Physics of Everyday Life 2
Physics of Everyday Life 2 PHYS 1020
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This 12 page Class Notes was uploaded by Mrs. Peter Toy on Friday October 30, 2015. The Class Notes belongs to PHYS 1020 at University of Colorado at Boulder taught by Staff in Fall. Since its upload, it has received 14 views. For similar materials see /class/232123/phys-1020-university-of-colorado-at-boulder in Physics 2 at University of Colorado at Boulder.
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Date Created: 10/30/15
261 Steven Pollock 2007 Phys 1120 The following are the lecture notes written by Steve Pollock StevenPollockColoradoEDU for 1120 in an earlier semester The ve been modi ed a bit here for the second edition of Knight 1st class Intro Syllabus introduction to electrostatics What follows is a summary of some key points of this Chapter not quite an alternative to the text but perhaps a di erent perspective Welcome 1120 is the 2nd semester of calculusbased Physics We ll be studying electricity magnetism and light the foundations of our technological society Let s begin by reviewing some highlights from last semester Physics 1110 can seem a little overwhelming there were a lot of facts and ideas in that class But they are all tied together with a few basic underlying principles that re ect our universe and how it works Phys 1110 was primarily about mechanics how and why things move The key elements of Phys 1110 were the following 1 kinematics the description of motion velocity and acceleration 2 dynamics the explanations of why things move as they do The essential ideas of dynamics are stated in Newton s laws Newton 1 Bodies will continue in a state of uniform unchanging velocity unless acted on by a net outside force Newton 2 Fma forces cause acceleration another word for change in velocity because a AV At or more precisely dvdt dZXdtz This is a vector equation forces and acceleration have direction and magnitude To be a bit more accurate Newton s second law really says 211 m or if you like Fnet ma 262 Steven Pollock 2007 Phys 1120 Newton 3 The force on A by B is equal and opposite to the reaction force on B by A or FAB FBA For every force applied on a body there is an equal and opposite force applied to whatever caused that force Other important and useful concepts extensions of Newton s laws 1 Total energy is conserved Energy is a defined mathematical quantity which can take various different forms kinetic energy potential energy thermal energy chemical energy electrical energy You really only focused on the first two last semester Recall kinetic energy is given by the formula KE 12 m vquot2 m is mass and v is velocity KE is a number a scalar 2 Momentum is conserved if there are no net external outside forces acting Momentum is also a defined quantity mV massvelocity It s a vector it has a direction Finally we learned Newton s universal law of gravity any two massive objects attract one another with a force of magnitude G is a constant of nature r is the distance between the objects M s are the masses of the objects Then you applied these ideas and learned about e g gravity friction and contact normal forces39 circular motion springs simple harmonic motion vibrations waves and more Together Newton s laws and the conservation laws constitute one of the most amazing and important intellectual breakthroughs in human history Physics I was concerned with and described very successfully a lot of everyday stuff baseballs juggling balls airplanes air tracks Olympic divers Tai Chi masters fireworks the moon helium balloons beds of nails fire extinguishers pendula water waves Most of this is quot17th centuryquot physics understood by Isaac Newton and used today by engineers architects physical therapists etc 263 Steven Pollock 2007 Phys 1120 Physics 1120 concentrates on mostly 19th century discoveries electricity magnetism and light and the 20th and 21st century applications of these ideas Many of the phenomena described by this physics are also everyday but perhaps a little higher tech than what we saw last semester Now we want to describe and understand microwave ovens light bulbs stoves computers lasers and so on Much of what we ll be studying will feel a little more abstract but it s all very real By the end of the semester you will develop some good intuitions about electricity currents lights and radiation We begin in Ch 26 of Knight Electric charge and Electric Fields quotElectrostaticsquot Last semester our quotfavoritequot force was gravity But there are other types of forces that have been studied since Newton We will spend a good portion of this semester studying electric forces and