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MIDTERM II

# MIDTERM II - Nicholas Charles Miller PHY183 Spring 2010...

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Unformatted text preview: Nicholas Charles Miller- PHY183, Spring 2010 - Physics for Scientists and Engineers I 1 Midterm II Nicholas Miller __________________________________ PRINT NAME: __________________________________ Do not open exam until instructed to do so. Nicholas Charles Miller- PHY183, Spring 2010 - Physics for Scientists and Engineers I 2 Midterm II Nicholas Charles Miller- PHY183, Spring 2010 - Physics for Scientists and Engineers I 3 Midterm II Quadratic Formula ax 2 + bx + c = 0, x = [ − b ± √ b 2 − 4 ac ] / (2 a ) Logarithms and Exponentials ln( ab ) = ln( a )+ln( b ) , ln( a/b ) = ln( a ) − ln( b ) , ln( a b ) = b ln( a ) ( a b ) c = a bc Geometry Circle: circumference=2 πR , area= πR 2 Sphere: area=4 πR 2 , volume=4 πR 3 / 3 Trigonometry a A B b C sin α = A C , cos α = B C tan α = A B X41 X42 X43 α γ β sin α A = sin β B = sin γ C A 2 + B 2 − 2 AB cos γ = C 2 Polar Coordinates x = r cos θ, y = r sin θ , r = radicalbig x 2 + y 2 , tan θ = y/x SI Units and Constants quantity unit abbreviation Mass m kilograms kg Distance x meters m Time t seconds s Force F Newtons N=kg m/s 2 Energy E Joules J=N m Power P Watts W=J/s Pressure P Pascals Pa=N/m 2 1 lb=4.448 N, 1 hp=745.7 W, 1 liter=10 − 3 m 3 g = 9 . 81 m/s 2 , G=6 . 67 × 10 − 11 Nm 2 /kg 2 1 atm=1 . 013 × 10 5 Pa, v sound = 331 radicalbig T/ 273 m/s Calculus ( d/dx ) f ( g ) = ( df/dg )( dg/dx ) ( d/dx )( fg ) = f ′ g + fg ′ , ( d/dx )( f/g ) = ( f ′ g − fg ′ ) /g 2 ( d/dx )sin( ax ) = a cos( x ) , ( d/dx )cos( ax ) = − a sin( x ) ( d/dx ) e ax = ae ax , ( d/dx )ln( x ) = 1 /x ( d/dx )tan( ax ) = a sec 2 ( ax ) , ( d/dx ) x 2 n = nx n − 1 integraltext dx sin( ax ) = − cos( ax ) a , integraltext dx cos( ax ) = sin( ax ) a integraltext dxe ax = e ax a , integraltext dx 1 /x = ln( x ) integraltext dxx n = x n +1 / ( n + 1) 1-D motion, constant a ∆ x = (1 / 2)( v + v f ) t v f = v + at ∆ x = v t + (1 / 2) at 2 ∆ x = v f t − (1 / 2) at 2 (1 / 2) v 2 f − (1 / 2) v 2 = a ∆ x Nicholas Charles Miller- PHY183, Spring 2010 - Physics for Scientists and Engineers I 4 Midterm II Range : R = ( v 2 /g ) sin 2 θ Trajectory : y = v y t − (1 / 2) gt 2 , x = v x t Forces, Work, Energy, Power & Momentum F net = ma , Gravity: F = mg, PE = mgh Friction: f = μN , Spring: F x = − kx, PE = (1 / 2) kx 2 W = Fx cos θ, KE = (1 / 2) mv 2 , P = ∆ E/ ∆ t = Fv p = mv, I = F ∆ t = ∆ p X cm = ( m 1 x 1 + m 2 x 2 + ··· ) / ( m 1 + m 2 + ··· ) Elastic coll.s: v ′ 1 x − v ′ 2 x = − ( v 1 x − v 2 x ) v ′ 1 x = [( m 1 − m 2 ) v 1 x + 2 m 2 v 2 x ] / ( m 1 + m 2 ) v ′...
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MIDTERM II - Nicholas Charles Miller PHY183 Spring 2010...

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