How Things Work I
How Things Work I PHYS 6050
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Date Created: 09/21/15
Question Carousels and Roller Coasters When the wine glass was directly above my head was there a force pushing up on the wine glass that kept the glass against the tray Observations About The Experience Carousels amp Roller Coasters of Weight You can feel motion with your eyes closed When you are at equilibrium You feel pulled in unusual directions a supportforce balances yourweight You sometimes feel weightless supportforce acts on your lower surfaces You often can t tell when you re inverted Weightf rce ads thr ugh my ur b dy You feel internal supporting stresses You identify these stresses as weight amuses and poielongate 5 mm andRolercoaslels e The Experience Acceleration of Acceleration and Weight When you are accelerating Fictitious force felt while accelerating a support force usually causes acceleration Feeling caused by your body s inertia support force acts on your surfaces Directed opposite your acceleration inertia resists acceleration throughout your bod Proportional to the acceleration You feel internal supporting stresses Apparent weight felt due to the You misidentify these stresses as weight combined EffeCtS 0f QraVltatlonal and fictitious forces Carousels Part 1 Riders undergo uniform circular motion Riders follow a circular path Riders move at constant speed UCM involves centripetal acceleration Acceleration points toward the circles center Depends on speed and circle size Acceleration velocity2 radius Carousels Part 2 Centripetal acceleration requires force directed toward circle s center This centripetal force is a true force Centripetal acceleration yields a fictitious force called centrifugal force Force is directed away from circle s center An experience of inertia not a real force camseis and Roller Coasters 9 Question When the wine glass was directly above my head was there a real force pushing up on the wine glass that kept the glass against the tray 157005915 and R009 Coaslels m Roller Coasters Part 1 Hills During hill descent acceleration is downhill fictitious force is uphill apparent weight is weak and into the track At bottom of hill acceleration is approximately upward fictitious force is approximately downward apparent weight is very strong and downward Roller Coasters Part 2 Loops At top of looptheloop acceleration is strongly downward fictitious force is strongly upward apparent weight is weak but upward Choosing a Seat As you go over cliffshaped hills acceleration is downward fictitious force is upward higher speed a more acceleration and force First car goes over cliff slowly Last car goes over cliff quickly Last car has best weightless feeling Garden WSYQWQ 1 Garden Watering Garden Watering 2 Question Water pours weakly from an open hose but sprays hard when you cover most of the end with your thumb When is more water coming out of the hose When the hose end is uncovered When your thumb covers most of the end Garden WSYQWQ 3 Observations About Garden Watering Faucets allow you to control water flow Faucets make noise when open Longer thinner hoses deliver less water Water sprays faster from a nozzle Water only sprays so high Ajet of water can push things over Garden Watering 4 Faucets Limiting Flow Water s total energy limited by its pressure Maximum kinetic energy limited by total energy Maximum speed limited by kinetic energy Water has viscosity friction within the fluid Water at the walls is stationary Remaining water slows due to viscous forces Garden WSYQWQ 5 Viscous Forces Oppose relative motion within a fluid Similar to sliding friction waste energy Fluids are characterized by their viscosities Garden Watering 6 Hoses Limiting Flow Water flow through a hose Increases as 1viscosity Increases as 1hose length Increases as pressure difference Increases as pipe diameter4 Poiseuille s law Garden new 7 Water Flow in a Hose Garden mm x Viscous drag increases with ow speed Faster ow causes quicker drop in pressure Flowing water loses energy to viscous drag Faster new leads to more viscous energy loss Question Water pours weakly from an open hose but sprays hard when you cover most of the end with yourthumb When is more water coming out of the hose When the hose end is uncovered When your thumb covers most ofthe end Gm Witsmg a WWW 1n Accelerating Outward Flows Bend Water in steadystate ow can accelerate Acceleration must be partly to the side Forward acceleration would expand water ackward accelerat ion would compress water ration De ecting water away from a surface Involves acceleration awayf is cau e surface ed by a outward pressure gradient higherpressure nea urfa luvverpress re awayfrum surface causes water to travel slower near the surface causes speed c a g cmquot mm M Mammy 2 Inward Bend Law mum manual Iliuh limmin De ecting watertoward a surfa involves acceleration toward su e sed by inward pressure gradient el faster near the surface Inward Nozzles Bend Speeding Water Up Water passing through a narrowin speeds up experiences pressure drop Water passing through a widening slows d experiences a rise in pressure WWW WWW T es of Nozzles yp Flow Laminar Flow Nearby regions of water remain nearby Viscosity dominate o Turbulent Flow Nearby regions of water become separated Inertia dominates w WWW WWW Reynolds Water and Number Momentum Reynolds number controls type of ow Below about 0 Laminar ow Viscosity dominates Above about 2300 Turbulent ow Inertia dominates Water carries mome um Momentum is transferred by impulses im e pressure imbalance sur ce area time Large transfers long times large surface areas or large pressure imbalances Moving water can be hard to stop Miriam Lam sum mammals Question meandescent Light Bubs An incandescent light bulb contains some gas with the lament would removing the gas affect the bulbs energy ef ciency Make it more ef cient Make it less ef cient No chan e Thermal Black Body Radiation Spectrum