Ch. 1--A Little Bit of Magic

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Chapter 1

A LITTLE BIT OF MAGIC

A.) Your World is an Illusion:

1.) The world you think you know is nothing like the world that is.

2.) An outrageous claim? You'll see.

B.) The Atom:

1.) Look at the room in which you sit. Better yet, look at the palm ofyour hand. What you perceive is something that appears massive, substantive.In your world, substance is all around you . . . and yet it isn't.

2.) The so-called fundamental building block of matter is the atom. Sotake an atom. What do we know about it?

a.) To begin with, it is small. The diameter of a typical atom is 10-10

meters across (that is .0000000001 meters, or one angstrom).

b.) Atoms are made up of positively charged protons and neutralneutrons in the nucleus at the atom's center, and negatively chargedelectrons "orbiting" the nucleus.

c.) Normal atoms are electrically neutral because they have as muchpositive charge as negative charge in them.

i.) An atom that has gained or lost electrons, thereby becomingcharged, is called an ion.

d.) The type of atom you happen to be looking at is identified by thenumber of protons in its nucleus. This number is called the atomicnumber.

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i.) Examples: All Hydrogen atoms have one proton; all Heliumatoms have two protons; all Lithium atoms have three protons, etc.

e.) The number of protons and neutrons in the nucleus is called theatomic weight.

d.) Although the number of protons in a particular kind of atom isfixed, the number of neutrons can vary. There will be a typical atomicweight that is most likely, but if you happen to be dealing with one of theoddballs, the atom is called an isotope.

i.) Examples: Normal Hydrogen has one proton and no neutrons.Deuterium is the isotope of Hydrogen that has one proton and oneneutron. Tritium is the isotope of Hydrogen that has one proton andtwo neutrons.

e.) The electron orbits the nucleus moving at around 14,000 milesper second. It is interesting to note that at that speed, given the size ofthe orbit, the electron orbits the nucleus approximately 1016 times everysecond (that's 10,000,000,000,000,000 times per second).

3.) Let's take a closer look at a hydrogen atom. If we take it and do alittle magic on it so that it's nucleus expands up to the size of a super ball witheverything else expanding proportionally, what will we end up with?

a.) We will end up with a 2.5 inch diameter super ball nucleus with apoint sized electron orbiting the super ball approximately four milesaway. That is to say, if the super ball was located here on PolytechnicSchool's campus, the electron would be located somewhere down in themiddle of San Marino.

b.) In other words, we would be left with a super ball sized proton, apoint sized electron, and in between, four miles of absolutely nothing. Puta little differently, of the approximately thirty-five trillion cubic feet(that's 35,000,000,000,000 cubic feet) making up the volume of thatexpanded spherical atom, only about 0.005 cubic feet would be occupiedby what you and I would call real matter.

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4.) Conclusion: Atoms are made up almost entirely of space.Consequence? Take an object, any object. Take your body, for instance.

a.) If we could somehow extract all the space from your body, whatwould be left would be a tiny speck of matter that would probably take amicroscope to see, and that would weigh one to two hundred pounds (i.e.,your original weight).

b.) Your body is almost entirely made up of space, and yet it does notappear to be so. You do not look at your hand and say, "Ah, yes. Space!"That is not what your hand seems to be.

c,) In my country, something that appears to be what its not is calledan illusion. And in fact, that is exactly what your physical world is.

5.) A Note: When all of this is pointed out to people, a commonly askedquestion is, "Why do objects appear to be solid if they aren't, really?" A relatedquestion is, "Why do atoms appear solid?"

Just so you know, there are three reasons why atoms appear solid (hence,why your physical world appears . . . well, physical).

a.) First, the electrons that "orbit" the nucleus move so fast that theygive the appearance of a solid atom (remember, they do the equivalent of1016 cycles per second around the nucleus).

i.) This can be analogized by an electric fan. If the blades of a fancould be made to move fast enough--DON'T TRY THIS AT HOME--THE BLADES OF YOUR TYPICAL HOUSEHOLD FAN DON'TMOVE FAST ENOUGH--you could actually try to force your fingersinto the moving fan blades and not be able to do it.

ii.) How so? Even though there would be space between theblades, and even though you would be hurt if you could get your fin-gers into one of those spaces as the blades turned, the blades wouldbe moving at such high speed that your finger would never be able topenetrate beyond the superficial surface created by the blade motion.

iii.) As such, you would have the appearance of a solid--the surfacecreated by the blade's motion--even though the reality of the situationwas that of a structure that was not solid.

