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48 Pages

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SCI 206
Stefan Idziak

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Topic 1 Thursday, October 05, 2006 1:56 PM Topic 1: Motion From Lecture Newton's Laws • What are the 3 ways to describe motion? o Position, velocity, and acceleration • How can we describe position? o We use a vector, because it can tell us direction and distance (from some defined start point) • What are the 2 parts of velocity? o How fast we are going (speed) o What direction we are going in (direction) • What is acceleration? o It is how fast (and in what manner) our velocity is changing • What is Newton's first law? o An object that is not subject to any net outside forces moves at constant velocity • What is Newton's second law? o The force exerted on an object is equal to the product of the object's mass times its acceleration o The acceleration is in the same direction as the force • What is Newton's third law? o 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 Gravity and Componential Motion • What is gravity? What determines the effect we will experience due to gravity? o It is a downward force produced by the earth which acts on us, pulling us down o The gravitational effect we experience is always an acceleration of ~10 m/s2 -- REGARDLESS of our mass • This means that (neglecting air resistance) a feather falls just as fast as a brick • Why doesn't gravity cause us to fall through the floor? o Because of the "normal force": an upward force produced by the surface we are standing on that counteracts the gravitational force so that we don't move • Describe the motion of a projectile launched at some angle with respect to the horizontal. o We can break up its initial velocity into horizontal and velocity components • Its horizontal velocity will never change, because there are no forces present to change it (recall Newton's First Law) • Its vertical velocity will be subject to gravity, so its upward progress will slow, eventually become zero, then start to head downwards • If you wanted to shoot a monkey in a tree, where should you aim? (Assume that the monkey will drop and fall downwards as soon as the shot is fired). o You should aim straight at the monkey (not above it or below it), because once the bullet is in the air and the monkey has dropped, both objects are subject to the same force (only gravity), and so they will meet at some point Work and Energy • What is the difference between kinetic and potential energy? o Kinetic energy is the energy of movement: the amount of this one possesses is related to one's velocity o Potential energy is stored: the amount of this one possesses is related to its ability to unleash energy • Discuss energy conversions. o Energy cannot be created or destroyed, but it can be converted from one form into another o The types of conversions which occur and their efficiencies affect the things we see in the real world • For example, some materials bounce better than others because they do a better job of converting kinetic energy to elastic potential (while others just convert kinetic into heat) • Discuss work, in particular the way it is related to potential energy. o To do work on something is to exert a force on it and cause it to move some distance in the direction of that force o Work is related to potential energy because we can give an object potential energy by doing work on it • For example, lifting a ball from the ground to a table Friction • Imagine a scenario where (with friction present) you are pushing a block horizontally across the floor. Describe the different forces acting on the box. o There is gravity acting downwards, and the normal force acting upwards o There is the human pushing force acting in the box's forward direction, and friction acting opposite to that • The pushing force must exceed the frictional force in order for the box to start moving from rest • Discuss the 2 kinds of friction. What kind of energy is produced by friction? o Static friction is friction that opposes the initiation of movement o Kinetic friction is friction that slows down movement which has already started o The energy lost from friction (remember that we would expect a given amount of energy produced given the work we put into moving something…so when we have reduced energy due to friction, where does that energy go?) becomes HEAT • Explain the "spiky" model of friction. o On a microscopic level, the two interacting surfaces are not smooth but rather have many small bumps and crevices, almost like interlocking teeth • Thus moving the surfaces across each other requires energy to overcome this interlocking mechanism o When starting from rest, more of the "teeth" are "locked together" and thus the frictional force experienced is greater o When already moving, there are fewer teeth interlocked and thus the force is smaller o If you press the two surfaces together (i.e. if the one on top is heavier), again the "teeth" "interlock" more, and so friction increases (this is why friction is related to the normal force) • Explain why a tablecloth can be pulled out from beneath a dinner set. o It is simply a function of the frictional force between the tablecloth and the dinner plates: can we pull the tablecloth fast enough that it overcomes the frictional force which is causing the plates to stick to the cloth? If so, the cloth will come right out from beneath them... Rotational Motion • Describe the motion of a tennis ball connected to a string being flung around in the head in a CIRCULAR pattern. o Its speed is always the same, but its velocity changes since its direction is always changing o It has an acceleration that is always the same in magnitude but always changing in direction (though it is always pointed towards the middle) • The force creating this acceleration (since f = ma) is known as the "centripetal force", and it is embodied in the tautness of the string o If at any time in the motion the ball was separated from the string, it would fly off in a line tangent to the circle (this is why we feel like we're falling out of the car when we go around curves) • Recall the experiment where a water-filled bucket was rotated vertically in a circle. What determines whether the water falls out? o The relevant relationship here is that the centripetal force (discussed earlier) is related to the velocity of the motion • And the centripetal force is made up of the tension which swinging the bucket exerts on the arm PLUS the gravitational force - so if the necessary centripetal force isn't even as much as the gravitational force, then the remainder of the gravitational force will be used to allow the bucket to spill • Why do figure skaters spin faster when they bring their arms close into their body? o Because something called angular momentum is conserved, which is a function of rotational inertia (analogous to mass) and rotational speed (analogous to velocity) o As long as torque (a force which affects rotational velocity) is not added to or removed from the system, angular momentum must stay constant - and so if we reduce our rotational inertia by bringing our weight closer to the axis of rotation, the rotational velocity must increase to counteract this • Why did Idziak's tricks with the strings and the hourglass work better when the hourglass was spinning? o Because the hourglass wants to conserve angular momentum, and it does this by continuing to spin on the same axis o If it were to wobble (i.e. become unstable), this would constitute spinning on another axis and cause angular momentum to not be conserved - thus it