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PHYSICS 7E (21)
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# Entire Physics 7E Lecture/Textbook Notes.doc

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Department
Physics
Course
PHYSICS 7E
Professor
Herbert J.Hopster
Semester
Fall

Description
Physics 2E 1 Chap 12 Fluid Mechanics • Density • o o SI - 1000 kg/m^3 = 1 g/cm^3 • Pressure • o o SI - 1 Pa = 1 N/m^2 o  1 atm = 1.013 *10^5 Pa = 101325 N/m^2 o a fluid of uniform density o    pressure (Pa) = pressure at surface (Pa) + (density(kg/m^3)) (gravity(m/s^2))(change in hight(m))  o absolute/gauge (as in a tire) o  absolute: 2 atm in tire + 1 atm outside = 3  gauge: amount actually in the tire = 2 atm o work energy w/pressure o Physics 2E 2  o compressible gas (i.e. air) o  density increases as pressure increases    density = (constant)(pressure)  how much does a layer of air with hight h off the ground (sea level) and hight dh contribute to pressure    what hight is air have 1/2 the density it does at sea level  Physics 2E 3  • Buoyancy • o Archimedes's principle o  a fluid exerts an upward force on a immersed body equal to the weight of the fluid displace by the body  partly submerged object   • Fluid Flow • o types o  Steady (laminiar) flow    turbulent flow  Physics 2E 4  o Continuity o    Volume    Volume flow rate    mass flow rate    When an ideal liquid flows to a larger cross section    velocity in the smaller section (1) is > velocity in the bigger section (2)  pressure in the small section (1) is < pressure in the bigger section (2)   usually fluids flow in the opposite way (bigger to smaller/high to low pressure) for this reason o Bernoulli's equation o Physics 2E 5   (potential energy due to pressure) + (kinetic energy) + (gravitation potential energy) = constant throughout flow of an ideal liquid   y isnt that - ? o Torricellis law (when p1 = p2 in this equation) o  • Surface tension • o liquid molecules are attracted to themselves, causing the surface of a liquid to stay together • Viscosity • o internal friction in a fluid o causes the velocity of where liquid meets wall = to 0 m/s o  this is known as boundary layer  o Hagen-Poiscuille law o   velocity = (pi)(radius)^4(a)(p)/(8)(viscosity)(length) • Turbulence • o happens when a critical speed is reached and flow is no longer laminar o higher viscosity = higher critical speed needed Physics 2E 6 Physics 2E 7 Chap 14 Periodic Motion • restoring force • o a force that trys to return a system to equilibrium o  i.e. spring being stretched tries to restore itself back to being relaxed o is needed for oscillation • common measurement • o amplitude |x| - maximum magnitude of displacement from equilibrium o cycle - one complete round trip o  ex: a spring moves 1 meter to the left of equilibrium and is let go, the cycle is 2 meters o period (T) - time for one cycle o  ex: time it takes for the spring to go back to its starting position (stretched and let go, time it takes to reach its stretched position) o frequency (f) - # of cycles in 1 unit of time o  SI Hz - 1 cycle/second    frequency = 1/period o angular frequency o    angular frequency = (2pi)(frequency) = (2pi)/(period) • springs • o o  Force (external) = (spring constant)(displacement) • Simple harmonic motion • o when the restoring force is directly proportional to the displacement from equilibrium o also known as a harmonic oscillator o does not depend on amplitude (distance of displacement from equilibrium) Physics 2E 8 o o  restoring force of spring (or any body in SHM) = -(constant) (displacement)   N = -(N/m)(m) o o  angular frequency = sqrt(constant/mass)   rad/s = sqrt((kg/s^2)/(kg)) o o  instantaneous acceleration of a body in SHM = -(constant)(displacement from equilibrium)/(mass)  - means acceleration and displacement always have opposite signs o o  displacement = (amplitude)cos((angular frequency)(time) + (phase angle))  o o  o   v(t) max at x = 0 = o o  a(t) max at xmax = o Physics 2E 9 o o Energy in SHM o  o when there are 2 bodies independent of each other (atoms) o    o LC current o    q = x = charge  I = v = current  1/C = k = capacitance  L = m = inductance • simple pendulum • o o  the restoring force is mgsin(-), but (-) is so small that we can forget him and call this SHM