Spring 2007 - Scott Pratt PHY231 Spring 2007 Introduct 1...

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Unformatted text preview: Scott Pratt- PHY231, Spring 2007 - Introduct 1 Midterm 3 (lecture students) Scott Pratt Do not open exam until instructed to do so. Scott Pratt- PHY231, Spring 2007 - Introduct 3 Midterm 3 (lecture students) Quadratic Formula ax 2 + bx + c = 0, x = [- b ± √ b 2- 4 ac ] / (2 a ) 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 A B C 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 = p 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 Temperature T ◦ C, ◦ K or ◦ F T ◦ F = 32 + (9 / 5) T ◦ C Pressure P Pascals Pa=N/m 2 1 cal=4.1868 J, 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, 0 ◦ C=273.15 ◦ K, N A = 6 . 023 × 10 23 R = 8 . 31 J/(mol ◦ K)=0.0821 L atm/(mol K), k B = R/N A = 1 . 38 × 10- 23 J/K, σ = 5 . 67 × 10- 8 W/(m 2 K 4 ) v sound = 331 p T/ 273 m/s H 2 0: c ice , liq ., steam = { . 5 , 1 . , . 48 } cal/g ◦ C L F,V = { 79 . 7 , 540 } cal/g, ρ = 1000 kg/m 3 . 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 Range : R = ( v 2 /g ) sin2 θ Forces, Work, Energy, Power, Momentum & Impulse F = ma , Gravity: F = mg, PE = mgh Friction: f = μN , Spring: F =- 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- v 2 =- ( v 1- v 2 ) Rotational Motion ∆ θ = (1 / 2)( ω + ω f ) t, ω f = ω + αt ∆ θ = ω t + (1 / 2) αt 2 = ω f t- (1 / 2) αt 2 α ∆ θ = (1 / 2) ω 2 f- (1 / 2) ω 2 ω = 2 π/T = 2 πf, f = 1 /T Rolling: a = αr, v = ωr a c = v 2 /r = ωv = ω 2 r τ = rF sin θ = Iα, I point = mR 2 I cyl . shell = M R 2 , I sphere = (2 / 5) M R 2 I solid cyl . = (1 / 2) M R 2 , I sph . shell = (2 / 3) M R 2 L = Iω = mvr sin θ, ( θ = angle between v and r) KE = (1 / 2) Iω 2 = L 2 / (2 I ) , W = τ ∆ θ Gravity and circular orbits P E =- G M m r , ∆ P E = mgh (small h ) F = G M m r 2 , GM 4 π 2 = R 3 T 2 Gases, liquids and solids P = F/A, P V = nRT, ∆ P = ρgh h (1 / 2) mv 2 i = (3 / 2) k B T ideal monotonic gas: U = (3 / 2) nRT = (3 / 2) P V F bouyant...
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This note was uploaded on 04/10/2008 for the course PHY 231 taught by Professor Smith during the Spring '08 term at Michigan State University.

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Spring 2007 - Scott Pratt PHY231 Spring 2007 Introduct 1...

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