tends to not do this From Textbook Chapter 1 Chapter 2 [do I need to have anything here?] Topic 2 Sunday, October 08, 2006 12:28 AM Topic 2: Resonance From Lecture Waves • What is a pulse on a string? Describe some characteristics of it. o It is a "bump" that travels along a string o It has a defined direction and has the ability to be reflected off the ends of the string o It does not cause the string itself to move - it only causes sections of the string to be displaced vertically • What is a transverse wave? Identify the following features of a tranverse wave: amplitude, node, antinode, velocity, wavelength. o A transverse wave is one where the displacement created is vertical • If we have a transverse wave on a string, what force causes the vertically- displaced portions of the string to oscillate "up and down"? o The tension on the string acts as a restoring force to bring it back to the middle, but it overshoots and goes to a maximum amplitude on the other side • Explain how longitudinal waves work. o Longitudinal waves are those where the displacement is longitudinal - i.e. along the length of the wave • It is a series of compressions and stretches (aka rarefactions) • Discuss how sound is a longitudinal wave. What implications does this have for the necessary conditions for hearing sound? o Sound waves are simply longitudinal waves in air - and the analog of "compressions" and "rarefactions" are regions of high and low air pressure o The implication is that we must have air in order to hear sound - because to hear sound is simply for our ear to detect the pattern of air pressure changes • Recall the demo where a bell in a vacuum was rung, and no sound was heard • How are the speed, frequency, and wavelength of a wave related? What implication does this have for sound in different mediums? o Speed = frequency x wavelength o The implication is that sound travels at different speeds in different mediums, and so when sound passes from one medium to another, the speed will change: thus either frequency or wavelength must change • Frequency does NOT change, and so wavelength does - thus the sound we hear is different • Give an example of a wave traveling through different mediums. o If we pluck a guitar string, first the string vibrates in the form of a characteristic wave, and then it causes the air around it to vibrate - and we hear that in our ear Doppler Effect • Explain what the Doppler Effect is. Give an example. o It is the phenomenon where a sound will sound different if its source is traveling either toward you or away from you than it would if the source was stationary o This is why the siren from a police car or fire truck will appear to change in tone if you are standing on the side of the road and the car comes towards you, passes you, and continues on away from you • How does the Doppler Effect work? o It is because the sound waves are either compressed (coming towards you) or expanded (going away from you), and thus the altered wavelengths are perceived differently How do sonic booms work? • o This is an extreme application of the Doppler Effect whereby the source of sound created is so loud that the waves are compressed so much that they all arrive at essentially the same time at a single spot, and an extremely loud sound is created Oscillations & Resonance • Explain how a pendulum is an example of a simple harmonic oscillator. o It is because if we pull the mass to the left or right then let go, the tension in the string will cause the mass to swing back in the direction of the equilibrium position, and in fact surpass it and go to an extreme on the other side o The force that does this (and is definitive of simple harmonic oscillation) is a "restoring force": a restoring force always tries to bring the mass to equilibrium • Discuss the relationship which the restoring force has to the object's distance from the equilibrium point. What implication does this have for the period of a given pendulum? o The restoring force is linearly proportional to the object's distance from equilibrium: the further away the object is, the stronger the force is which wants the object to return • It consists of the force created by the tension of the string and gravity o The implication is that for a given pendulum, its period will always be the same… • Regardless of how far away you initially bring the pendulum • And also regardless of what the MASS of the swinging object is o The ONLY FACTOR that can change the pendulum's period is the length of the string • Explain how pendulum clocks work. o There is a circle with 30 teeth (a gear), and an apparatus attached to a pendulum o The apparatus is positioned such that every time the pendulum completes an oscillation (period = 2 seconds), the apparatus clicks past one "tooth" o Thus, every time the gear completes a full revolution, we know that it has been one minute (60 seconds) • Describe the motion of a mass on a spring, and why it is a harmonic oscillator. o Firstly, there is an equilibrium point - where the spring is neither stretched nor compressed o If we (for instance) pull the mass such that we are not at the equilibrium point and the spring is stretched, we will feel tension because the restoring force in the spring wants to return the mass to the equilibrium point o It is a harmonic oscillator because if we release the mass, it will accelerate back towards the equilibrium position and overshoot it to the other side, compressing the spring and creating another restoring force that pushes the mass again back to the equilibrium position from the other side • How do we adjust the frequency of these things? o Bigger mass = lower frequency o Stiffer spring = higher frequency • Explain what the concept of resonance is. o The "resonance frequency" is the frequency at which an oscillator "naturally" likes to oscillate o We can increase the amplitude of the oscillations if we add energy to the system at a frequency identical to this natural, "resonant" frequency • How does resonance apply to shock absorbers in cars? o Well, here we want to REDUCE the amplitude of the oscillations (so we will go up and down less) o So the shock absorbers are designed to compress and expand at a frequency DIFFERENT than the one at which the car is bouncing up and down - this will reduce the amplitude of the movement and make the ride more comfortable • How does resonance apply to pushing a child on a swing? o Here the relevant principle is that of pushing the child right when he gets to the apex of his swing - because when we do that, we are adding energy at the same frequency as the one at which he is oscillating o That is why we can get him swinging very high in a relatively short time if we do this (as opposed to, say, pushing him back before he has reached the height of his swing) • How does resonance apply to breaking a wine glass with sound? o It applies because if we play sound at a certain frequency, it will cause the air to (of course) also move at a certain frequency o Now, the sides of the wine glass also vibrate (ever so subtly) in response to the air o If we get the air to vibrate at the resonant frequency of the wine glass, the oscillations of the glass will increase until the glass breaks • How can water have an effect on resonance? o [I forget which demo this was, but] if water was the medium in which energy was being added to some system at that system's resonant frequency, the water could potentially dampen its effects Standing Waves and Sound • Explain how a standing wave on a string works. o If we have a string that is stationary at both ends, we can pluck it and cause a wave to be created at (one of) the