o • Torsional pendulum Physics 2E 10 • o o • physical pendulum • o o when CM is below pivot, system is at equilibrium o • damped oscillations • o o o  where b is dampening constant. o o o types of dampening o  small dampening (like air)  Physics 2E 11   over dampening (sqrt of a - )    critical dampening (sqrt of 0)    sometimes called desirable, x approaches 0 asap • forced oscillations • o o F = driving force o o  reg w = driving angular frequency o Physics 2E 12 Physics 2E 13 Chap 15 Mechanical Waves • mechanical waves travel through a medium • o transverse o   perpendicular w/displacement  crest/trough o longitudinal o   parallel with displacement  compression/rarefaction o through a solide o  S (secondary) waves    transverse, slower  P (primary) waves    longitudinal, faster • waves transport energy, not matter, from one region to another • sinusoidal waves • o periodic waves w/simple harmonic motion that are easy to analyze o every particle in a sinusoidal wave's medium undergoes SHM w/the same frequency o o  wavelength(m) = (wave speed(m/s))(period(s)) Physics 2E 14 o o  wave number = (2pi)/(wavelength) o o  wave velocity = (angular frequency)/(wave number) o o  wave function for x moving to the right (kx + wt) for x moving to the left o o • Power of a wave • o power = F(y) V(y) o o o  J • average total energy density • o o  J/m • wave intensity • o intensity - time average rate at which energy is transported by the wave per unit area o I = Power/Area o o  for a circle o W/m^2 Physics 2E 15 o • interference • o the overlapping of waves o superposition - shows displacement of 2 waves interfering o   only works for linear waves o o  acts the same way as a free end o o Physics 2E 16  acts the same way as a fixed end • standing waves • o boths waves vs. o o  shows 2 wavelength  antinodes: constructive interference (highest amplitude)  nodes: destructive interference (amplitude is always 0) o • normal modes of a string • o an oscillating wave w/boundary conditions (standing wave) in which all particles of the system move sinusoidally with the same frequency o o  wavelength of standing wave = 2(length)/n o o  frequency of a standing wave = velocity(n)/(2)(Length)   harmonic series  fundamental frequency/first harmonic   n = 1 Physics 2E 17  second harmonic/first overtone   n = 2 Physics 2E 18 Chap 16 Sound and Hearing • sound range • o ultrasonic o  above 20k Hz o audible o  20-20k Hz o infrasonic o  below 20 Hz • displacement of sound wave • o o  A = displacement amplitude  o o  pressure amplitude = (bulk modulus)(displacement amplitude)(K)(sin(kx- wt))   Physics 2E 19 o o  at a single point in time. y(x,t) and p(x,t) will move to the right at wave speed v = w/k (where v usually = speed of sound, 344m/s) • speed of sound • o o  speed of longitudinal wave in a fluid = sqrt((Bulk modulus)/(density)) o o  speed of longitudinal wave in a solid rod = sqrt((Young's modulus)/ (density))   a bulk solid depends on its surroundings, and does not fit this definition o Physics 2E 20 o  speed of longitudinal wave in a gas = sqrt((ratio of heat capacities)(Bulk modulus)/(density))   ratio of heat capacities for air is 1.40 • sound intensity • o o  intensity of a sinusodial sound wave = (1/2)(displacement amplitude)^2(angular frequency)^2sqrt((density)(bulk modulus))  W/m^2 o o  sound intensity level = (10 decibels)log(intensity/10^-12)  decibles o examples in slides lecture 13 (addition of two intensities and sensitivity of ear) • standing sound waves and normal modes • o tube with both ends fixed o Physics 2E 21    displacement node = Ymin = pressure antinode = Pmax  displacement antinode = Ymax = pressure node = Pmin o because ears detect pressure variations in the air, a person will hear no sound if you are at a pressure node or displacement antinode o if one end is open, that end is a pressure node/displacement antinode (A) o harmonics o  of an open pipe o     where n = # of displacement node = pressure antinode  stopped pipe   Physics 2E 22   can only have odd numbered n's • Resonance and Sound • o similar to of a string: happens at normal modes • Interference of waves • o superposition of waves with same frequency o  y = y1 + y2 = displacement  p = p1 +p2 = pressure o two speakers driven by the same amplifer o  constructive happens