fr = µ k mg = ma a = µ k g Force ∑F = ma F G = mg weight = mass (kg) * g = N Atwod’s machine: a = ((m 2 – m 1 ) / (m 1 + m 2 ))g if m 2 > m 1 , m 2 falls and m 1 rises and a is positive if m 1 > m 2 , m 1 falls and m 2 rises and a is negative T = (2 m 1* m 2 / m 1 + m 2 )g Pendulum (accelerometer): ma = F T sin θ (horizontal) 0 = F T cos θ – mg (vertical) tan θ = F T sin θ / F T cos θ = ma/mg = a/g Energy: V = √2gy o F T = (3cosθ-2cosθ)mg F x = F cos θ F y = F sin θ Power P = W/t 1hp = 726W P = FV Springs F s = -kx W = ½ kx 2 ½ mv 1 2 + ½ kx 1 2 = ½ mv 2 2 + ½ kx 2 2 Work – Energy W = fd or W=fdcosθ K = ½ mv 2 W = ΔK = ½ mv f 2 – ½ mv o 2 ΔU = W ext = mgh ΔU = -W G = mgh U grav = mgy ΔE = ΔK + ΔU = 0 ½ mv 1 2 + mgy 1 = ½ mv 2 2 + mgy 2 Atwood’s Machine (work) v b

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