string's resonant frequency o The wave travels down to one end and is reflected -- and this pattern maintains itself for some period of time o We say it is a "standing" wave because a pattern of oscillation is produced such that there appears to be no movement • Explain the concept of harmonics. o A string has many harmonics, and they are simply the term used for the frequencies associated with the natural "standing wave" conformations which the string can assume o Yes, that is right: a string can have more than one type of standing wave - theoretically, any number of wavelengths within the string is possible as long as the ends stay as nodes • Why is a sound heard when we rub the top of a wine glass with our finger? o Because due to friction, when we rub our finger we are actually dragging it to some degree, and causing the glass to deform slightly o This deformation creates a wave in air which produces the sound we hear o Continuously rubbing the finger adds energy (helps the glass deform more) and thus makes the sound louder • Why is a sound produced when we hit the end of a metal pole on the ground? o Because (again) the metal deforms ever so slightly, and we get a wave in air that makes the sound • Explain why sound can be created by blowing into an organ pipe. What happened when we put this tube over a flame from a Bunsen burner, and why? o Blowing into a pipe creates a longitudinal standing wave using the air inside the tube • One end is closed (a node, where compression can take place) and the other is open (an anti-node) • The standing wave goes at a frequency that we can hear, and that is the sound we perceive o Note that the fundamental wavelength is TWICE the length of the tube, because only one end is a node o When we put this over a flame, we could see the flame moving around in the air because of the changes in air pressure coming out of the pipe • Explain why sound can be created by blowing across the mouth of a beer bottle. o It is because when we blow, we are activating a mass-spring system such that the air in the neck of the bottle moves up and down due to the force we provide with our breath (by "pushing it down") vs. the restoring force of the air in the wide part of the bottle that pushes it back up o The frequency produced by this oscillation is perceived by our ears • How do we show that sound is a compression/rarefaction wave? o Recall that we had a tube of (some gas), with holes in the top…and also a flame o We created a longitudinal sound wave in the tube, and where the regions of pressure were low (i.e. the nodes), the flames shot up higher because it was a stable environment for the flames to work • Explain how a loudspeaker works. o There is an electromagnet, which consists of two magnets that can move towards or away from each other depending on the current in the coil o As the magnets move, they cause a paper cone to move, and this causes a pressure wave in air that we perceive as sound • What happens when we mix up the red and black wires in a stereo system? What is the name for this phenomenon? o When we do that, we send the wrong signals to the speakers, and so the air pressure waves created cancel each other out by the time they reach us, and we perceive a very soft noise - this is called "destructive interference" o When the wires are correctly plugged in, the sound waves created are the same as each other, so "constructive interference" occurs and we hear a loud sound From Textbook Chapter 9 Topic 3 Sunday, October 08, 2006 12:28 AM Topic 3: Balloons, Bubbles, and Pressure From Lecture Ideal Gas Law: Pressure, Density, Temperature, etc. • Discuss the structural differences between a solid and a liquid. o A solid is structural and arranged in a periodic manner, such that if we know the location of one molecule, we can infer the location of all other molecules in that structure o Conversely, the molecules in gas are much farther apart from each other, and there is no defined structure • What happened when we ran an air hose through liquid nitrogen? Why? o We caused some of the gases in the air to condense into liquids, while some others remained as gas o The result was that a combination of gas and liquid came out the other end o This is a property of gases - at certain temperatures, the molecules come together close enough that the substance takes on the consistency of a liquid • Explain how the concept of pressure applies to a gas. o Recall that pressure = force / area o And the individual molecules in some sample of gas push against the walls of their container, and create pressure • Explain how a steam engine works. o It's all about this pressure principle - you evaporate water and now we have lots of steam in a confined space o Thus it will create pressure against the walls, and this pressure can be used to crank an engine • Why does a balloon make a loud sound when it pops? o It is because there is a sudden release of pressure from the gas molecules which were previously inside, pushing out against the fabric of the balloon • When this pressure is suddenly released, a loud sound is made o Note that the pressure inside is (definitely) greater than the pressure outside because the pressure inside needs to keep the balloon stretched out • Explain gaseous temperature on a molecular level. o Temperature of some sample of gas is related to how quickly the molecules of gas are moving around o Note that if they move around faster, they will bump into the walls with more force and thus create greater pressure as well - that's why if a gas is in a container than can expand, heating the gas will cause the container to expand • How do we apply the molecular explanation of temperature to making bombs and popcorn? o Both things involve the principle of heating something up so that it expands so much and so rapidly that an "explosion" is caused • Either the bursting of the kernel into a piece of popcorn • Or the bomb exploding • Explain gaseous density on a molecular level. o Density is just how many gas molecules there are in a given area o Again, when the density is higher, the pressure will be higher because more gas molecules will be hitting the sides of the container • How does this apply to using a straw? o We are basically sucking the air out of the straw, meaning that there is less pressure available to push the liquid down o Thus liquid is able to come up the straw and into our mouth :) • What does the Ideal Gas Law tell us? o PV = nRT, or P = number density x R x T o Pressure is proportional to density of particles times temperature Atmospheric Pressure and Buoyancy • Explain the "box" model of atmospheric pressure. o If we are talking about the atmospheric pressure acting on a single person, imagine that the column of air above him is divided into boxes o Gravity acts (as it always does) on these boxes, and so there is a downward force on the person created by all this air • However, there are also air boxes which push up to counteract this (that is why we are not crushed) o As we get higher on this "pile" of boxes, there is more air pushing up and less air pushing down, so the air pressure we experience is less • Why was it hard to pull those rubber disks apart when the air was removed from inside them? o Because removing the air meant that the air pressure in the "container" was reduced to zero, all the air from outside wanted to get in so that pressure could equilibrate o This air created a force which opposed the efforts to pull the discs apart • Why does it not hurt to lie on a bed of nails? o Because the pain which we traditionally think nails cause is due to pressure, which (recall) is related to force and area