then we ll move on to magnetic forces different but related These forces have been known about for 1000 s of years and most likely you have discovered for yourself that e g rubbing the carpet and touching someone can make annoying sparks and rubbing a balloon on your shirt can make it stick to the wall for a while So what s going on If you d like a more quotexperimentalquot or quotphenomenologicalquot background visit my old 2020 Here I m just going to summarize the conclusions of lots of often quite simple experiments It all boils down to a quotnewquot force of nature arising from a new relevant physical property of matter electric charge There are two and only two distinct types of electric charge Positive charges and Negative charges These are just NANTES we could have called then quotNorthquot and quotSouthquot charges or quotChocolatequot and quotVanillaquot Though our choice of names provide useful metaphors Ben Franklin was one of the first people to experiment with and begin to understand quotelectrostatic forcesquot between static or slowly moving charges Ben postulated the following simple rules 1 Electric charges of the same sign repel each other 2 Electric charges of opposite sign attract each other Summary There are more rules but this is already the basis of electrostatics gt lt gt lt 264 Steven Pollock 2007 Phys 1120 The central idea we hold now about charges is this The world is made of atoms Everything Atoms themselves contain parts which are electrically charged The nucleus made of protons and neutrons is positively charged The electrons which quotorbitquot around the nucleus are lectrons negatively charged Opposite charges attract remember that s what holds the electron in orbit Not gravity The naming choice which is which electrons are protons are is a human convention established by Ben Franklin As we ll see it s a little bit of bad luck he didn t do it the other way around but he didn t so we have to stick with this Sony for the pun When you rub things you might separate quotquot an quotquot charges tearing apart some atoms but you can never create a new isolated electric charge You just move them around The total amount of charge adding positive and negative algebraically is conserved That s why calling them quotquot and quotquot was such a good idea because adding one quotquot to one quotquot gives you ZERO a neutral system Similarly adding 2 s to 2 s gives 0 We can QUANTIFY charge how MUCH charge does something have We have a standard metric unit the quotCoulombquot or quotCquot We usually call the charge on any object quotQquot and measure it in Coulombs We call the amount of charge on one proton by the special name quotequot Thus one proton has charge Qproton quotequot 16El9 C Note the symbol quotequot represents a certain small amount of positive charge An electron has charge Qelectron e l 6El 9 C Confusing You might think an electron should have charge quotequot but no it has charge quotequot Electrons are negative Proton and electron have exactly equal and opposite charges so an atom which has equal numbers of protons and electrons has total charge Q0 Notice how small quotequot l C is a LOT of charge It is an experimental fact that objects don t have any old charge charge comes in quotchunksquot In fact quotequot is the SMALLEST amount of charge that any observed object has other than 0 Conclusion charge is not a quot uidquot it comes in units of quotequot So quotequot is sometimes called quotthe elementary chargequot Well quarks have charges of e3 or 2e3 ask me about that some time 265 Steven Pollock 2007 Phys 1120 Detour some terminology METALS good conductors of electricity Charges easily flow through them Metals have lots of highly mobile nearly free electrons that can flow wherever they want in or on the metal Metals are shiny and malleable eg gold silver copper iron We ll see why later in the course If you take even a thin wire of metal and connect two charged objects charges flow easily through the metal Like charges repel opposite charges attract so the net tendency is for things to try to quotneutralizequot if possible Most materials are IN SULATORS wood rubber concrete ceramic Also called DIELECTRICS Electrons can t flow through them they re basically stuck to atoms Rubbing these materials might drag a few electrons off You can POLARIZE insulators That means that they re still neutral but the charges have separated a little The plus and minus on the neutral ball shown can t really move much but they can separate a little forming a small DIPOLE with quotquot on one side and quotquot on the other The rod on the side is pushing the quotquot away likes repel and pulls on the quotquot opposites