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 R , area= R 2 Sphere: area=4 R 2 , volume=4 R 3 / 3 Trigonometry a A B b C sin = A C , cos = B C tan = A B X41 X42 X43 sin A = sin B = sin C A 2 + B 2 2 AB cos = C 2 Polar Coordinates x = r cos , y = r sin , r = radicalbig x 2 + y 2 , tan = 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 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 = N , Spring: F x = kx, PE = (1 / 2) kx 2 W = Fx cos , 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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