All materials contain electric charges The specthm Thermal energy makes charges accelerate and 39quottenS39ty f Accelerating charges emit electromagnetic elemomagnet39c Waves waves from a 1 All materials emit electro magnetic waves thermal radiation black body depend only on its temperature WWW Mammal Incandescent Operation Issues Bulbs Part 1 Features Tungsten lament yields light Electric wires deliver power l Glass bulb protects lament Inert gas ll prolongs life Filament temperature Determines color temperature and ef ciency Higher temperature yields higher ef ciency 7 Higher temperature shortens lament life I Filament heating Heats due to power lost by an electric current Requires thinner lament at higher voltages Salinamt Balloons MW Question A helium balloon has mass yet it doesn t fall to the oor Is there a real force pushing up on the helium balloon Observations About Balloons Balloons are held taut by the gases inside Some balloon oat while others don t Hotair balloons don t have to be sealed Characteristics Air is a gas Consists of individual atoms and molecules Particles kept separate bythermal energy d it n Particles bounce aroun Helium balloons leak even when sealed in free fall m Wm WM r and Air and Pressure Density Air has pressure Air particles exerts forces on container walls Average force is proportional to surface area Average force per unit of area is called pressure Air has densit Air particles have mass Each volume of air has a mass Average mass per unit of volume is called density MW Air Pressure and Density Air pressure is proportional to density Denser particles hit surface more often Denser air a more pressure MW Pressure Imbalances Balanced pressure exerts no overall force Forces on balloon39s sides cancel Unbalanced pressure exerts overall force Forces on balloon39s sides don39t cancel Forces push balloon toward lower pressure Air pressure also pushes on the air itself Air itself is pushed toward lower pressure Myquot 5 The Atmosphere Air nearthe ground supports air overhead Air pressure is highest near the ground Air density is highest near the ground Key observations Air pressure decreases with altitude A balloon feels more force at bottom than top Imbalance yields an upward buoyant force Archimedes Principle A balloon immersed in a uid experience an upward buoyant force equal to the weight ofthe uid it displaces Myquot 11 ColdAir Balloon in Air A rubber coldair lled balloon the cold air it displaces experiences a downward net force in cold air sinks in cold air lts average density is greaterthan that of cold air I E 2 Air and Temperature Air pressure is proportional to temperature aster particles hit surface more an harder Hotter air a more pressure saloons 13 An Aside About Temperature Air has temperature Air particles have thermal kinetic energy Average thermal kinetic energy is proportional to absolute temperature SI absolute temperature kelvins or K 0 K is absolute zero no thermal energy left Step size 1 K step same as 1 00 step HotAir Balloon in Air A rubber hotairfilled balloon contains fewer air particles than if it were cold weighs less than the cold air it displaces experiences an upward net force in cold air floats in cold air Its average density is less than that of cold air saloons 15 Helium vs Air Replacing air particles with helium atoms reduces the gas s density helium atoms have less mass than air particles leaves the gas s pressure unchanged less massive helium atoms travel faster amp hit more Helium Balloon in Air A rubber heliumfilled balloon has same particle density as air weighs less than the air it displaces experiences an upward net force in air floats in air Its average density is less than that of air Question A helium balloon has mass yet it doesn t fall to the floor Is there a real force pushing up on the helium balloon Balloons 15 Ideal Gas Law Pressure Boltzmann constant Particle density Absolute temperature Only applies perfectly to independent particles Real particles are not completely independent Wale Steam andtel Water Steam and Ice Wale Steam andcg 2 Question A glass of ice water contains both ice and water After a few minutes of settling how do the temperatures ofthe ice and the water compare The ice is colder than the water The water is colder than the ice They re at the same temperature Obsenations About Water Steam and Ice Water has three forms or phases Ice is typically present below 32 F or 0 C Water is typically present above that Steam is typically present at high temps The three phases sometimes coexist Wale Steam andcg 4 Phases of Matter Solid fixed volume and fixed shape Ice a transparent lowdensity solid Liquid fixed volume but variable shape Water a transparent middensity liquid Gas variable volume and variable shape Steam an invisible gas Wale Steam andcg 5 Ice and Water Melting temperature Below it solid ice is the stable phase Above it liquid water is the stable phase At it the liquid and solid phases can coexist Coexistence is a form of equilibrium Dynamic equilibrium molecules swap Turning ice to water takes latent heat MeltingFreezing Part 1 Any change that causes more water molecules to leave the solid than return to it causes the ice to melt Any change that causes more water molecules to return to the solid than leave it causes the water to freeze MeltingFreezing Part 2 To melt ice add heat or increase pressure unique to water amp ice To freeze water remove heat or reduce pressure unique to water amp ice Wale Steam andcg a Question A glass of ice water contains both ice and water After a few minutes of settling how do the temperatures ofthe ice and the water compare The ice is colder than the water The water is colder than the ice They re at the same temperature Wale Steam andcg 9 Water and Steam Liquid and gas can coexist over a broad range of temperatures But at equilibrium liquid density remains nearly constant gas density increases with temperature Equilibrium gas pressure Vapor Pressure Dynamic