attract Because the quot is a little closer the pull is a bit stronger than the push and so the ball and rod feel a small net attractive force That s why balloons stick to the wall if you rub them first rubbing charges the balloon the charged balloon polarizes the neutral wall and then they attract A few special materials are somewhere in between e g Silicon and Germanium called quotSEMICONDUCTORSquot More about them later they re more complicated There is a simple little device for studying charges called an Metal ELECTROSCOPE It looks like this Ball If it s uncharged the metal foils just hang down like pendulum Metal bobs But if you put some electric charges onto the metal ball they conducmr repel one another and spread out all over the whole scope Thus Thin light both foils get charged with the same charge and repel each other metal foils and stick out a little The more charge on the electroscope the more the foils repel and they stick out farther You can NOT tell what the sign of the net charge on the electroscope is simply by looking at it If its net the foils repel If its net the foils repel So all you can do is see HOW charged it is 266 Steven Pollock 2007 Phys 1120 There are various ways to charge objects like electroscopes or pith balls The simplest is to touch then with something else charged Charges will repel each other and spread out This is charging by CONDUCTION There s another way by INDUCTION you bring a big charge nearby but NOT touching polarizing the object you re interested in Then you ground the object you re interested in connecting it Via a conductor to perhaps literally the ground allowing some charges to leave the object Conductor owing into the earth Specifically electrons are free quotgroundquot to run along conductors and they can get much farther These Charges ran away away by going to the ground So they do Then you disconnect the grounding wire and the object in question is left partly charged even though no charged object ever touched it Interestingly it doesn t matter WHERE exactly you touch the conducting wire to the ball if you give those electrons a chance to run away they ll take it A human body can be a decent conductor I recall a Star Trek where aliens called us quotugly bags of mostly waterquot Salty water is a conductor In the lab just touching the ball you can serve as the quotconductor to groundquot Metal wires are much BETTER conductors than you but they don t contact the ball as efficiently so it s a bit of a tossup Air has water vapor in it and water is a quotpolar 39 moleculequot the H s tend to be a little quotquot and Anexcess onmobject the 0 tends to be a little quotquot on the other side 132118213 ltgcgteacehgohilr Excess charges on objects can quotleakquot to the 39 39 39 water vapor and thus get to ground because the charges can attach to the appropriate side of H20 molecules and drift away This is one reason why you get shocked MORE in the winter the air is dry and so you stay charged up for longer and you can also hold more charge before it leaks Electrostatics demos should work better winter semester Air itself without water vapor in it is an insulator If you build up enough charge though insulators can quotbreak downquot and allow the charge to ow E g you can tear apart N2 or 02 molecules in the air leaving lots of charged quotionsquot that act sort of like the water vapor above as a means to hook up and carry away charges to ground Such a breakdown in air is pretty spectacular that s what lightning is See the last page of my notes for this chapter if you d like to learn a little more about lightning 267 Steven Pollock 2007 Phys 1120 COULOMB39S LAW The explanation of charges above was qualitative but not much later late 1700 s Charles Coulomb made the story quantitative after many difficult experiments by finding a formula describing the force between any two pointlike charged objects a distance r apart Q1 F k Q1 Q2 m2 Bu 3C1 This important law is called quotCoulomb s lawquot It s already ahnost enough to understand much of chemistry biology solid state physics plasmas The constant quotkquot is 899E9 N mA2CA2 It s a constant of nature Coulomb s law tells you the MAGNITUDE of the force The direction is along the line between the charges repulsive if the charges are the same attractive if they are opposite Notice that Coulomb s formula doesn t really care which you call quot l quot and which quot2quot the force is the SAlVlE That s just Newton s 1H law The force ON 1 BY 2 is equal and opposite to the force ON 2 by 1 F 12 F2l Example if you have one C of charge and another C of charge 1 m away the force between the charges is k Q1 Q2r 2 899E9 N m 2CA2 lClClmquot2 9 