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# PHYSICAL SCIENCE PHYS 1010

UGA

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This 18 page Class Notes was uploaded by Heath Hane III on Saturday September 12, 2015. The Class Notes belongs to PHYS 1010 at University of Georgia taught by Caillault in Fall. Since its upload, it has received 48 views. For similar materials see /class/202488/phys-1010-university-of-georgia in Physics 2 at University of Georgia.

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Date Created: 09/12/15

Heisenberg Uncertainty Principle Quantum Mechanics o Heisenberg Uncertainty Principle HUP position and momentum cannot be known simultaneously to arbitrary high precision o Uncertainty referees to measurements the scale used determines accuracy Intuitively accuracy seems to be continuous 0 There is a limit to how accurate a measurement can be in nature Planck39s constant 1034 Electron Diffraction Exhibits wave properties I PX 0 PXMVX PX0 i DXh 9 9 D Vertical axis X 9 9 9 D 0 Amount of diffraction 7L w 7L wavelength W with of slit 0 Can find the amount of the diffraction by the angle at which the dark band is from the horizontal 0 De Broglie39s 7L hmvy From the above equations we can gather 6 hmvyW Uncertainty lies within the width of the slit Ax w called Apx Inthe picture it refers to PX a s Py ignore th atAlso Ris suppose to be Pymvy r APXva Derived from a oppositeadjacent To derive Heisenberg Formula From giveninformation hmvyw APxva Hmv yjAx c e hAx APX h APx Ax a AxAPxgt h 2 o M must be in urderwith 103934 o h 1121 Physics Notes 101011 Copenhagen Interpretation 0 Experiment 1 S creen Weak light 1 photon second gt gt i 0 Experiment 2 I Same experiment as above Weak light 1 but the slit 1s in a dlfferent photon second I position gt gt 1 03 meter 0 Experiment 3 I Now both slits are covered by weak llght 1 transparent detectors that photon second give off a signal ie gt clicking gt gt I You never hear the detectors click at the same time because the light is too weak 1 03 meter 391 0 Experiment 4 No detectors Weak light 1 I photon second Interference pattern gt An interference pattern is created because the light waves now have to interfere with each because there are gt no detectors I Time 03mc 03m3x10 8ms 10A9 s So the light from one of the W slits only had a billionth IDA9 of a second to interfere with the light from the other slit before it hit the screen This is why you did not hear the clicks from the detectors in experiment 3 at the same time WaveParticle Duality 0 Lights behave sometimes as a wave and sometimes as a particle o It depends on what the experimenter tries to measure the difference between experiment 3 and experiment 4 o Copenhagen Interpretation 1 Complementarity 2 properties wave nature and particle nature can t be seen simultaneously 7 Experiment 3 particle nature 7 Experiment 4 wave nature 7 Never particle and wave at the same time 7 Example When ipping a coin you either gets heads or tails never both Copenhagen where Bohr was when this was discovered 7 Could also be called Bohr s Interpretation with Heisenburg Uncertainty Principle 2 Collapse of wave function Uncertainty 9Ce1tainty Wave function can t measure 39 i n and momentum at th same time Physics Notes 817 pages 8 11 in 50 Physics Ideas You Really Need to Know Newton s Laws Email notes to 39voylesugaedu Newton s First Law Law of inertia Latin word iners inactive An object at rest stays at rest and an object in motion stays in motion at the same speed and direction UNLESS acted on by a net unbalanced forcequot Ex Walking with a shallow pan of water makes water spill because it wants to stay at rest OR if you constantly walk with a shallow pan of water it will spill when you stop because it wants to stay in motion Ex seat belt head rest coffee on a bus etc Lame joke Buckle up it s the law of inertia Speed 60 mph Direction east Velocity 60 mph east Veocity changes if either speed or direction changes Force push or pull Acceeration change in velocity because of change in speed Net unbalanced force Something that causes a change in velocity slide chair across floor and friction keeps it from sliding through wall Net force of O standing on floor and the floor exerts pressure keeps gravity from pulling us down into the earth Newton s Second Law The greater the force F the greater the acceleration A The greater the mass M the smaller the acceleration Aquot FMA Ex A block and a feather will fall at the same speed in a vacuum A is proportional to F and A is inversely proportionate to M Mass matter in an object Never changes Weight gravity acting on mass Changes by location Air resistance on earth causes a styrofoam ball to fall more slowly than a baseball Newton s Third Law For every force there s an equal and opposite forcequot Ex If you exert force an on a table by pushing it the table also exerts a force on you You feel the tension in your hands Ex A fish swimming The fins push the water back and the water pushes the fish forward Same principle applies to birds birds wings push air down and the air pushes the birds up Ex Wall of death Cyclist rides on walls of Wall of Death without falling Physics Notes 819 Pages 1215 in 50 Physics Ideas You Should Really Know Kepler s Laws Background Pattern of stars is mostly fixed which explains constellations Planets move in relation