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b.) Second, when you squeeze something and register its solidness,you are essentially trying to force the electrons of the atoms making upthe structure into smaller orbits. The resistance you encounter when youtry to squeeze something is due to the electrons' unwillingness to do that(i.e., to be forced into smaller orbits). Put a little differently, because theelectron is moving so fast, it would take an enormous amount of work tomove it out if its orbit and into a smaller one.

c.) The third reason that atoms appear solid is that the wavelengthsof light that your eyes are sensitive to are so long in comparison to thegaps that exist within atomic structures, the light that you see simplycan't bring out the fine, structural subtlety of matter at the atomic level.

6.) In summary: All around you are objects that seem to be substantive,yet none of them have much real substance to them at all. In fact, the physicalworld that you perceive is a first class illusion.

C.) Times, They Are A Changing:

1.) Still not convinced that your perception of the world is not as close tothe reality of the world as you think? Let's try again.

2.) Time is a measure of the rate at which the moment passes. Youthink time runs the same everywhere. It doesn't. Time at the sea shore runsmore slowly than time in the mountains.

3.) Poppycock you say? It's true. Sure, you'd need cesium clocks--clocksthat are accurate to a ten-thousandth of a second over a thousand years--tomeasure the effect, but it is there.

4.) In fact, scientists have used cesium clocks to show this phenomenon.

a.) Two cesium clocks were set so that they were exactly alike.

b.) One of the clocks was put on the first floor of a building. Theother clock was put on the third floor of the building.

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c.) The two clocks were left alone for a couple of years, then broughtback together for comparison. What was observed was that the clock onthe first floor ran more slowly than the clock on the third floor.

5.) This is not slight of hand. Don't expect Penn and Teller (they aremagicians, for those of you who don't know) to come popping out of this book toshow you the slight of hand. This is a part of the reality of your world. Youdon't observe this kind of time variation because you are never in a situation inwhich it is obvious (i.e., you are never in a situation in which you are close toextremely massive objects), but it is nevertheless a part of the reality of yourworld.

6.) In short, time--a measure of the rate at which the moment passes--isnot the same everywhere. The rate at which the moment passes depends uponwhere you are, and upon the massiveness of the objects that are around you inthe space in which you reside. Time in your frame of reference will alwaysappear to be running normally, but time in one frame will not always be thesame as time in another frame . . . and that's the truth (thank you Ruth Buzzie).

Note: The consequence of all of this is that in Relativity, space is notviewed as a nice, homogeneous, three dimensional void. It is instead viewed as afour dimensional structure with the fourth dimension being time. In other words,in Einstein's view of the world, time is quite literally a part of the fabric of space.

D.) Mass and Free Falling Objects:

1.) Still not convinced? I have more!

2.) A ten kilogram object weighs more than a one kilogram object (duh!).

a.) That is to say, a ten kilogram object is gravitationally pulledtoward the earth with ten times the force than is the case with a onekilogram object.

b.) Put a little differently, if you drop a ten kilogram object on yourright foot, then from the same height drop a one kilogram object on yourleft foot, I can guarantee that the experience of your right foot is going tobe less pleasant than the experience of your left foot.

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3.) This is all very obvious, very reasonable. What is not so obvious andreasonable is the experimentally determined fact that if you take those twoobjects and drop them side by side from the same height, assuming air frictionis the same for both, the two will reach the ground at the same time. That is, thetwo will drop side by side until they reach the ground.

4.) In other words, even though the ten kilogram object is being pulledtoward the earth with a greater force, it accelerates at the same rate as thelighter object.

So how can this be?

5.) To understand what is going on, you need to understand what is goingon with the idea of mass.

6.) According to most sixth grade science classes, the mass of a bodyidentifies how much stuff there is in the body. If a body's mass is big, there's alot of stuff in it. If the body's mass is small, there is little stuff in it.

a.) What is additionally pointed out in the sixth grade is that if youtake an object to the moon, it's weight will change because the moon willgravitationally pull at the object less than was the case on earth, but itsmass--the amount of stuff in the body--will remain the same.

b.) Unfortunately, this is a very simplistic view of mass. In fact, theidea of mass was originally devised to measure a couple of very specificsomethings.

7.) There are characteristics that are true of all material objects. Forinstance, all objects have a tendency to resist changes in their motion.

a.) Example: A rock placed in space will not suddenly, sponta-neously accelerate for no reason. It will sit in its place until a forcemakes it move.

b.) The unwillingness of an object to spontaneously change its motionis called inertia. As the amount of inertia an object has is intimatelyrelated to how much "stuff" there is in the object and, hence, how muchforce will be required to accelerate the object, quantifying the idea of inertia

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is important. Early scientists satisfied that need by defining an inertia-related quantity they called "inertial mass."

c.) The idea is simple. A platinum-iridium alloy cylinder, currentlyhoused in a vault at the Bureau of Weights and Measures in Sevres nearParis, France, is defined as having one kilogram of inertial mass. Allother inertial mass values are measured relative to that cylinder. Thatis, an object with the same amount of resistance to changing its motion asdoes the standard is said to have "one kilogram of inertial mass." Anobject with twice the resistance to changing its motion is said to have twokilograms of inertial mass; one-half the resistance implies one-half kilo-gram of inertial mass, etc.