o In this case, we are spreading out the area of the pressure source by putting many nails, and thus the total pressure is not too bad • What would happen if the cabin of an airplane became de-pressurized, and I failed to put on my oxygen mask? o All the intestinal gas we have (which is now kept at a certain density because of the atmospheric pressure from outside) would now be subjected to less atmospheric pressure, and so it would expand (very uncomfortable!) • What is Archimedes' Principle of Buoyancy? o "An object partially or wholly immersed in a fluid is acted on by an upward buoyant force equal to the weight of the fluid it displaces." • What phenomenon was observed with the Playdoh boat, and why did this happen? o This is a demonstration of Archimedes' Principle: when it was shaped like a real boat, the volume of water it displaced was greater than the volume of water it displaced when we condensed it into a ball o Thus when we had the greater volume of water, the buoyant force supporting the boat (equivalent to the weight of this greater volume) was big enough to support the boat's weight o But when we had the smaller volume of water, the buoyant force was less, while the boat was the same weight - but this time it was insufficient to hold the boat up • Why do we float higher in the Dead Sea than in our bathtubs? o It is because salt water is denser, so the weight of the volume of water we displace is greater than the same volume in regular water o Thus this greater weight means there is a greater buoyant force keeping us up • How does our weight change when we are in water? o Our weight is essentially equivalent to the normal force that needs to be produced by the surface we are standing on in order for us to not fall through o When we are in water, this normal force is reduced because the downward force produced by gravity on our body is (partially) counteracted by the buoyant force Balloons • How does a hot air balloon work? o We have to think about PV = nRT, and the relationships which that equation represents o The idea is that we use a fire to warm the air inside the hot air balloon…and this increases the kinetic energy of the molecules, causing one of the following things to happen: • All molecules remain in the area and pressure increases (molecules hitting the wall more frequently and at greater speeds) • Some molecules leave the area and pressure remains the same (molecules hit the wall at the same rate even though they are moving faster, because there are fewer molecules) o Since it is an open system, pressure cannot be different and so the latter option occurs. This reduces the density of the balloon to the point where it rises (can you explain this using Archimedes' Principle?) • Why did a balloon float when put at the top of a tube with dry ice at the bottom, yet outside the tube it sinks? o This is again an application of Archimedes' Principle: remember that the buoyant force depends on the weight of the air you have displaced o In regular air, this weight is not sufficient to keep the balloon afloat (it does have SOME weight!) • However, the gas evaporating from the dry ice is "heavy", so the buoyant force created is enough to keep the balloon afloat • What is the source of the energy that causes a balloon to fly around the room when you suddenly let the air out of it? o It's because when we were blowing up the balloon, we added energy to the system because the elastic material resisted stretching • Why do helium balloons act as they do? o Again, it's all about buoyancy. Think about the weight of the air displaced by the balloon. Now think about the weight of the balloon (plus, of course, the helium inside) o If the balloon is lighter, of course it will rise... Bubbles • How does soap work? o It is made up of molecules where one end of the molecule is hydrophobic (and thus can interact with oil) and the other is hydrophilic (and thus can interact with water) • This is why soap is good at removing oil - because it can cluster around the oil droplet, then the whole thing can be washed away with water • How did he create that sheet of bubbles? o He created a very sheet-like balloon-like structure where there was water in the middle, and then soap on either side such that the hydrophilic end of the molecules were touching the water Hydraulic Pump • Explain the principle behind the hydraulic pump. o This takes advantage of the principle that within a body of fluid, the pressure is the same everywhere o So we can supply a lot of pressure at one location in the fluid with a medium force but very small area • At the other end of the fluid, we can put a pump with very large area, meaning that having equivalent pressure in this area would mean having an even greater force o The "catch" is that the bigger weight will much less further than the smaller weight because work must always be equal, and work = force x distance…thus if we have small force and big distance, the other end will have large force and small distance • Basically, this allows us to move heavy things with little but prolonged effort, instead of much but instantaneous effort From Textbook Section 5.1 Topic 4 Sunday, October 08, 2006 12:28 AM Topic 4: Electricity From Lecture Current • Describe how electrons move in solids. o Think of the crystal lattice model of solids which was shown in class o There are spaces between the molecules where electrons can move freely - and since they carry negative charges, their movement constitutes a current • These electrons are known as conduction electrons • What happens in non-ideal situations with respect to electron movement through metal? o Firstly, the entire metal is not a single crystal lattice, so an electron will not be able to travel through a single "corridor" all the way through the metal o Secondly, there are "crystalline defects" such that the lattices could be bent and again prevent the electrons from traveling very far in a straight path • Describe a simple circuit consisting of a battery and a light bulb. o There are positive and negative terminals in the battery - the electrons leave (are repelled by) the negative terminal, go through the light bulb, then back to the positive terminal where they are "sucked in" (remember that positive attracts negative) • Note however that when we think about the path of current, we reverse this (it is as if we are thinking about the way POSITIVE charge moves, although no positive entities actually move -- it is instead the electrons) • Note also that the battery "pumps" charge - it does NOT store it in the sense of having a reserve of electrons • Note thirdly that the energy of the charges as they leave the battery is affected by the voltage of the battery (as a matter of fact, if it were not for resistance, voltage would equal current, which is the amount of charge passing a given spot per unit of time) • If we take the same circuit but sever the line that connects the light bulb back to the positive terminal, what will happen? o No electrons will move and the bulb will not light up, because there is no positive terminal to attract the electrons through the circuit back to it • Why does the bulb light up? o Because there is enough resistance in the wire that it becomes extremely hot, to the point where the wire glows Resistance • Explain the conceptual/molecular model of resistance. o Remember how there are crystalline imperfections (and such) that prevent electrons from moving through metal o The big-picture ultimate result of this is that electron movement (current) is slowed down to some degree o All this lost energy is converted to heat • What is Ohm's Law, and how does it apply