equilibrium molecules swap Turning water to steam takes latent heat EvaporationCondensation Part 1 Any change that causes more water molecules to leave the liquid than return to it causes the water to evaporate Any change that causes more water molecules to return to the liquid than leave it causes the steam to condense EvaporationCondensation Part 2 To make water evaporate add heat or expand the steam or lower the relative humidity To make steam condense remove heat or compress the steam or raise the relative humidity Boiling Part 1 Evaporation bubbles can form inside water Bubble pressure is the vapor pressure When vapor pressure exceeds ambient pressure the bubble survives and grows Boiling occurs when bubbles can nucleate seed bubbles form bubbles can grow Need for latent heat stabilizes temperature Air Conditioners 1 Air Conditioners Question If you operate a window air conditioner on a table in the middle of a room the average temperature in the room will become colder become hotter stay the same 0 Observations About Air Conditioners They cool room air on hot days They emit hot air from their outside vents They consume lots of electric power They are less efficient on hotter days They can sometimes heat houses too Air Conditioners 4 Heat Machines Air conditioners use work to transfer heat from cold to hot are considered to be heat pumps Automobiles use flow of heat from hot to cold to do work are considered to be heat engines Air Conditioners 5 Thermodynamics Rules governing thermal energy flow Relationships between thermal energy and mechanical work disordered energy and ordered energy Codified in four laws of thermodynamics Air Conditioners 6 0th Law Law about Thermal Equilibrium lftwo objects are in thermal equilibrium with a third object then they are in thermal equilibrium with each other Air Conditioners 7 1st Law Law about Conservation of Energy Change in internal energy equals heat in minus work out where Internal energy thermal stored energies Heat in heat transferred into object Work out external work done by object Order versus Disorder It is easy to convert ordered energy into thermal disordered energy It is hard to converting thermal energy into ordered energy Statistically order to disorder is oneway Air Conditioners 9 Entropy Entropy is measure of objects disorder Includes both thermal and structural disorders Isolated system s disorder never decreases Entropy can move or be transferred Aw Conmtioners W 2nd Law Law about Disorder Entropy Entropy of a thermally isolated system never decreases Air Conditioners 11 3rd Law Law about Entropy and Temperature An object s entropy approaches zero as its temperature approaches absolute zero More on the 2nd Law According to the 2nd Law Entropy of a thermally isolated system can t decrease But entropy can be redistributed within the system Part of the system can become hotter while another part becomes colder Natural Heat Flow Heat naturally flows from hot to cold Removing heat from a hot object L entropy Adding heat to a cold object 1 entropy Entropy of combined system increases 1 J ofthermal energy is more disordering to a cold object than to a hot object Unnatural Heat Flow Heat can t naturally flow from cold to hot Removing heat from cold object L entropy Adding heat to hot object 1 entropy More entropy removed than added Energy is conserved but L total entropy To save 2nd law we need more entropy Ordered energy must become disordered Air conditioners Part 1 Moves heat against its natural flow Flows from cold room air to hot outside air Converts ordered into disordered energy Doesn t decrease the world s total entropy Uses fluid to transfer heat working fluid Fluid absorbs heat from cool room air Fluid releases heat to warm outside air Air conditioners Part 2 Evaporator located in room air transfers heat from room air to fluid Condenser located in outside air transfers heat from fluid to outside air Compressor located in outside air does work on fluid and creates entropy Evaporator Part 1 Heat exchanger made from long metal pipe Fluid approaches evaporator as a high pressure liquid near room temperature A constriction reduces the fluids pressure Fluid enters evaporator as a low pressure liquid near room temperature Evaporator Part 2 Working fluid evaporates in the evaporator Breaking bonds uses thermal energy Fluid becomes colder gas Heat flows from room air into fluid Fluid leaves evaporator as a low pressure gas near room temperature Heat has left the room Clocks 1 Clocks Cocks 2 Question You re bouncing gently up and down at the end of a springboard without leaving the board s surface If you bounce harder the time it takes for each bounce will become shorter become longer remain the same Obsenations About Clocks They divide time into uniform intervals They count the passage ofthose intervals Some involve obvious mechanical motions Some seem to involve no motion at all They require an energy source They have limited accuracy NonRepetitive Clocks Measures a single interval of time Sandglasses Water clocks Candles Common in antiquity Poorly suited to subdividing the day Requires frequent operator intervention Operator requirement limits accuracy Repetitive Motions An object with a stable equilibrium tends to oscillate about that equilibrium This oscillation entails at least two types of energy kinetic and a potential energy Once the motion has been started it repeats spontaneously many times RepetitiveMotion Clocks Developed about 500 years ago Require no operator intervention Accuracy limited only by repetitive motion Motion shouldn t depend on externals temperature air pressure time of clay clock s store of energy mechanism that observes the motion Some Specifics Terminolo Period time of full repetitive motion cycle Frequency cycles completed per unit oftime Amplitude peak extent of repetitive motion Application In an ideal clock the repetitive motion39s period shouldn39t depend on its amplitude am A Harmonic Oscillator A