billion Newtons about a million pounds of force I told you a Coulomb was a LOT of charge Many books including Knight don t use the symbol quotkquot instead they replace k l l 1 2 With So Coulomb s law is written F1 2 4723980 3 30 4723980 r Coulomb s law should look a little familiar remember Fgrav G M1 M2 rquot2 compared to Felec k Q1 Q2 rquot2 One difference mass is always positive39 Fgrav is ALWAYS attractive But there are 2 signs for charges Felec can attract or repel VERY llVlPORTAN T Coulomb s law tells you the force between a pair of charges If you have MORE than two charges you must draw a picture and add up all the Coulomb electric forces from all the other charges You CANNOT just add the magnitudes Forces add as vectors 268 Steven Pollock 2007 Phys 1120 Example You have 3 charges arranged as shown Let mass M11 g and charge Q1 2 uC 4 uc 2 uC 3 uC In these notes I ll use the symbol quotuquot for the Greek letter quotmicroquot or 10A6 it should be a quotmuquot or u 2 m 3 m Suppose Q23 uC Q3 4 uC What is the force and the resulting acceleration of charge Q1 Answer You must consider both forces on Q1 separately and then in the end add them as vectors We want Fnet F12 F13 the force on 1 by 2 PLUS the force on 1 by 3 The magnitudes are straightforward by Coulomb s law F12 k Q1 Q2 r12quot2 k Q1 Q2 3mquot2 60E3 N F13 k Q1 Q3 r13quot2 k Q1 Q3 2mquot2 18E3 N What about the directions Just draw the arrows remember like charges repel opposites attract F F 13 Look carefully at my labels and the directions in this figure Do they make sense to you Do you see e g that F12 is to the left Set up a conventional coordinate system where right is quotXquot left is quotXquot then put the above together to get the total force in the X direction as Fnet 60E3 18E3 12E3 The answer is NOT the sum of 6 and 18 but the difference The resulting net force is positive or in other words to the right Acceleration Fm 12E3 N 1E3 kg 12 ms 2 To the right NOTE All Coulomb forces always simply add up as vectors Charges NEVER quotblock each other outquot If I wanted to know the force on Q2 above I d find the forces from Q1 and Q3 and add them as vectors Q1 doesn t in ANY way ever quotblock outquot the force from Q3 even though it s in the middle This is called superposition Electric forces quotsuperposequot add up on top of each other If you have several charges and want to know the forces somewhere you merely ADD or superpose all the individual force vectors one from each charge 269 Steven Pollock 2007 Phys 1120 In ELECTROSTATICS we assume charges are fixed in place and then you might watch how one extra quottestquot charge responds ie what forces it feels The principle of superposition says it s easy enough just add up superpose the force vectors arising from ALL the other charges in the problem lint add the forces on q by all other charges quotiquot In the picture we see an example with three fixed charges plus the one quotqquot we re interested in Can you tell from the picture which of the charges have the SAIVIE sign as q and which have the OPPOSITE sign Here s the quotproblem solving approachquot Pick the ONE charge you re interested in I called it quotqquot above Draw ALL the force arrows on this one charge you re interested in coming from every OTHER charge in the problem Use Coulomb s law to get the magnitude of each force and just look at the signs of charges to get the directions right opposites attract likes repel Then add the force vectors If you don t remember how to find components of vectors and add any two vectors please review that See the last page of notes An example of sugergosirtg forces Two protons Qe and an electron Qe are p1 aligned as shown What is the force on the electron l 0quot 10 m Answer A H e We need to figure out Ftot Fepl Fep2 10 3910 m lOAl m the force on the electron from the first proton PLUS P23 the force on the electron from the second proton It s always helpful to draw a force diagram to help solve the problem Since proton and electron have opposite charges the forces are both attractive on the electron You should convince yourself that the distance from the electron to either one of the protons is r SqrtlOquot10m 2 10A10mA2 l410quot10m Can you also see that the force vector is tipped at 45 degrees Coulomb s law says Fepl k e e l 4ElOm 2 12E8 N By symmetry Fep2 is the same can you see this continued on next page 2610 Steven Pollock 2007 Phys 1120 But Ftot Fepl Fep2 is NOT just 2l2E8 You must add vectors not magnitudes To do this use components FtotX Fepl X Fep2X 12E8Ncos45 12E8Ncos45 17E8 N Ftoty Fep1 Fep2y 12E8Nsin45 12E8Nsin45 0 Think about why Ftoty0 Think about signs look at the picture The final result is thus Ftot 