to resistance? o It is voltage = current x resistance : it means that the bigger the voltage is, the faster the current will move BUT this is tempered by the resistance of the material it is moving through • If the material has a very high resistance, the electrons will move slow (even with high voltage) and all that energy will be lost as heat • Why did the light bulb dim when we put the wires in liquid nitrogen? Why did it brighten with another material? o It is because the coldness had different effects on the conductivity (i.e. resistance) of the wires • When resistance was decreased, more current was available to the light bulb and so it brightened • When resistance was increased, less current was available and so it dimmed Power • Give the 3 equations for power, and comment on each. o Power = energy / time : power is energy released per unit time o Power = voltage x current : power is increased by increasing voltage and/or current o Power = current2 x resistance : this is just a consequence of the above equation • Explain the term "kilowatt-hours". o It is the amount of energy consumed when you run a 1-kilowatt appliance (i.e. an appliance that draws power at a rate of 1 watt, or joule / sec) for 1 hour • Note: as said in parentheses, the units of power are watts (volts x amps) AC vs. DC • What is the difference between AC and DC? o AC (alternating current) is different from DC (direct current) in that the direction of the current is constantly changing o In order to accomplish this, the voltage source changes polarities as well - thus a voltage graph would form a sinusoidal curve • Explain the strategy involved in bringing power from outside a city to the homes inside the city. How is this related to AC vs. DC? o The central problem is that we want to bring a LOT of power in from the country to the city - and so since P = IV, we can choose to either carry at high currents or high voltages o Since P = I2R, high currents are bad because we will lose power due to resistance at a squared rate o Thus we carry the power using lines with high voltage: and this is easier with alternating current than with direct current because AC at high V and low I can more easily be converted to low V and high I (which we want once we're inside the city) • Why don't bulbs have to convert AC back to DC? Why do electric appliances have to do this? o Firstly, the central problem is that due to the sinusoidal voltage pattern of alternating current, there are times when there is absolutely no voltage • With bulbs, this is OK because although (yes) they turn on and off, this happens so rapidly that the human eye cannot tell • With electrical appliances, this is not OK because they will turn off and we will lose data - thus we have to convert AC to DC using (?) Magnets and Electricity • How do we create a magnetic field using electricity? How do we control the strength of this field? o When we put a current through a wire, a magnetic field is produced • Often we put current through a COIL to strengthen the magnetic field which is produced o The strength of the filed depends on the current and the number of windings in the coil • What advantage do we gain by placing a magnetic metal (such as iron) in the center of the coil? o The iron bar has magnetic domains which can be oriented by an external magnetic field (such as that produced by the coil), and thus create its own field that amplifies the total magnetic strength of the electromagnet • What would happen if the individual coils were free to move? Which demo in class demonstrated this? o They would be attracted to each other because each individual coil creates a N-S magnet that causes it to be attracted to other magnets o Remember the coils wrapped loosely around the wooden cylinder - when electric current coursed through the coils, they clustered together in the middle • Discuss the vice-versa situation. What effect does a magnetic field have on an electric field? Explain the demo which demonstrated this. o The overall principle is that a changing magnetic field creates an electric field o There were 2 demos which demonstrated this: • Firstly, recall the demo where you had to turn a crank very fast and light up a light bulb: here the theory is that turning the crank caused a changing magnetic field which created an electric field that caused current to flow through the wires and light the light bulb • Secondly, there was a demo with a large green coil and then a red coil that fit inside of it. An electric current was sent through the inner red coil, which created a magnetic field. This magnetic field acted on the outer coil and produced a current which went through it Lenz's Law, Generators, and Transformers • What is Lenz's Law? Explain how this describes the behavior we observe if we push a magnet into a coil. o Current induced by a changing magnetic field always produces a magnetic field that opposes the change. o So let's think - if we push a magnet into a coil, that magnetic is producing an electric field that causes voltage, which further causes current to go through the coil • But as we recall, this current is also going to create its own magnetic field - and Lenz's Law tells us that the new magnetic field will oppose the one created by the original magnet, and thus we will feel resistance as we attempt to push the magnet further down into the coil • Furthermore, where does the work that our hand is doing go? It becomes electrical energy (the current) • What happens once the coil passes through the other side, and why? o The opposite occurs: now the magnetic fields are aligned such that the coil tries to suck the magnet back in o This happens because essentially the magnetic field created by the magnet wants to be constant • How does a generator work? o We have two coils, and we connect them to a light bulb such that charge could flow from one coil through the light bulb, to the other coil, then back to the original coil o We put a magnet between the two coils and we spin it at a high rate o This causes a changing magnetic field in the vicinity of the coils, and (as we said earlier) causes current to flow through them o Since the "N" end of the magnet is always acting on one coil and the "S" on the other, current flows through the system (the coils act as the "+" and "-" terminals of a battery) o When the magnetic is flipped, the current just flips direction: thus we are essentially creating AC power • Explain the modified guillotine, and what it demonstrated. o There was a guillotine created such that the "axe" is a magnet o The axe was made up a metal/coil sort of thing capable of holding an electric current, and then there was a magnet in the place where the head was supposed to be - thus as it swung through, a current was generated in the axe, which created a magnetic field that opposed the original magnetic field…and the axe stopped • Notably, if we replaced the axe with something that had spaces and therefore could not hold a current, the axe's motion was not stopped • What does a transformer do, and how does it work? o A transformer can either convert current from one voltage to another, or keep it at the same voltage • In either scenario, transformers add a measure of safety because they isolate the source of AC power from the appliance that consumes it, so if there is ever a power surge, the appliance (and the person using it!) will not be damaged o A transformer works using magnetic induction - that is, the ability of a changing magnetic field to create electricity • We have two electric coils: a primary coil and a secondary coil • A magnetic material called the "transformer core" runs through both the