system with a stable equilibrium and a restoring force that s proportional to its distortion away 39om that equilibrium A period that s independent ofamplitude Examples Mass on a spring W55 Question You re bouncing gently up and dovm at the end of a springboard without leaving the board s surface If you bounce harder the time it takes for each bounce will remain the same Limits to the Accuracy Fundamental limits Oscillation decay limits preciseness of period Practical Limits Sustaining motion can in uence the period erving the period can in uence the period Sensitivity to temperature pressure wind mm Pendulums Pendulum almost a harmonic oscillator Period proportional to lengthgravity 2 Period almost independent ofamplitude Pendulum Clocks Pendulum is clock s timekeeper El For accuracy the pendulum pivot centerofgravity distance is tern Erature stabilized adjustable furlucal gravity Effects streamlined to minimize air drag motion sustained measured gently Limitation clock mustn39t move I Balance Ring Clocks A torsional spring causes a balancering harmonic oscillator to twist back and forth Gravity exerts no torque about the rings pivot and has no in uence on the perio W Twisting is sustained and measured w39th minimal quot3 effects on the rings motion 39 mm mm minquot Quartz Oscillators Part 1 Crystalline quartz is a harmonic oscillator Crystal provides the inertial mass Stiffness provides restoring force Oscillation decay is extremely slow Fundamental accuracy is very high Quartz Oscillators Part 2 Quartz is piezoelectric mechanical and electrical changes coupled motion is induced and measured electrically Quartz Clocks Electronic system starts crystal vibrating Vibrating crystal triggers electronic counter Nearly insensitive to gravity temperature ressure and acceleration Slow vibration decay leads to precise period Tuningfork shape yields slow ef cient vibration 0954517 Atomic Clocks Electrons orbit the nucleus ofan atom Only certain orbits are possible due to quantum mechanical nature of universe Associated with each these orbitals is a speci c amount oftotal energy Quantum leap from one orbital to another involves a speci c amount of energy mama Atomic Clocks energy is a speci c frequen y Light ofa speci c frequency carries a certain amount ofenergy per packet Atoms can only emit or absorb light of speci c frequencies the ones that carry just the right energy to shi electrons between orbita s Associated with a speci c amount of c Houncm Halls 1 Bouncing Balls Emmy Halls 2 Question If you place a tennis ball on a basketball and drop this stack on the ground how high will the tennis ball bounce To approximately its original height Much higher than its original height Much less than its original height Observations About Bouncing Balls Some balls bounce better than others Underinflated balls bounce poorly Balls don t bounce higher than they started Ball can bounce from moving objects Bouncing from Rigid Motionless Surfaces Approaching ball has collision KE During impact ball has elastic PE Rebounding ball has rebound KE Some collision energy becomes thermal Lively balls lose little energy Dead balls lose much energy In general rebound KE lt collision KE Houncm Halls 5 Coefficient of Restitution Measure of a ball s liveliness Ratio of outgoing to incoming speeds Coefficient of restitution Outgoing speed Incoming speed Bouncing from Elastic Motionless Surfaces Both ball and surface dent during bounce Work is proportional to dent distance Denting surface stores amp returns energy Lively surface loses little energy Dead surface loses much energy Surface has a coefficient of restitution too Bouncing from Moving Surfaces Incoming speed gtApproaching speed Outgoing speed gt Separating speed Coef cient of Restitution becomes Coef cient of restitution eparating speed Approaching speed Ball and Bat Part1 Ball a roaches home plate 100 kmh quot Bat approaches pitcher at 100 kmh Approaching speed is mh Ball and Bat Part 2 Approaching speed is 200 kmh Separating speed is 11 m h Baseball s Coef cient of Restitution 055 Ball and Bat Part 3 Separating speed is 110 kmh 5 Bat approaches M pitcher at 100 kmh Ball approaches MWquot pitcher at 210 kmh Wm m 11 Question Ifyou place a tennis ball on a basketball and drop this stack on the ground how high will the tennis ball bounce To approximately its original height Much higherthan its original height Much less than its original height Bouncing s Effects on Objects Bouncing involves momentum transfer Momentum transferred while stopping Momentum transferre while rebounding A better bounce transfers more momentum Bouncing can involve energy transfer Together these transfers govern bouncing Identical elastic balls transfer motion perfectly m a w Wqu 1 The Sea and Surfing m a w Wqu 2 Question You oat motionless in an inner tubejust far enough from the shore that the waves aren t breaking on top ofyou You will drilt shoreward at the speed of the waves drilt gradually but steadily shoreward move in a circle as each wave passes but make little or no progress toward shore Observations About The Sea and Surfing The sea is rarely calm it has ripples on it The broadest ripples waves travel fastest Waves seem to get steeper near shore Waves break or crumble near shore Waves bend after passing over sandbars You can sometimes ride waves The Tides art The moon s gravity acts on the earth The moon s gravity isn t uniform Law has The Tides Part 2 There are two tidal bulges in the oceans As the earth rotates these bulges moves Almost 2 high and 2 lowtides per day Strongest tides are near equator Weakest tides are near poles m a w Wqu a The Sun s Influence Sun s gravity affects tides Strongest tides are when and sun are aligned Weakest tides are when moon and sun are at right angles m a w Wqu 7 Tidal Resonance Waterin a con ned channel can slosh back and orth Bl It s another harmonic oscillator Mla Period depends on inertia and stiffness of the restoring force Ifthe sloshing