17E8 pointing directly leftwards Yet another example An electroscope is designed as two hanging quotpithquot balls each of mass m as shown A total charge Q is put on the scope and has split itself evenly between the two balls The balls are a distance quotrquot apart that s the distance between centers What is the tension in the wire holding one of the balls m m on on Answer The method to solve it is to draw a force diagram for either one say the lefthand pith ball There are THREE forces on it gravity down Fgmg T electric left Felec k Q2Q2r 2 and lt O tension T points in the direction of the wire Felec l Fgrav Draw the force diagram like this and use Newton 11 which says that in equilibrium when nothing is accelerating the balls just hang there Ftot0 ie Fg Fe T 0 or solving for T which is what we re after T Fg Fe By symmetry the magnitude of tension in the other wire will be the same although the direction is different In this problem F g and Fe are perpendicular so adding them as vectors is relatively easy the magnitude of the sum is by Pythagorus T SqrtFg2 Fe 2 Sqrtmg2 k Q2Q2rquot2 2 Can you see this If not draw Felec Fgrav for yourself Knight ends this chapter with an intro to the Efield quotthe field modelquot This is a really important idea but I m going to talk about it in my Ch 27 notes since that s what that whole chapter is about I just want to finish this one with a short mathematical review 2611 Steven Pollock 2007 Phys 1120 Here s a brief REVIEW of some of the important aspects of vectors Any vector F can be described by its X F 1 and y components given by Hypotenuse F Fsme Fix F costheta and F Fsintheta J z 9 Opposue This comes from quotSOHCAHTOAquot Sin is Opposite over Hypotenuse F X F0089 Cos is Adjacent over Hypotenuse Adjacent Tangent is Opposite over Adjacent My convention a vector F has magnitude F written without bold font You can also go the other way given the X and y components of a vector the hypotenuse ie the magnitude is given by Pythagorus F SqrtFXquot2 Fy 2 And given FX and F y you can find theta arctanFyFX 1 When you add vectors the graphical method is quottip to F tot FHFZ tailquot as shown F2 I Mathematically the way to add vectors is this xFl39 ifF F1 F2 then FX FlX F2X Fy Fly F2y ie components just add like plain old numbers just watch signs To add F1 and F2 first find the X and y components of F1 and F2 with sin s and cos s and then add these to get FX and F y Finally use Pythagorus to get the magnitude of the total Often you do have to be a bit careful about minus signs F E g in this picture F FX F costheta Fy F s1ntheta 9 F X Can you see the reason for that minus sign in the FX equation FX is to the LEFT 2612 Steven Pollock 2007 Phys 1120 UNIT vectors Instead of talking about quotcomponentsquot of a vector it s often convenient to think about vectors as having a length and a direction E g a vector pointing 3 m to the right is quot3 m longquot amp points in the Xdirection The UNIT VECTOR is all about that second part the direction think of an abstract vector that points in a particular direction but has a standard size or you could say a size of ONE That s why we call it quotunitquot as in quotonequot It s an ironic name because this unit vector has no quotunitsquot in the physics sense of that word where we normally think of quotmetersquot or quotmeterssecondquot or quotNewtonsquot or whatever as quotunitsquot So this unit vector has NO physics units its length is not quot1 mquot or quot1 Newtonquot it s just quot l quot a pure number except it s not a number its a pure arrow We call the unit vector that points in the X direction either 2 which you pronounce quotXhatquot or sometimes we ll call it i ihat So in 3D you use Xyz or ijk it s just two different conventions This is the main trick to understand 2 has magnitude one Not 1 meter or 1 anything else The magnitude is just the pure number one If you then WANT to describe say a force vector which is 3 Newtons strong in the X direction it would be written F 3 N y The number out front has units the 2 does not it lVlERELY gives direction If the vector has 2 components it might be e g F3N 2 4N 7 This is a vector pointing quotup and righ quot it has magnitude 5 N do you see why And one last thing our text uses 9 rhat to be quotthe unit vector pointing in the radial directionquot What s that what s quotradialquot It just means a unit vector pointing away from the origin towards some given point think of a polar coordinate system where you indicate a point by drawing an arrow straight from the origin out towards that point We ll use this occasionally but it s not such a big deal for right now
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