coils • We put electric current from an outside source through the primary coil. What happens? The current creates a magnetic field, which is passed onto the transformer core so that it gets its own magnetic field • Now, what effect will this new magnetic field have on the secondary coil? Well, it is a changing magnetic field and so current will be produced in the coil • This current can be used to power appliances! o The most useful aspect here is the fact that WE CAN CONTROL the voltages produced (which further affects the current in the coils) • This is because the voltage is affected by the number of turns in the coils, because the number of turns determines the magnetic field which will be produced • In fact, the following ratio exists: Domestic Applications: House Power, Fuses, Circuit Breakers, Ground Fault Circuit Interrupters • Describe the path of electricity from a power plant to a home. o We take electricity from the power plant to the edge of a city using a transmission line at about 500,000 V (remember that we want high V, not high I) o Then we transform the voltage to 5,000 V and use another transmission line to bring power to our street o Then we transform it again to 120 V and use another transmission line to bring it to our house • Describe the roles of the different holes in a wall plug. o The two thin lines are for "live" and "neutral" • The neutral line stays around 0 V, and the live line alternates between a high positive and a high negative voltage (remember that it is AC) • Thus the path of current will either be neutral -> appliance -> high negative, or high positive -> appliance -> neutral o The rounded hole is the "ground" line, and it provides a path for electricity to go such that it cannot harm us in the case where a short circuit occurs and the electricity cannot pass through the appliance as it usually does • Because normally, what would happen? All that electricity would just keep going through the wire, the wire would get hot, then we would have a fire • The ground line allows us to send electricity through it (in emergency situations) and into the ground, so that there is no danger • Describe what a fuse is, and how it works. o A fuse is something that prevents us from the dangers of short circuits • What is a short circuit? It is when we have a circuit with an appliance which is designed to let charge go through it, use the charge to power itself up, etc…but then for some reason the wiring messes up and a SECOND path is created for charge to go from the positive to negative terminal of the battery • Only this time, the new route was unplanned and so there are no appliances on this path which can use the energy. So what happens? The wire, which is not properly equipped to handle the heat which will be generated by all this current, will get hot and then dangerous things can happen o A fuse is made of a wire that melts very quickly should this case occur, and when it melts the circuit will be broken and then we are all safe • Describe what a circuit breaker is, and how it works. o A circuit breaker performs a role similar to that of a fuse, only it does not have to be replaced o There are 2 strips of metal, one of which expands more quickly than the other o When there is lots of heat, the bottom one expands faster, causing a bending action - it bends so much that the metal is no longer connected to the wire, and again contact is broken and electricity stops moving • Describe what a ground fault circuit interrupter is, and how it works. o GFCI's perform a role slightly different than fuses and circuit breakers: their job is not to detect an overload of current, but rather to detect current leaks • The idea is that usually current goes to an appliance, then comes back. If this fails but the current still has a way of leaving the system, the wires will not get hot - so circuit breakers won't help However, this situation can still be dangerous because (for • instance) if all that current is going into a body of water, anyone sitting in that water will be dead • So GFCI's have a way of detecting whether or not that current is returning o The way it works is that we have a coil, and two wires running through it - one of the wires has current going to the appliance, and the other has it coming back • So what happens due to the current going through these wires? A magnetic field is produced, which causes current to go through the coil, which will produce an opposing magnetic field, etc.  But wait! There are TWO wires in the coil, and current is going opposite ways. So in fact, the magnetic fields cancel out and the surrounding coil is unaffected • So what happens if the current coming back isn't the same as the current going away (i.e. there is a leak somewhere)? A magnetic field WILL be produced, and then the GFCI is designed such that a switch opens and the circuit is disrupted - everyone's safe! From Textbook Section 10.3 Section 11.1 Section 11.2 Section 11.3 Topic 5 Sunday, October 08, 2006 12:28 AM From Lecture Magnetism/Electricity Theory • What are the ways in which magnetism and electricity differ? o A single given object must be both north and south magnetized, but in terms of electricity it can carry exclusively a negative charge or exclusively a positive charge • What are the way in which they are the same? o They are both the same because there are two different states which they can be in (positively/negatively charged, and north/south pole) o Opposite poles/charges create magnetic or electric fields that can be described using electric field lines (or magnetic flux lines) • The idea is that if we were to throw an electrically charged particle (or a magnetized particle) in there, it would experience force along those lines • Talk about some of the relationships between electricity and magnetism. o A changing electric field creates a magnetic field o A changing magnetic field creates an electric field (note that the magnetic field which this subsequently produces will be opposed to the original magnetic field, as per Lenz's Law) o Magnetism and electricity are different in that magnetic fields do not require any medium to move on, while electric fields do (they need electrons)! Antennas, Tank Circuits, and Radios • Explain how we send information using antennas. o OK, so the idea here is that charge moves up and down the antenna (it is vertically polarized), and the idea is that it sends an electric field out into space o And this electric field (vertically polarized) produces a horizontally polarized magnetic field (remember a changing electric field makes a magnetic field), and this travels out in the atmosphere to get to the antennas of the "receiving" radios • Explain how a tank circuit and an antenna interact to send out signals from a radio transmitter. o OK, so for let's consider what a tank circuit is. It's very simple: we have a capacitor, where a coil of wire connects the two sides • So obviously, our start state is that all this negative charge is on one plate, and in going to the other plate it goes through this coil • As it goes through the coil, the changing electric field in the coil creates a magnetic field • This magnetic field grows to a maximum strength when all the charge has left the capacitor plate • But the magnetic field causes the charge to keep moving so that it accumulates on the other plate, and our end game is just like our start state except the charges are flipped • The take-home message: the capacitor switches states with a regular frequency - and we can use this to control the charge which it sends up an antenna • Lenz's Law is important here because the law is all about the desire