time matches the tidal period resonance L L j Standing and Traveling Waves Sloshing involves standing waves Water exhibits xed nodes and antinodes Open water surf involves traveling wave Wave crests and troughs shift continuously Mummm Water Waves Sloshing involves deep water waves the whole liquid moves back and forth Sur ce waves only affect the liquids top lentcmsll gt viilazily m a mm in Water s Motion Surface water circles as the wave passes Circling is strongest at surface Motion is weak about 12 wavelength deep m a HMSWW 11 Question You oat motionless in an inner tube just far enough from the shore that the waves aren t breaking on top ofyou You will drilt shoreward at the speed of the waves drilt gradually but steadily shoreward move in a circle as each wave passes but make little or no progress toward shore m a HMSWW 2 Wavelength Longer the wavelength of sur ce wave faster it travels deeper water moves as it passes more energy it contains for a given amplitude Tsunamis are very long wavelength very deep very high energy waves and not strictly surface waves either sum 7mm Balls and Frisbees sum new Question A smooth gentle river is owing past a cylindrical post At the sides of the post is the water level higher lower or equal to its level in the open river7 Observations About Balls and Frisbees Balls slow down in ight The faster a ball goes the quicker it slows Spinning balls curve in i Frisbees use airto support themselves mm mm Aerodynamic Forces Drag Forces push the object directly downstream result from slowing the uid ow transfer downstream momentum to the object Li orces push the object at right angles to the ow result from de ecting the uid ow transfer sideways momentum to the object sum humus Drag amp Lift Sur ce friction causes viscous drag Turbulence causes pressure drag De ected ow causes li De ected ow causes induced drag Perfect Flow Around a Ball Outward bend in 39ont high pressure slow ow Inward bend on sides low pressure fast ow Outward bend in back high pressure slow ow a Pressures balance so only viscous drag Sallsand 7mm Question A smooth gentle river is owing past a cylindrical post At the sides ofthe post is the water level higher lower or equal to its level in the open n39vei aim Wm Onset of Turbulence Rising pressure slows uid Fluid accelerates backward as pressure rises Fluid loses speed but its pressure rises Viscous drag slows ow near surface Surface layer of uid loses total energy Fluid loses both speed and pressure If surface ow stops turbulence ensues Imperfect Flow Low Speeds Pressure rises in front Pressure drops on side Big wake forms behind Wake pressure is approximately ambient Ball experiences large pressure drag Sallsand m 10 Boundary Layer Flow near sur ce forms boundary layerquot At low Reynolds number lt100000 boundary layer is laminar slowed by viscous dra At high Reynolds numbergt100000 boundary layer is turbulen not slowed much Imperfect Flow High Speeds Pressure rises in front Pressure drops on side Small wake forms behind Wake pressure 39s approximately ambient Ball experiences small pressure drag Tripping the Boundary Layer To reduce pressure drag initiate turbulence in the boundary layer trip delay ow separation on back of ball shrink the turbulent wake Examples Tennis balls and Golf balls Sallsand Mweesl Sallsand m 14 Spinning Balls Spinning Balls Magnus Force Wake Force Sur ce pulls ow with it Sur ce pulls ow with it One side experiences longerinward bend That side has lower pressure and faster ow Overall ow is de ected Magnus lilt force Wake is asymmetric Overall owis de ected Wake de ection li force Sallsand Mweesls Sallsand m it Frisbees Starting Flight Above Frisbee air ow bends inward low pressure high speed No quot11 Below Frisbee 39 ai ow bends outward high pressure low speed Pressure imbalance lilts the Frisbee Mm New Mm MW 18 Vortex Shedding Stable lift Trailing airflow unstable 7 A er vortex is shed Frisbee has li Frisbee is pushed y air Air ow around Frisbee has angular momentum cw angular momentum Wheels 1 Wheels Wheels 2 Question You are in a tremendous hurry and you want your car to accelerate as quickly as possible when the light turns green Tire damage is not an issue Will you accelerate faster if you burn rubber skid your wheels or if you just barely avoid skidding your wheels Obsenations About Wheels Without wheels objects slide to a stop Friction is responsible for stopping effect Friction seems to make energy disappear Wheels eliminate friction or so it seems Wheels can also propel vehicles but how Wheels 4 Friction Opposes relative motion of two surfaces Acts to bring two surfaces to one velocity Consists of a matched pair of forces Object 1 pushes on object 2 Object 2 pushes on object 1 Equal magnitudes opposite directions Comes in two types static and sliding Wheels 5 Types of Friction Static Friction Acts to prevent objects from starting to slide Forces can vary from zero to an upper limit Sliding Friction Acts to stop objects that are already sliding Forces have fixed magnitudes Wheels 6 Frictional Forces Increase when you push the surfaces more tightly together roughen the surfaces Peak static force greater than sliding force Surface features can interpenetrate better Friction force drops when sliding begins Wheels 7 Question You are in a tremendous hurry and you want your car to accelerate as quickly as possible when the light turns green Tire damage is not an issue Will you your wheels or ifyou just barely avoid skidding yourwheels accelerate faster ifyou burn rubberquot skid Wheels x Friction and Wear Static friction No work is done no distance No wear occurs Sliding friction r is done distance in direction of force Wear occurs Work is turned into thermal energy Wheels 5 Conserved Quantity 39 I39Qy A directionless scalar quantity Can39t be created or destroyed Transferable between objects via work Can be converted from one form to another Wheels 10 Forms of Energy Kinetic energy of motion Potential sto