to fixed stars One night Mars will be in one place in relation to stars while another night it may be closer to another set of stars Because planets move it is known that they are not stars Mars will go west to east one night prograde and at some point in time it will go east to west retrograde Retrograde Motion East to west movement of planets top to bottom in geocentric view Prograde Motion West to east movement of planets bottom to top in geocentric view Definitions for Views Before Kepler Geocentric world view Earth is center of everything Ptolemaic How Ptolemy accounted for retrograde motion lf Mars moved in its own circular path an epicycle and an orbit around Earth then retrograde was explained When problems were pointed out Ptolemy added epicycles within epicycles and had to move earth from the center It all became too cumbersome and was somewhat discounted Heliocentric world view Sun is center of everything Copernicus How Copernicus accounted for retrograde motion The planets farther from the sun are moving more slowly in their orbits than those closer to the sun The retrograde motion of Mars occurs when Earth passes by slower moving Mars Eventualy Copernicus had to add epicycles in order to match observations Therefore it still vvasn t a perfect model Mars isjust an example planet Kepler Notes Realized that circles were not accurately depicting retrograde even though he agreed with Copernicus lntroduced the elliptical orbit instead of circles into the Copernican system For an ellipse there are two points called foci singularfocus so that the sum of the distances to the foci from any point on the ellipse is a constant a b constant The amount of flattening of the ellipse is termed the eccentricity Below the images are increasing in eccentricity Major axis is from one side of the ellipse to the other the long axis Kepler s First Law The orbits of the planets are ellipses with the sun at one focus of the ellipse which means that the Earth is farther away from the sun at some parts of the year than others However the eccentricity is very slight The image below is an overexaggeration Definitions Perihelion closest to the sun Aphelion farthest from the sun Planet Kepler s Second Law The line joining the planet to the Sun sweeps out equal areas in equal times as the planet travels around the ellipse Traves the larger arc on the left side of the sun at the same speed as it does on the smaller arc which means that planets do not always travel Perihelion same speed The two triangular sections have equal areas Kepler didn t know it but the conservation of angular momentu explained his second law Conservation of angular momentum Lmass speed and radius When radius decreases speed increases Explains why you spin faster in a chair when you pull in your arms and slow down when you stretch out Aph elion Kepler s Third Law P2A3 Pperiod Time it takes to orbit A Semimajor axis half of the major axis which is the average distance of the planet to the sun measured in astronomical unit or AU All the planets obeyed the thIrd law Orbi Sat n tal Peri Jupiter od Yea rs Venus Mercury Semimajor Axis AU Physics Notes 822 Chapter 4 Newton s Cannon Law If you drop a cannon from a mountain it will fall straight down If you launch a cannon from a mountain it will land far out If you launch a cannon even fasterfrom the mountain then it will land even farther out If you shoot a cannon atjust the right speed from a mountain it will follow an elliptical orbit If you shoot the cannon slightly faster the orbit will be a circle If you increase the speed even more it will form another ellipse in which the orbit is close to the mountain at the top of the Earth and rather far away from the bottom of the Earth This is all hypothetical This explains the moon s orbit around the earth Gravity is pulling it into the earth but because it is not at rest it stays in motion If it were in motion at a slower speed it would actually crash into the Earth This follows Newton s second law FMA ForceMass times Acceleration He knewthere was a force acting on the moon because of the acceleration of the moon So what is the force acting on the moon If you swing a tennis ball on a string it will continue to move in a circle with a fixed radius Rstring from hand to ball because of the tension caused in the hand This follows Newton s first law With no tension the ball does not move Newton used this analogy to figure out why the moon moved With the moon the thing that causes that tension is gravity Tennis ballmoon Hand tensiongravity lnversesquare law This explains the force of gravity This is the proportionality but you need a constant for calculations Force is quot 39to Mass 1 X Mass 2Distance squared If two objects are one meter apart and you separate them so that they are two meters apart their force will decrease by 4 times The distance is from the center of one sphere to the other Constant of proportionality needed to change a proportion to an equation which would be G in the inversesquare law The value for the gravitational constant must be the same universally Newton s Universal Law of Gravitation F G M1M2 d2 This is the physical reason that explains Kepler s law concerning perihelion and aphelion movement Newton explained that because of the gravitational pull between planets and the Sun the p2a3 makes sense Velocity 2 n radius period 