of magnetic fields to remain constant - and so when the magnetic field builds up in the coil, it wants to release it and it does so by keeping the charge moving through o And then we connect the tank circuit to the antenna, and it causes charge to go up and down the antenna which forms an electric field in the air • What degree of control do we have over this sent information? o We can control the frequency of the electrical "oscillations" in the tank circuit: • Changing the capacitance of the capacitor: the more charge it holds, the longer it takes to go to the other plate, the longer the period is • Also, we can change the inductor's inductance (i.e. how much the coil opposes the movement of charge through it) • Explain how a tank circuit and an antenna interact to RECEIVE signals on a radio. How is this relevant to "tuning" our tank circuit? o So here the idea is that the radio receiver will sense the waves, and so a wave will go down the receiving antenna o The antenna is of course connected to another tank circuit, and so if we set the tank circuit at the right frequency, the electric waves coming off the antenna will BUILD THIS UP (resonant energy transfer), and it'll go crazy! AM Radio • What is the frequency range of AM radio? What is the significance of this? o The range is 550 kHz - 1600 kHz • OK, so this means that signals broadcasted for AM radio (i.e. those waves coming off the antenna) have to have frequencies in this range o Furthermore, of course there isn't just one AM station, so the stations have to share this range and they each have an even smaller amount of frequency to work with • And remember the pitch of sound that comes off the antenna will depend on the frequency, so if we are restricted to a smaller range it means that we can't broadcast as good quality of sound o Furthermore, the corresponding wavelength for these frequencies is approximately 300 m, which is HUGE • And note that the radio transmitters usually like their antenna to be exactly 1/4 of the wavelength, so it means they are 75 m high • On the other hand, the radio receivers don't have 75 m to work with, so instead they sense the magnetic part of the radio electromagnetic wave • What is the meaning of amplitude modulation? What are the implications of this? o The idea is that AM radio encodes information by varying the amplitude of the waves it sends out - so perhaps greater amplitudes mean higher pitches, etc. o The consequences of this are that we can listen to AM radio from farther away than FM radio - it doesn't all cut out at once, rather as we go farther away we will still be able to hear the waves that originally had larger amplitudes FM Radio • What is the frequency range of FM radio? What is the significance of this? o It is 88 MHz - 108 Mhz o So this a bigger range than AM, which means that we can broadcast a wider range of frequencies for each station and so the sound quality is better o It also means that the length of the antenna is smaller, because the corresponding wavelength to such a high frequency is very short • What is the meaning of frequency modulation? o OK, so this means that FM radio transmitters encode their sound information differently: instead of varying the amplitude of the waves they send out, they vary the frequency o This means that the amplitude will always be full (which also contributes to the better sound quality), but also means that when you get out of range of an FM station, ALL the frequencies of sound drop out Television • Give an overview of the path of electrons in a television o OK, so we warm up a cathode (negatively charged) so that electrons leave it o The first thing they run into is a negatively charged grid which repels most of the electrons coming off the cathode o However, the ones which are going straight and have enough energy get through o They are then attracted by an anode o After they get through the anode, they go through a focusing coil - a coil which is literally wrapped around the tube • This coil produces a magnetic field that causes the electrons to all go into a straight line o Then we get to the deflecting coils, which are placed all around the tube and produce fields to deflect the electrons to the precise part of the screen where they need to be o Then they hit the phosphor on the screen and make it glow white (or if there are less electrons, then maybe some gray) - and we get a picture • Talk more about how the actual image is produced on the phosphor screen. o OK, well certain parts of the screen glow when we hit them with electrons • And the idea is we take the electron beam and we go across the screen really fast, filling in all the spots - either make the spot white, grey, black, etc. o We get through the total image 30 times per second (so stuff is fast!) -- however at this rate, it flickers • Or we can do "interlaced" where we only fill in every other line, but we get through 60 images per second Color TV • How do we create the appearance of color? o The idea is that for every individual spot of phosphor we used to have, we now have 3 different spots which glow either red, green, or blue when they are heated • And so we can hit one or several of these to make any color we want - and they are so close together that they appear to be a single color to our eyes o We do this by having 3 electron guns and putting a "shadow mask" in front of the phosphor screen such that when electrons come out of the electron gun and go through the phosphor screen, it can only hit a certain color of phosphor, and so we know that each electron gun will only make one color • Magnets can really mess up the configuration of this shadow mask, so that's why you shouldn't bring magnets near a TV • Notably, the "degauss" button is supposed to fix any weirdness caused by magnetism From Textbook Section 13.1 Topic 6 Sunday, November 26, 2006 9:39 PM Topic 6: Microwaves and CD's From Lecture Waves, Velocity, and Light • What are the important units for the wave representation of light? Define them and explain how they are related. o Velocity = how fast the light is going (we know that this is 3 x 10^8 m/s in air) o Wavelength = the length of one "unit" in the wave o Frequency = how many wavelengths are traversed in one second o They are related as follows: Velocity = wavelength x frequency • Comment on the constancy of the speed of light. o As stated earlier, we know it to be roughly 3 x 10^8 m/s in a vacuum o However, when light is going through other materials (such as glass), it is different o The idea is that the speed of the wave can change depending on the medium through which it travels • Discuss the light spectrum. o So obviously light is going to look different to us depending on what the frequency of the wave is • In general, the frequencies for these waves are WAY higher than the frequencies for, say, AM radio o The frequencies range from (428,000 GHz) infrared -> visible light -> ultraviolet (750,000 GHz) • For the more hardcore of us, the full spectrum: radio -> microwave -> infrared -> visible -> UV -> X-ray -> Gamma ray Microwaves • Talk about microwaves generally, and also microwaves specifically (as in the ones which we will actually use). o General information: they range from 0.3 Ghz to 300 Ghz, and the associated wavelengths are 1 mm to 1 m o The ones which we use specifically (in real microwaves) are 2.45 Ghz frequency and 12 cm in wavelength • How do microwaves heat food? What implications does this have for what we can and cannot heat in a microwave? o The idea is that we create an oscillating electric field within the microwave - meaning that the "plus" and "minus" ends flip back and forth rapidly o