Gravitational Ma netic Electric Electrochemical Chemical Nuclear red in forces between objects lastic Wheels 11 Wheels 2 Types of Energy Ordered Energ Organized in chunks eg work Disordered Energy Fragmented eg thermal energy Sliding friction disorders energy Converts work into thermal energy Rollers Eliminate sliding quot friction at roadway Are inconvenient vgiwiy a underthe object Falling Halls 1 Falling Balls ram Halls 2 Question Suppose that I throw a ball upward into the air After the ball leaves my hand is there any force pushing the ball upward Observations About Falling Balls A dropped ball Begins at rest but acquires downward speed Covers more and more distance each second A tossed ball Rises to a certain height Comes briefly to a stop Begins to descend much like dropped ball ram Halls 4 Type of Force Weight earth s gravitational force on object Falling Halls 5 Weight and Mass An object s weight is proportional to its mass weight cc mass weight constant mass On the Earth s surface that constant is 98 newtonskilogram called acceleration due to gravity Acceleration Due to Gravity Why this strange name force mass acceleration Newton s 2nd law 1 newton E1 kilogrammeterlsecond2 de nition 98 newtonskilogram 98 metersecond2 98 metersecond2 is an acceleration Acceleration due to gravity actually is an acceleration On Earth s surface all falling objects accelerate downward at the acceleration due to gravity Why Things Fall Together Increasing an object s mass increases the downward force on it makes it need more force to accelerate These effects balance out perfectly am Sills x A Falling Ball Falling ball accelerates steadily downward Acceleration is constant and down rd Velocity increases in the downward direction Falling from rest stationary Ve ocity s arts a zero and increases downward Altitude decreases at an ever faster rate WW Falling Downward m WWW WW mutuallyquot am 0 Duns snm39s 43m 2 ts r ma Ji m s7 425m ozslrmum s new A Falling Ball Part 2 A falling ball can start by heading upward Velocity starts in the upward direction At some point velocity is momentarily zero Velocity becomes more and more downw rd Altitude decreases at ever faster rate all th swam Falling Upward Throws and First Arcs Am 035 m aamm Gravity only affects quot73quot 35 vertical mo ion 5 L55 A ball can coast y horizontally while 2 quotquot 55X falling vertically mm W W amquot Dismcsdnwn eldtml slam 1 Skating Skating 2 Question A rotary lawn mower spins its sharp blade rapidly overthe lawn and cuts the tops of the grasses off Would the blade still cut the grasses if they weren t attached to the ground Obsenations About Skating When you re at rest on a level surface If not pushed you stay stationary If pushed you start moving in that direction When you re moving on a level surface If not pushed you coast steadily and straight If pushed you change direction or speed Physics Concept Inertia A body at rest tends to remain at rest A body in motion tends to remain in motion slam 5 Newton s First Law First Version An object that is free of external influences moves in a straight line and covers equal distances in equal times Skating 6 Physical Quantities Position an object s location Velocity its change in position with time Newton s First Law Second Version An object that is free of external influences moves at a constant velocity Physical Quantities Position an object s location Velocity its change in position with time Force a push or a pull slam 9 Newton s First Law An object that is not subject to any outside forces moves at a constant velocity skating in Question A rotary lawn mower spins its blade rapidly overthe lawn and cuts the tops of the grasses off Would the blade still cut the grasses if they weren t attached to the ground Skating 11 Physical Quantities Position an object s location Velocity change in position with time Force a push or a pull Acceleration change in velocity with time Mass measure of objects inertia Newton s Second Law The force exerted on an object is equal to the product of that objects mass times its acceleration The acceleration is in the same direction as the force force mass acceleration Violins and Pipe Organs 1 Violins and Pipe Organs llolrrs and F99 Organs 2 Question Sound can break glass Which is easiest to break A glass pane exposed to a loud short sound A glass pane exposed to a certain loud tone A crystal glass exposed to a loud short sound A crystal glass exposed to a certain loud tone Observations About Violins and Pipe Organs They can produce different pitches They must be tuned They sound different even on same pitch Sound character is adjustable Both require power to create sound Can produce blended or dissonant sounds Strings as Harmonic Oscillators A string is a harmonic oscillator Its mass gives it inertia Its tension gives it a restoring force It has a stable equilibrium Restoring forces proportional to displacement Pitch independent of amplitude volume String s Inertia and Restoring Forces String s restoring force stiffness set by string s tension string s curvature or equivalently length String s inertial characteristics set by string s mass per length Fundamental Vibration String vibrates as single arc up and down velocity antinode occurs at center of string velocity nodes occur at ends of string This is the fundamental vibrational mode Pitch frequency of vibration is proportional to tension inversely proportional to string length inversely proportional to mass per length Overtone Vibrations String can also vibrate as two halfstrings one extra antinode three thirdstrings two extra antinodes etc These are higherordervibrational modes They have higher pitches They are called overtones String Harmonics Part 1 o In a string the overtone pitches are at twice the fundamental frequency One octave above the fundamental frequency Produced by two halfstring vibrational mode three times the fundamental frequency An octave and a fth above the fundamental Produced by three