4Ei2 d3 p2 GM M a3 p2 Newton s version of Kepler s third law It applies to all of the solar system GM ALL cases of orbits Applications The Earth and moon The moon must exert a force on the earth since the earth is exerting one on the moon according to Newton s 3rd law Remember If the distance is greatforce is small if distance is smallforce is great The greatest pull on the moon is from the side of the Earth near the moon and vice versa Because the right side when it s closer to the moon feels like it s being pulled to the right the left side feels like it s being pulled in the opposite direction which gives rise to the tides The sun s gravitational force on the Earth is greater than the force from the moon because the mass is greater However the tide is affected by the moon because of the earth s diameter paired with the moon s distance from the Earth Halle s comet Using the Universal Law of Gravitation Halle calculated the semimajor axis of the orbit using the period of 76 years Using Kepler s first law he figured out when it would return 1956 and so it was named after him Disco very of Neptune When some mathematicians sawthat Uranus wasn t acting as it was supposed to according to physics they used the universal law of gravity in 1845 to predict the existence of Neptune Mercury Misbeha ved Too lts orbit changed from on ellipse to another called the procession of the perihelion orbit Because of the previous experience of Neptune people considered there was another planet between Mercury and the sun but there s no Vulcan The reason Mercury misbehaved was because Newton s not completely right Physics 824 chapter 5 in 50 Things You Should Really Know About Physics What is energy Quantity often understood as the ability to do work Work Force X Distance Remember Force Mass X Acceleration Acceleration Speed Time Distance Speed X Time So Work Mass X Speed2 Ex If you move a table ten feet you have exerted force for a certain distance therefore you have done work However if you push on a wall you have exerted force since the wall has not moved you have not done work Weight MassX Gravity A book weighs more on Earth than on the moon Weight is a force because gravity is an acceleration Example Lifting a book which has weight from the floor to a counter is work Types of Energy Type One Kinetic Energy Mechanical Energy Kinetic Energy E 12MV2 Example Moving hand in the air Type Two Gravitational potential energy Mechanical Energy Gravitational Potential Energy Mass X GravityX Height MGH Example If a pen is on a counter it has potential energy If you place the pen higher on a shelf then it has a higher potential energy because it took more work Called potential energy because it has the potential to convert the energy to kinetic energy Just before an object hits the ground it has reached its maximum speed Type Three Therma Heat Example Rubbing hands together converts kinetic energy into heat A way to cause thermal energyfriction Type Four Sound Example Hitting a drum converts the kinetic energy from your hand into sound waves that travel through the air causing you to be able to hear the sound Type Five Chemical Example The chemicals in a battery make it work Type Six Electromagnetic Example Light all manifestations of light visible ultraviolet xrays radio waves Solar power can be converted into other energy Type Seven Nuclear Examples Fission atom s nuclei splitting and fusion atom s nuclei fusing Type Eight Rest EMC2 Conservation of Energy Conservation Law Conservation of mechanical energy szV2 MGH szV2 MGH The left side of the equation and the right side are measured at two separate times Example When holding a billiard ball at the top of a track it has potential energy When released it rolls down a track gaining kinetic energy When it reaches the bottom it has no potential energy However it will not climb all the way up the other side of the track once it reaches the bottom because friction slows the ball The equation does not take friction into account Example If you pull on a pendulum causing it to have 0 Kinetic Energy and let it go it will have 0 Potential Energy at the bottom and then 0 Kinetic Energy at the other side When it comes back to you it will have 0 Potential Energy at the bottom and 0 Kinetic Energy near you again Conservation Law Conservation of angular momentum Kepler s 2quotd Law Conservation Law Conservation of momentum Momentum Mass X Velocity Conservation of Momentum Mass X VelocityA Mass X VelocityB Mass X VelocityA Mass X VelocityB Again both sides of the equation are measured at two separate times Example On the air track when the two objects collide the energy must be conserved The moving object transfers its energy to the object at rest Use the air track in order to take away the friction that messes up the equation Physics Notes 826 Chapter 6 imple harmonic motion SHM Periodic motion very regularly about an equilibrium position in a sinusoidal pattern Sinusoidal refers to sine wave A body in SHM will experience a restoring force proportional to its displacement and in opposite direction INSERT PICTURE FROM WEBLINKS Period How long an object takes to get back to its original position Amplitude Distance from equilibrium to its new position Examples spring a box on a spring will spring back when pulled away from its equilibrium an object that moves in a uniform circular