Third exam on Chaps. 15-20 – Tuesday, Nov. 25th Bring: Announcements Physics lecture today 4 PM – Professor Brian Matthews from U. Oregon – “Tolerance and Intolerance in Protein Structure and Function” Third exam on Chaps. 15-20 – Tuesday, Nov. 25th Bring: Equation sheet (8.5 x 11) Calculator Clear head Extra problem solving session ? Sunday night 10-11 PM ? Monday evening 6-7 PM ? Other ? 9/18/2018 PHY 113 -- Lecture Review 15-20

Advice for preparing for exam: Review lecture notes and text chapters Prepare equation sheet Work problems using equation sheet and calculator From homework From previous exams From on line quizes Topics: Simple harmonic motion & resonance Wave motion, standing waves, sound waves The physics of fluids Thermodynamics & the ideal gas law 9/18/2018 PHY 113 -- Lecture Review 15-20

Simple harmonic motion & resonance Hooke’s law: Simple pendulum: 9/18/2018 PHY 113 -- Lecture Review 15-20

The notion of resonance: Suppose F=-kx+F0 sin(Wt) According to Newton’s second law: 9/18/2018 PHY 113 -- Lecture Review 15-20

Physics of a “driven” harmonic oscillator: “driving” frequency “natural” frequency (mag) (W=2rad/s) w 9/18/2018 PHY 113 -- Lecture Review 15-20

The phenomenon of wave motion The wave equation position time 9/18/2018 PHY 113 -- Lecture Review 15-20

Solutions: y(x,t) = f (x ± vt) The wave equation: Solutions: y(x,t) = f (x ± vt) function of any shape Moving “pulse”: Periodic wave: “wave vector” not spring constant!!! 9/18/2018 PHY 113 -- Lecture Review 15-20

Superposition of waves: “Standing” wave: 9/18/2018 PHY 113 -- Lecture Review 15-20

Constraints of standing waves: (  = 0 ) 9/18/2018 PHY 113 -- Lecture Review 15-20

String instruments (Guitar, violin, etc.) The sound of music String instruments (Guitar, violin, etc.)  Couples to sound in the air 9/18/2018 PHY 113 -- Lecture Review 15-20

Longitudinal waves propagating in a fluid or solid Sound waves Longitudinal waves propagating in a fluid or solid 9/18/2018 PHY 113 -- Lecture Review 15-20

Sound intensity: (energy/(unit time × unit area)) Periodic sound wave In terms of pressure: Sound intensity: (energy/(unit time × unit area)) Decibel scale: 9/18/2018 PHY 113 -- Lecture Review 15-20

“Wind” instruments (standing waves in air) 9/18/2018 PHY 113 -- Lecture Review 15-20

The “Doppler” effect v=sound velocity observer moving, source stationary observer source vS=0 d toward away 9/18/2018 PHY 113 -- Lecture Review 15-20

Pressure: P=force/area 1 (N/m2) = 1 Pascal The physics of fluids. Fluids include liquids (usually “incompressible) and gases (highly “compressible”). Fluids obey Newton’s equations of motion, but because they move within their containers, the application of Newton’s laws to fluids introduces some new forms. Pressure: P=force/area 1 (N/m2) = 1 Pascal Density: r =mass/volume 1 kg/m3 = 0.001 gm/ml Note: In this chapter Ppressure (NOT MOMENTUM) 9/18/2018 PHY 113 -- Lecture Review 15-20

Density: r =mass/volume Effects of the weight of a fluid: P(y+Dy) rgDy y P(y) Note: In this formulation +y is defined to be in the up direction. 9/18/2018 PHY 113 -- Lecture Review 15-20

For an “incompressible” fluid (such as mercury): r = 13.585 x 103 kg/m3 (constant) Example: r = 13.595 x 103 kg/m3 9/18/2018 PHY 113 -- Lecture Review 15-20

Buoyant force for fluid acting on a solid: FB=rfluidVdisplacedg FB - mg = 0 rfluidVsubmergedg - rsolidVsolidg = 0 A Dy mg 9/18/2018 PHY 113 -- Lecture Review 15-20

Bouyant forces: the tip of the iceburg Source:http://bb-bird.com/iceburg.html 9/18/2018 PHY 113 -- Lecture Review 15-20

Effects of the weight of a “compressible” fluid on pressure. y-y0(mi) P (atm) 9/18/2018 PHY 113 -- Lecture Review 15-20

½ mv22 + mgh2 = ½ mv12 + mgh1 + (P1 A1 Dx1– P2 A2 Dx2) Energetics of fluids: Dx1 =v1D t Dx2 =v2D t A1 Dx1= A2 Dx2 m = r A1 Dx1 K2 + U2 = K1 + U1 + W12 ½ mv22 + mgh2 = ½ mv12 + mgh1 + (P1 A1 Dx1– P2 A2 Dx2) P2 + ½ rv22 + rgh2 = P1 + ½ rv12 + rgh1 9/18/2018 PHY 113 -- Lecture Review 15-20

Bernoulli’s equation: P2 + ½ rv22 + rgh2 = P1 + ½ rv12 + rgh1 Example: Suppose we know A1, A2, r, P, y1, y2 P + ½ rv22 + rgy2 = P0 + ½ rv12 + rgy1 9/18/2018 PHY 113 -- Lecture Review 15-20

DEint = Q - W Thermodynamic statement of conservation of energy – First Law of Thermodynamics DEint = Q - W Work done by system Heat added to system “Internal” energy of system 9/18/2018 PHY 113 -- Lecture Review 15-20

How is temperature related to Eint? Consider an ideal gas  Analytic expressions for physical variables  Approximates several real situations Ideal Gas Law: P V = n R T temperature (K) volume (m3) gas constant (8.31 J/(moleK)) pressure (Pa) number of moles 9/18/2018 PHY 113 -- Lecture Review 15-20

Review of results from ideal gas analysis in terms of the specific heat ratio g º CP/CV: 9/18/2018 PHY 113 -- Lecture Review 15-20