halfstring vibrational mode etc String Harmonics Part 2 Integer overtones are called harmonics Bowing or plucking a string tends to excite a mixture of fundamental and harmonic vibrations giving character to the sound Producing Sound Thin objects don t project sound well Air flows around objects Compression and rarefaction is minimal Surfaces project sound much better Air can t flow around surfaces easily Compression and rarefaction is substantial Many instruments use surfaces for sound Plucking and Bowing Plucking a string transfers energy instantly Bowing a string transfers energy gradually Rhythmic excitation at the right frequency causes sympathetic vibration Bowing always excites string at the right frequency The longer the strings resonance lasts the more effective the gradual energy transfer liolrrs and F99 Organs 12 Question Sound can break glass Which is easiest to break A glass pane exposed to a loud short sound A glass pane exposed to a certain loud tone A crystal glass exposed to a loud short sound A crystal glass exposed to a certain loud tone Air as a Harmonic Oscillator A column of air is a harmonic oscillator Its mass gives it inertia Pressure gives it a restoring force It has a stable equilibrium Restoring forces proportional to displacement Pitch independent of amplitude volume Air s Inertia and Restoring Forces Air s restoring force stiffness set by pressure pressure gradient or equivalently length Air s inertial characteristics set by air s mass per length essentially density Fundamental Vibration OpenOpen Column Air column vibrates as a single object Pressure antinode occurs at column center Pressure nodes occur at column ends Pitch frequency of vibration is proportional to air pressure inversely proportional to column length inversely proportional to air density Fundamental Vibration OpenClosed Column Air column vibrates as a single object Pressure antinode occurs at closed end Pressure node occurs at open end Air column in openclosed pipe vibrates as half the column in an openopen pipe at half the frequency of an openopen pipe Air Harmonics Part 1 o In openopen pipe the overtones are at twice fundamental two pressure antinodes three times fundamental three antinodes etc all integer multiples or harmonics ln openclosed pipe the overtones are at three times fundamental two antinodes five times fundamental three antinodes etc all odd integer multiples or harmonics Air Harmonics Part 2 Blowing across column tends to excite a mixture of fundamental and harmonic vibrations Elurwer Cars 1 Bumper Cars Emmet Cars 2 Question You are riding on the edge of a spinning playground merrygoround If you pull yourself to the center of the merrygo round what Will happen to its rotation It will spin faster It will spin slower It will spin at the same rate Observations About Bumper Cars Moving cars tend to stay moving It takes time to change a car s motion Impacts alter velocities amp ang velocities Cars seem to exchange their motions Heavily loaded cars are hardest to redirect Heavily loaded cars packthe most wallop Emmet Cars 4 Momentum Translating bumper car carries momentum Momentum A conserved quantity can t create or destroy A directed vector quantity Measures difficulty reaching velocity Momentum Mass Velocity Exchanging Momentum Impulse The only way to transfer momentum Impulse is a directed vector quantity Impulse Force Time Because of Newton s third law if object 1 gives an impulse to object 2 then object 2 gives an equal but oppositely directed impulse to object 1 Emmet Cars 6 HeadOn Collisions Cars exchange momentum via impulse Total momentum remains unchanged The leastmassive car experiences largest change in velocity Elurwer Cars 7 Angular Momentum A spinning car carries angular momentum Angular momentum A conserved quantity can t create or destroy A directed vector quantity Measures difficulty reaching angular velocity Angular momentum Moment of inertia Angularvelocity Newton s Third Law of Rotational Motion For every torque that one object exerts on a second object there is an equal but oppositely directed torque that the second object exerts on the first object Exchanging Angular Momentum Angular Impulse The only way to transfer angular momentum Angular impulse is a directed vector quantity Angular impulse Torque Time Because of Newton s third law if object 1 gives an angular impulse to object 2 then object 2 gives an equal but oppositely directed angular impulse to object 1 Glancing Collisions Cars exchange angular momentum via angular impulse Total angular momentum about a chosen point in space remains unchanged The car with smallest moment of inertia about that chosen point experiences largest change in angularvelocity Changing Moment of Inertia Mass can t change so the only way an object s velocity can change is if its momentum changes Moment of inertia can change so an object that changes shape can change its angular velocity without changing its angular momentum Emmet Cars 12 Question You are riding on the edge of a spinning playground merrygoround If you pull yourself to the center of the merrygo round what will happen to its rotation It will spin faster It will spin slower It will spin at the same rate Raw 1 Ramps Question Can a ball ever push downward on a table with a force greater than the balls weight Obsenations About Ramps Lifting an object straight up is often difficult Pushing the object up a ramp is usually easier The ease depends on the ramps steepness Shallow ramps require only gentle pushes You seem to get something for nothing How does distance figure in to the picture Type of Force Support force Prevents something from penetrating surface Points directly away from that surface Physics Concept Net Force The sum of all forces on an object Determines object s acceleration Newton s Third Law For every force that one object exerts on a second object there is an equal but oppositely directed force that the second object exerts on the first object Raw 7 