when the waves are in phase - D1 + D1 or D1 + (D1 + λ)  destructive happens when the waves are out of phase - D1 + (D1 + λ/2) • beats • o superposition of waves with different frequencies o o o  frequency of beat = frequency1 - frequency2 • Doppler effect • o moving listener/stationary source o Physics 2E 23    frequency listener hears = (frequency from source)((1 +/- (velocity of listener/speed of sound wave))  + for approaching, - for receding o moving source/stationary listener o    frequency listener hears = (frequency from source)(1/(1+/- (velocity of source/speed of sound wave))) o both sources moving o    frequency listener hears = (frequency from source)((speed of sound)+/-(velocity of listener))/((speed of sound)-/+(velocity of source))  upper signs: approaching  lower signs: receding o electromagnetic waves (Doppler effect for light) o    freqency of observer = (frequency from source)sqrt((speed of sound - particle's velocity)/(speed of sound + particle's velocity))  when v is positive, the source is moving directly away from the receiver  when v is negative, the source is moving directly toward the receiver • Shock waves • o supersonic - when the velocity of source is greater than the velocity of sound o  the Doppler effect no longer describes the sound wave in front of the source o shock wave o Physics 2E 24   o mach number o  Physics 2E 25 Chap 32 Elecromagnetic Waves • Photo Electric effect • o when light hits metal, an electron is emitted o energy in light/energy of photon at a certain frequency o    energy of a photon = (plank's constanta 6.63*10^-34 J/s) (frequency) o power of a light source o    power = (# of photons/time)(energy of photon) • light has both wave and particle nature • o • plane wave • o o  velocity of wave propagates in the x direction  E - electric field  B - magnetic field  E orthogonal B  right hand rule curves from E to B • electromagnetic wave in a vacuum • Physics 2E 26 o o  electric field = (magnetic field)(speed of electromagnetic wave) o o  magnetic field = ( o o  speed of wave = 1/( o c = v • sinosodual waves • o o  transverse polarization o sinusoidal electromagnetic plane waves propagating in the + x direction o o  where kx - wt = constant  Physics 2E 27 • • speed of electromagnetic waves through a medium (dielectric) • o o  velocity = (speed of light)/sqrt(dielectric constant) = (speed of light)/ (index of refraction) • energy in electromagnetic waves • o energy density of B = energy density of E o poynting vector S o  energy flow per unit area and per unit time (instantaneous energy flow density)   o   poynting vector = (E x B)/permeability  Physics 2E 28  the other equations (below) show E times B, not cross product...but momentum seems to show S = EB/mu...idk y  J/s m^2 or W/m^2 o intensity in a sinusoidal wave o    intensity = average poynting vector = (Emax)(Bmax)/ (2 permeability) • momentum of a wave • o o  momentum density = (EB)/(permeability * speed of light^2) = poynting vector/speed of light^2 o o  momentum flow rate = (EB)/(permeability * speed of light) = poynting vector/speed of light • radiation pressure • o momentum is responsible for radiation pressure o average fore per unit area due to an electromagnetic wave o wave totally absorbed o  o wave totally reflected o  o • standing electromagnetic waves • o behave similar to normal waves (fn = nv/2L) o  now called cavity Physics 2E 29 o E has nodes at x = 0, lambda/2, lambda, ect. o  antinodes (max) at B nodes  sin function o B has nodes at x = lambda/4, 3lambda/4, ect. o  antinodes (max) and E nodes  cosine function Physics 2E 30 Chap 33 the Nature and Propagation of Light • optics • o the behavior of light and other electromagnetic waves • types of light • o coherent o  plane wave  laser light  all waves are in-phase o incoherent o  no phase relation o white light o  all frequencies (or wavelengths) o monochromatic light o  1 frequency o polarized o  o nonpolarized (natural light) o  • ray • o normal to the direction of the moving wave o  as far as i can tell, its the same thing as a poynting vector • Reflection vs Refraction • o Reflection o Physics 2E 31  specular    diffuse    law of specular reflection     o refraction o  when a wave passes through a differ
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