Since water molecules are polar, they will also flip back and forth because of the strength of this field, and this vigorous movement will create heat o Thus, we can heat things if… • The molecules are polar (so most commonly water) - all food has water in it • It is jello - because although it is a "solid", it is actually water within a matrix  The matrix is why it seems like a solid, but the free water molecules allow it to heat up o But we cannot heat things if… • The molecules are non-polar (such as a pure hydrocarbon like butane)  Note that vegetable oil does not work because it is impure • It is ice (because the molecules are frozen in place -- it's a solid! -- and cannot flip)  This is why frozen burritos sometimes heat up unevenly - because the ice in different parts of burrito is unequally subject to melting • The way we fix this is we make the defrost cycles in a microwave turn off occasionally to allow the heat to flow through the whole burrito • Explain the mechanism through which the oscillating electric field is created within the microwave. o OK, so let's start off thinking about the big picture. What we basically need is to create an electric field within the microwave that changes polarities at a frequency of 2.45 GHz o Now let's think about a tank circuit - remember that this is basically a capacitor where the plates are connected by an inductor (something that allows charge to flow through), and thus all that happens is that the negative charge goes from one plate to another, then back again, etc. o But as the charges are moving from plate to plate, a magnetic field is created, and it differs based on what direction the charges are going in - and so we say that the field changes (or oscillates) at some frequency o So the idea is the same with microwaves - this time we use something called a "magnetron", which is just a curved piece of metal - the tips of the metal are the capacitor plates, and the other part just allows the electrons to go through o So what we actually do is we line up EIGHT of these guys so that they form a circle - and they are "sharing" tips, so the tips alternate negative, positive, negative, positive, etc. o And so there will be alternating magnetic fields produced between the tips, and they change at a 2.45 GHz rate…and so we are almost there o What we do next is we attach a coil to the magnetron - and thus there will be an alternating current in the coil o And then connect an antenna to the coil - and so we'll have microwaves coming off this antenna and into the microwave • Explain what one problem with this is, and how we solve it. o OK, well since the inductor may be imperfect, and the energy of the waves is absorbed by the water molecules (making them flip), we have to give more energy to the inductor - and we do this by adding electrons to the negative terminals o The way we do this is in the middle of the magnetron, we have a hot cathode filament that will emit electrons o WAIT - when these electrons go free, they will just go to the positive terminals because of positive-negative force interaction, right? YES. o So we solve this by putting a magnetic field going straight up through the center that causes them to bend (remember what moving charge does in the presence of a magnetic field) • Discuss the issue of metal with microwaves. What do we use it for? o Well the fundamental principle to remember here is that when electric current goes through any given material, the higher the resistance, the more it heats up. Whereas the lower the resistance, the less it heats up o Metal Usage #1: think about the metal lining the edges of the microwave. It is very thick, so resistance is high and it does not get hot. In fact, it instead REFLECTS the waves back into the microwave • We have the same idea with the metal on the door - the holes in it which allow us to see through are acceptable because the hole is smaller than the wavelength of the microwave, so the waves will not go through o Metal Usage #2: recall the Michelina's pizza thing. We were able to not make it soggy because it sat on a tin sheet which had high resistance, thus got very hot and baked the pizza while boiling off any water • What are some of the safety issues we need to be aware of with microwaves? o Certain kinds of metal are DANGEROUS: • Near sharp point (like the crumples of a tin foil or the tines of a fork), the electric field can build up and we get sparks (maybe almost like a corona discharge?)  If a spark occurs near something combustible (like twist ties), we get a fire • Very thin metal, such as the gold rim of a plate or glass has large resistance and will heat up and melt o If there is nothing in the microwave but we turn it on, it'll just get really hot in there (nothing to absorb the energy) and bad things will happen - thus we have an auto-off switch for the magnetron o We don't allow the microwave to turn on if the door is open, because if we do - and someone puts their hand in there, they are TOAST - the whole hand will burn (not just the outside) Geometrical Optics • Explain what a convex lens does to light. o Think about its shape - it will focus parallel light to a spot at the focal point (this doesn't mean it makes objects smaller though!) • Although the wavelength of light limits how small that spot is o Thus it increases the energy density o It does this because as the light travels through the lens, the speed of light changes and so it curves • Explain how a magnifying glass/projector lens works. o It bends the light such that the image produced by a given object is BIGGER (think about and draw the diagram) o However when we are thinking about light going the other way through the magnifying glass, it is parallel beams of light and so they get focused (that's why we can burn ants by holding a magnifying glass over them) • Discuss the two kinds of mirrors. o Flat mirror - it reflects light "normally", where the incident angle is the same as the reflected angle o Parabolic mirror - it has a concave shape and so parallel rays of light will get focused to a point, and then diffused • What do light polarizers do? o Firstly we have to realize that in our world, light doesn't come all neatly aligned - the wavelengths could be straight up and down, or left and right, or diagonal o So a light polarizer "selects" a certain alignment of wavelength and only lets that through • Discuss two "real life" applications of polarization. o Polarizing sunglasses - these guys block horizontally polarized light, which is the main component of glare o Liquid crystal - this thing reorients light (i.e. changes its polarization), so let's think: if we put liquid crystal between a horizontal polarizer and a vertical polarizer, light which would normally be blocked would get through because it goes through the vertical polarizer so that we only have vertical light, but then the LC re-orients to make it horizontal, and so it gets through the horizontal polarizer too • We use this in liquid crystal displays with watches, where we use an electric field to turn the LC's re-orientation abilities on and off Sound and Data Storage • How could we store sound electronically, i.e. on a CD? o Let's imagine we are talking into a microphone. Throw a magnetic coil in there - it will vibrate in response to the sound waves which we create o The movement of the magnetic coil will create a corresponding electric waveform, which will have different voltages at different points o Now we measure the wave every so often and look at what voltage it is - then use binary to store these numbers • Note that the frequency (how
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