motion pendulums Sp ngs T Zmmk T period M mass K the spring constant measures the difficulty of pulling a spring A bigger box with the same spring would have a longer period and a smaller box would have a shorter period Also if the spring is difficult to pull then the period is shorter if the spring is easier to pull the period is longer Notice that the amplitude is not taken into consideration but it does not affect the period In the class example the mass of the weight on the end of the spring is the changing variable The spring constant does not change The massspring acts sinusoidally The heaviest spring s period was 1 second The lightest spring s period was slightly less than 1 second Pendulums T 21 xLg T Period L Length g The acceleration of gravity The mass does not affect the period In the class example the equal length pendulums with different masses swing at the same period The equal length equal mass pendulums swing at the same period Regardless of amplitude unless the amplitudes are enormously different two pendulums of equal length swing at the same period Two pendulums of the same mass but different lengths do not have the same period the pendulum with the shortest length has the shortest period Big Ben the pendulum inside keeps time Expression in England Put a penny on itquot If you put a penny on top of the pendulum you have changed the center of mass of the pendulum by moving it up The effect is that the effective length of the pendulum has shortened Putting one on bottom would lengthen the effective length Pennies are used to adjust the time of the clock Foucault pendulum named after French physicist If you hang a pendulum in a friction free environment it will swing forever If you swung a pendulum above the earth it would look like its position was changing when really the Earth underneath it is rotating The Smithsonian has an example that shows that the pendulum stays in one plane but because of the Earth s rotation it knocks down pegs in a circle very slowly Gravimeters If you swing a pendulum over a salt dome and one over an iron ore deposit you are controlling the g of the pendulum equation because the gravity is more prevalent over iron Ex In the Georgia mountains the gravity is lower than in other regions because of the higher altitude the distance away from the center of the Earth GRACE Gravity Recovery and Climate Experiment makes detailed measurements of Earth s gravity field since its launch in March 2002 Resonance When you push a child on a swing you push at the peak and it helps Tresses on a bridge weigh it down to keep the wind from blowing it around Physic Notes 829 Chapter 7 Hooke s Law F kA I L length of an unstretched spring AL change in the length of a spring K Spring constant FRestoring force Don t confuse with deforming force the force I put on the spring to make it smaller Notice that there is a negative sign which deals with the restoring force The object does not have to be a spring T 2pi times the square root of MK Remember that the higher the number the harder it is to pull the spring Restoring force is what causes a rubber band or spring to go back to its original size and deforming force is what temporarily deforms the object This process refers to an object s elasticity Elasticity an object can go back to its original shape and size If an object does not go back to its original shape like chewed gum it exhibits the property of plasticity Plasticity when you stretch an object and it does not go back to its original size Stress FA Force and stress end in the same sound Strain A L L Young s moduluscharacterized by Y measure of the differences in the stretchability of a material Young s modulus is the slope of the line in Hooke s Law K YA L Meaning the spring constant and Young s modulus seem to be interchangeable Y mx b Different types of stress and strain Linear if you are walking through an airport holding a suitcase the stress is on your bone and it stretches your arms If you carry a 40 lb suitcase it can stretch your humorous by 1 micron Just stretches in one direction Remember work is a force because WMg gacceleration of gravity Vogirgesqby j Stresses in all directions If you take a basketball under water and try to see what the pressure of the water puts on the basketball in all locations Shear If you move the front cover of a book it moves the back cover too I A v N v a v C Hooke s Law Young s Modulus Strain AL L If you continue to pull on a rubber band the relationship between stress and strain is no longer linear it no longerfollows Hooke s Law but it can still bounce back to its original shape Elastic limit the relationship becomes horizontal and the object becomes plastic It won t go back to the original state Breaking point past the elastic limit where an object breaks A slinky will break if you pull it too far Buildings and bridges are subject to stress and strain If you drive cars over a bridge it puts a little bit of strain on it but if you put too many cars it could get to the breaking point Arches are built on the concept of Hooke s Law The blocks on top of the arch exert a gravitational force on the blocks below Look at weblink The restoring force from the block below is equal to the gravitational force from the block below So the restoring and deforming forces are equal Spider webs are examples of stress and strain There s