Exam 3 Review. F P av A. m V

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1 Chapter 9: luids Learn the physics o liquids and gases. States o Matter Solids, liquids, and gases. Exam 3 Reiew ressure a ascal s rinciple change in pressure at any point in a conined luid is transmitted eerywhere throughout the luid. The Eect o Graity on luid ressure gd The density is deined as m V Measuring ressure Use a U-tube manometer. There are many units or pressure. Gauge pressure is the pressure aboe an atmosphere. gauge abs atm Buoyant orce rchimedes principle - luid exerts an upward buoyant orce on a submerged object equal in magnitude to the weight o the olume o luid displaced by the object. B gv luid low Continuity equation comes rom the conseration o mass

2 Bernoulli s Equation gy gy You need a lot o inormation to use Bernoulli s equation. Viscosity Real luids hae iscosity (luid riction). oiseuille s law is V t / L r 8 4 The unit o iscosity () is a-s. Turbulent low inoles the ormation o swirling ortices o luid. Compare it to laminar low. Viscous Drag ccording to Stokes law, or iscous drag on a sphere is proportional the sphere s elocity through the luid: D 6r Surace Tension The surace o a luid behaes like a stretched membrane under tension. Chapter 0: Elasticity and scillations stress will deorm a body and that body can be set into periodic oscillations. Elastic Deormations o Solids Elastic objects return to their original shape ater the stress is remoed. Hooke s Law or Tensile and Compressie orces Stress is deined as stress Strain is deined as the ractional change o length L strain L Hooke s law asserts that the stress is proportional to the stain. The proportionality constant is called Young s modulus

3 Y L L Beyond Hooke s Law the stress takes the material out o the elastic regime, permanent changes can occur. o Elastic limit is the stress where the elastic behaior ends. o urther stress can racture the solid at its breaking point. o The maximum stress that can be reached without breaking is called the ultimate strength. Ductile and brittle materials hae dierent behaior. o Ductile materials can stretch beore they racture. o Brittle materials racture abruptly. Shear and Volume Deormations The shear modulus x S L The bulk modulus V B V The negatie sign is needed since the olume decreases with the stress. Simple Harmonic Motion (SHM) n the icinity o stable equilibrium, small excursions lead to a restoring orce proportional to the displacement rom equilibrium. The maximum displacement rom equilibrium is called the amplitude. dissipatie orces are small, conseration o mechanical energy can be used to show that the mechanical energy is E total k The eriod and requency or SHM The period and requency o periodic motion are related T Not all periodic motion is simple harmonic. 3

4 The kinematic equations or simple harmonic motion can be ound rom the equations or uniorm circular motion. The angular requency or a spring-mass system k m Expressions or the period and linear requency can be ound. The maximum speeds and accelerations are m and a m Graphical nalysis o SHM a particle s position is gien by x( cos t ts speed and acceleration are ( sint a particle s position is gien by and a( cos t x( sin t ts speed and acceleration are ( cos t and a( sin t The position, elocity, and acceleration are sinusoidal (sine or cosine unctions). The endulum or small oscillations, the simple pendulum can be treated as a harmonic oscillator. g L The period o a physical pendulum is T mgd 4

5 Here d is the distance rom the center o mass o the pendulum to the point o support. Damped scillations Eentually dissipatie orces take energy out o the oscillating system. The amplitude o oscillations will decrease. orced scillations and Resonance When the driing requency is equal to the natural requency o the system, the amplitude o the motion is a maximum. Resonance can be destructie in mechanical systems. Chapter : Waes wae transports energy without transporting mass. wae can be thought o a large number o coupled harmonic oscillators. Waes and Energy Transport Waes transport energy. The intensity o a wae is 4r The latter relation holds or spherical waes. Transerse and Longitudinal Waes The particles oscillate perpendicular to the motion o the wae in a transerse wae. The particles oscillate along the line o motion o the wae in a longitudinal wae. Some wae hae both transerse and longitudinal properties. Speed o Transerse Waes on a String or a string under tension and with mass per unit length, n general, more restoring orce makes aster waes; more inertia makes slower waes. eriodic Waes eriodic wae repeat oer some time T. ery important relationship or waes is 5