Experiment If you push on a friend who is moving away from you how will the force you exert on yourfriend compare to the force your friend exerts on you You push harder Yourfriend pushes harder The forces are equal in magnitude COM Forces Present Part 1 On ball due to gravity its weight On ball due to support from table On table due to support from ball 0 All three forces have the same magnitude for the stationary ball Forces Present Part 2 1 On ball due to gravity its weight 2 On ball due to support from table Pair 3 On table due to support from ball Forces Present Part 3 On earth due to gravity from the b pair On ball due to gravity from the eart On ball due to support from table Pair On table due to support from ball Loop x Since the ball doesn t accelerate 2 and 3 must cancel perfectly Ram 11 Question Can a ball ever push downward on a table with a force greater than the balls weight Two Crucial Notes While the forces two objects exert on one another must be equal and opposite the net force on each object can be anything Each force within an equalbutopposite pair is exerted on a different object so they don t cancel directly Physical Quantities Energy A conserved quantity The capacity to do work Work The mechanical means of transferring energy work force distance where force and distance are in same direction Work Lifting a Ball Part 1 Going straight up Force is large Distance is small work force Forces on a Ramp Support Net Force Work Lifting a Ball Part 2 Going up ramp Force is small Distance is large work distance Work Lifting a Ball Part 3 Going straight up work force Going up ramp work distance The work is the same either way Physics Concept Mechanical Advantage Doing the same amount of work Redistributing force and distance A Mamaes 1 Automobiles mamaes 2 Question A car burns gasoline to obtain energy but allows some heat to escape into the air Could a mechanically perfect car avoid releasing heat altogether Obsenations About Automobiles They burn gas to obtain their power They are rated by horsepower and volume Their engines contain cylinders They have electrical systems They are propelled by their wheels mamaes 4 Heat Engines A heat engine diverts some heat as it flows naturally from hot to cold and converts that heat into useful work Natural heat flow increases entropy Converting heat to work decreases entropy Entropy doesn t decrease Some heat becomes work A Mamaes 5 Heat Pumps A heat pump transfers some heat from cold to hot against the natural flow as it converts useful work into heat Reverse heat flow decreases entropy Converting work to heat increases entropy Entropy doesn t decrease Some heat flows from cold to hot mamaes 6 Question A car burns gasoline to obtain energy but allows some heat to escape into the air Could a mechanically perfect car avoid releasing heat altogether mm x Internal Combustion mm 7 Efficienc y Engine As the temperature difference between hot Burns fuel and air in enclosed space and COM increases Produces hot burned gases 39Hears Change 39quot 9quotquot Py39quot reases Allows heat to ow to cold outside air A hem pumP becomes less emc39em Converts some heat into useful work A heat engine becomes more ef cient mm in mmm Four Stroke Induction Engine Stroke Induction Stroke ll cylinderwith fuel amp air Engine pulls piston out ofcylinder Compression Stroke squeeze mixture Low pressure inside cylinder R 4 Power Stroke burn and extract work Atmospheric pressure pushes Exhaust Stroke empty cylinder of exhaust fuel arid air mixmre quotquot0 CyliNder Elk Engine does work on the gases 7 2 du rin g this stroke mm 11 mm 2 Compression Power Stroke Stroke Engine pushes piston into cylinder 3 g Mixture burns to form hot gases Mixture is compressed to high Gases push piston out of cylinder Gases expand to lower pressure and temperature Gases do work on engine during this stroke pressure and temperature Engine does work on the gases during this stroke 0 minimquot Exhaust Stroke Engine pushes piston into cylinder High pressure inside cylinder Pressure pushes burned gases 1 out ofcylinder 4E Engine does work on the gases Ignition System Car stores energy in an electromagnet Energy is released as a high voltage pulse Classic points and spark coil Electronic transistors and pulse transformer during this stroke mgr WM Efficiency Engine Limits Step 1 Even ideal engine isn t perfect Not all the thermal energy can become work Some heat must be ejected into atmosphere However ideal ef ciency improves as the burned gases become hotter the outside air becomes colder Real engines never reach ideal ef ciency Fuel and air mixture after induction stroke Pressure Atmospheric Temperature Ambient III mummies Engine Step 2 Fuelair mixture a er compression stroke Pressure High Temperature Hot El mmm Engine Step 3 Burned gases alter ignition Pressure Very high Temperature Very hot I Nephew Engine Step 4 Burned gases alter power stroke Pressure Moderate Temperature High ZI Wham Engine Step 4a Burned gases alter extra expansion Pressure Atmospheric Temperature Moderate II Engine Step 4b Burned gases alter even more expansion Pressure Below atmospheric Temperature Ambient II Diesel Engine Uses compression heating to ignite fuel 7 Squeezes pure air to high pressuretemperature e ihieetsmei into air perweeh compression and power strokes 7 Fuel purhs upon entrylnto Superheated air Power stroke extracts work from burned gases High compression allows for high ef ciency mmamles Vehicle Pollution Incomplete burning leaves carbon monoxide and hydrocarbons in exhaust Accidental oxidization of nitrogen produces nitrogen oxides in exhaust Diesel exhaust includes many carbonized particulates Catalytic Converter Platinum assists oxidization of carbon monoxide and hydrocarbons to carbon dioxide and water Rhodium assists reduction ofnitrogen oxides to nitrogen and oxygen Catalysts supported on high speci c surface structure in exhaust duct catalytic
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