another web link If strain is 100 then that means that something that started off a foot long is now two feet long Spider webs can withstand tremendous pressure Up to 476 We go past the breaking point if we walk through a web but bugs don t Strength of steel is less than that of a spider web MPa Mega Pascal Used to measure pressure A spider web COULD stop a jet from flying but in order to spin that web you would need about 102 billion spiders Bimetallic strip used to convert a temperature change into mechanical displacement As you go away from the shore and into the ocean you can t know what time it is or where you are If you had a reference that said somewhere it is 4 o clock and you know it s noon then you can tell you re 4 hours from the place you came from This has nothing to do with Hooke s law Thermometers are usually based on bimetallic strips uncoils when heated coils when cool John Harrison improved a clock pendulum called the gridironpendulum made of iron and zinc One expands more than the other so they balance each other out and the bob on the end of the pendulum stays in the same position which has to do with thermal expansion Sailors needed this to see where they were They knew what time it was in their hometown and by looking at the time and the local noon they could figure out their locations The yellow and blue metal illustration A simple pendulum normally keeps time with the length being the important part of the clock However temperatures would make the length of the pendulum change Physics Notes 831 Fluid dynamics air can be considered fluid Something that does not have a solid structure and its movements Continuity equation conservation of mass flow rate P1A1V1 P2A2V2 The 1 and 2 s are subscripts With both sides being measured at different times one side equals the other P is actually standing for Greek symbol Ro which stands for Mass density P MassVolume AArea Lengch The V is actually a Greek symbol Look it up V Velocity LengthTime Put together you get MassTime Ex If you cover part of a water hose the water will spray faster because of this equation The density on both sides is the same because it s still water However the area of the opening changes so the second area decreases Therefore the velocity must increase on the second size because of conservation Ex Water flowing out of a faucet is wider at the top of the faucet Density hasn t changed Instead the area has decreased because the speed increased due to gravity Bernoulli equation Fluid form of Conservation of Enerqv Pressure ForceArea Ex If you press on a blown up balloon with force a push or pull it won t break because there is a large area If you press with a pen it will pop because the area of the pen is small Pressure E M energy A d volume volume Conservation of Mechanical Energy Kinetic Energy 12 Mass Velocity2 Kinetic EnergyVolume 2 Mass Velocity2Volume Gravitational Potential Energy Mass Acceleration of Gravity Height 12 Ro Velocity2 Potential EnergyVolume Mass Acceleration of Gravity Height Volume Ro Gravitational Acceleration Height Remember that P in this equation stands for R0 which means mass density BERNOULL EQUATION P1 12 P1V12 P1G1H1 P2 12 P2V22 P2GH2 Rememberthat P in this equation stands for R0 which means mass density Also 1 and 2 are subscripts and G is acceleration of gravity It s like the conservation of mass but with fluid This one has pressure in it too This explains how planes fly Remember large area slow flow rate Small area fast flow rate Fluid statics Something that does not have a solid structure that does not move Ex If you are immersed under water you can determine the pressure you feel from the surrounding fluid 102111 Antimatter No asymmetry info from book on test Youtube Video on Antimatter Antimatter highest octane fuel in the universe 102 of antimatter 1 oz matter 100 tons of rocket fuel Until recently we made antimatter in Chicago at the Fermilab We only had the ability to make very small amounts Any element can have antielement counterpart First made antimatter in 1955 If you had a penny size amount ofantimatter 110 oz it would be enough to launch a space shuttle 60 times Cosmic rays particles that exist in space Example Proton In 1932 Carl Anderson discovered antimatter He discovered it by observing a bubble chamber charged positrons and charged protons move in similar ways so they looked like they were the same thing Carl realized the positron was not a proton because the proton moved much slower Protons have greater mass than positrons which is why they move slower He observed the different tracks each made in the bubble chamber Positrons had identica l mass to electrons Particle Accelorator 2 types 1 Iquot Fixed ta rget9 29 GeV Ex Similar to a car crashing into a tree non moving object Colliding Beams9900 GeV Ex Similar to car crashing into another car moving toward it e Red not stable Yellow stable PET scan allows you to get visual of Positron Emission Tomography the brain FlLlDrli w IS Nucleus I39JiJ jT 739 PClSlerrl J w J Gamma Flaw nuetrino theoretically predicted to exist because without it some particles would be unbalanced Nuetrinos have low mass and neutral charge They do exist There are billions passingthrough your body every second They come from the sun 18 13 9F9 gt a010 e v i l J lepton positron nuetrino

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