6 eriod (T) While staring at a point in the wae, how long does it take or the wae to repeat itsel. requency () The number o times the wae repeats per unit time. The inerse o the period. Waelength () While looking at a photograph o the wae, it is the distance along the wae where the pattern will repeat itsel. mplitude () The urthest displacement rom equilibrium or the wae. Harmonic waes are sinusoidal periodic waes Mathematical Description o a Wae or a traeling wae y( x, cos[ ( t x/ )] or y( x, cos( t kx) The waenumber, k is and k k Graphing Waes ery useul way to understand the motion o the wae. rinciple o Superposition When two or more waes oerlap, the net disturbance at any point is the sum o the indiidual disturbances due to each wae. The waes pass through each other undisturbed. Relection and Reraction Relection o a wae can occur at a boundary between one medium and another. rope tied to wall is a good example. o The relected wae will return inerted i the boundary is a ixed point. o The relected wae will return upright i the boundary is ree to moe. The speed o the wae can change when traeling rom one medium into another. o The waelength changes. The requency does not. When the wae traels rom one medium into another, reraction can occur and its direction can change. 6

7 ntererence and Diraction Because o the principle o superposition, the interaction o coherent wae can hae dramatic eects. Coherent waes hae the same waelength and a constant phase relation. o Constructie intererence occurs when the phase relation between the coherent waes is 0,, 4, etc. o Destructie intererence occurs when the phase relation between the coherent waes is, 3, 5, etc. o therwise, the eect is between constructie and destructie. Diraction is the spreading o a wae around an obstacle. Standing Waes The constructie intererence o a incident and relected wae orms a standing wae. y( x, sin kxcos t or a standing wae on a string, the stationary ends are nodes. oints o maximum ibration are called antinodes. The possible waelengths or the standing waes are The requencies are n L n,,3, n n n,,3, L The lowest requency is called the undamental. These are the natural requencies o the string. n Chapter : Sound pply our understanding o waes to a ery important example. Sound Waes Longitudinal waes with an alternating series o compressions and rareactions. ressure nodes are displacement antinodes and ice ersa. The aerage human can hear requencies between 0 Hz and 0,000 Hz. The Speed o Sound Waes n general 7

8 a measure o therestoringorce a measure o theinertia mplitude and ntensity o Sound Waes There are two ways to describe a wae pressure or displacement. pressure node is a displacement antinode and a pressure antinode is a displacement node. The relation between pressure amplitude and displacement amplitude is p 0 s 0 The intensity is proportional to the square o the amplitude 0 p ntensity is measured on the decibel scale (0 db)log 0 0 The decibel scale more closely approximates the response o human hearing. Standing Sound Waes or a pipe with both ends open, o The ends are displacement antinodes. o ll harmonics are heard. o The requencies are n n L n n,,3, or a pipe with one end open, o The open end is a displacement antinode, the closed end is a displacement node. o nly odd harmonics are heard. o The requencies are n n 4L n n,3,5, Timbre The dierent mixture o undamental requencies and harmonics gie instruments and oices their unique quality and color. 8

9 The Human Ear The ear is remarkable deice. Loudness is related to intensity. The decibel scale approximates the response o the ear to loudness itch is the ear s response to requency. Beats Two sound waes with similar requencies interere. The interering waes combine and the enelope o the combining waes can be heard. The beat requency or two sound waes with requencies and is beat The Doppler Eect The requency experience by an obserer is inluenced by the motion o the source and the obserer. Used in many applications to measure elocity. o Moing source S / s>0 i source moes in the same direction as the wae. o Moing obserer ( / ) S S o>0 i source moes in the same direction as the wae. o Source and obserer moing S / / S the source moes aster than the speed o the wae in the medium, shock waes result. Echolocation and Medical maging Sonar is used to image objects underwater. Ultrasound is used to saely image inside the body. 9

Exam 3 Review. Chapter 10: Elasticity and Oscillations A stress will deform a body and that body can be set into periodic oscillations.

Exam 3 Review. Chapter 10: Elasticity and Oscillations A stress will deform a body and that body can be set into periodic oscillations. Exam 3 Review Chapter 10: Elasticity and Oscillations stress will deform a body and that body can be set into periodic oscillations. Elastic Deformations of Solids Elastic objects return to their original