In other words, the inertial mass of a body gives us a numerical wayof defining how much inertia an object has RELATIVE TO THESTANDARD. Put still another way, inertial mass is a relative measure ofa body's tendency to resist changes in its motion.

Note: Although France is a beautiful country, it would be terribly inconve-nient for laboratory scientists around the world if they had to travel to France everytime they wanted to determine an inertial mass value, so scientists furthergenerated a laboratory technique for measuring inertial mass. It utilizes what iscalled an inertial balance--a tray mounted on two thin blades that allow the tray tovibrate back and forth. The more mass that is placed in the tray, the slower the trayvibrates. A simple formula relates the tray's vibratory rate (its period of motion) tothe amount of inertial mass there is in the tray.

Although it works, using an inertial balance is a VERY CUMBERSOMEand time consuming operation.

8.) Another characteristic that is true of material objects, at least in thestandard Newtonian view, is that massive objects are attracted to othermassive objects.

a.) A measure of a body's willingness to be attracted to another body isrelated to what is called "gravitational mass."

b.) Just as was the case with inertial mass, to provide a quantitativemeasure of gravitational mass, scientists have taken an agreed uponobject as the standard against which all subsequent gravitational massmeasurements are made (again, this standard is housed today in Sevres,France).

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c.) The technique for measuring gravitational mass utilizes a bal-ance or electronic scale. The object is placed on a scale which consists of aspring-mounted pan. The gravitational attraction between the object andthe earth pulls the object toward the earth and compresses the spring inthe process. The scale is calibrated to translate spring-compression intogravitational mass (assuming that is what the scale is calibrated toread--in some cases, such scales are calibrated to read force, henceAmerican bathroom scales measure in pounds).

MEASURING GRAVITATIONAL MASS IS EASY.

9.) Somewhere down the line, someone noticed a wholly unexpected andprofoundly improbable relationship between gravitational and inertial mass. Itwas observed that if the same standard object was used for both, a secondobject with twice the gravitational mass relative to the standard would alsohave twice the inertial mass.

a.) THIS DOES NOT HAVE TO BE THE CASE.

b.) There is no obvious reason why a body with twice the resistance tochanging its motion (relative to the standard) should also have twice thewillingness to be attracted to other objects. The two characteristics arecompletely independent of one another, yet they appear to parallel oneanother to a high degree of precision.

i.) In fact, the best comparisons to date have accuracy to around2x1012 with no discrepancy found even at that order of magnitude.

10.) Scientists could have called the units of gravitational mass anythingthey wanted (I'd have suggest the Fletcher, but I wasn't around when thediscussion took place), but because they knew the parallel between gravita-tional mass and inertial mass existed, they decided to give gravitational massthe same units as inertial mass, or "kilograms."

That means that as defined, a body with two kilograms of gravitationalmass also has two kilograms of inertial mass.

a.) There is beauty in this choice.

i.) Newton's Second Law (i.e., F = ma) relates a body'sacceleration a to the force F that motivates it to accelerate.

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ii.) In Newton's Second Law, the proportionality constant--themass term m--is an inertial mass quantity. (This makes sense if youthink about it. The body's resistance to changing its motion is whathas to be overcome by the force, so the acceleration will be related tohow large the body's inertial mass is.)

iii.) Determining inertial masses in the lab is a pain in the arse--inertial balances are not easy devices to set up or use. Butgravitational mass is easy to measure. All you need is an electronicbalance. So when you or I or a lab technician needs to know a body'sinertial mass, all that has to be done is to measure the body'sgravitational mass on a scale . . . and we are done.

b.) Soooooo: Due to the parallel, most people no longer distinguishbetween gravitational mass and inertial mass. As the two arenumerically interchangeable, people nowadays simply refer to a body's"mass" and leave it at that.

11.) We are now ready to understand the brain teaser I stated at thebeginning of this section. Specifically, if a body whose gravitational mass is tenkilograms is attracted to the earth ten times as much as a body whosegravitational mass is only one kilogram, why will the two free fall toward theearth at the same rate?

a.) The answer is simple. A body with ten times the gravitationalmass also has ten times the inertial mass. That is, the body will have tentimes the force on it, but it will also have ten times the resistance tochanging its motion.

b.) The net effect? It does not matter how massive an object is, itsinertia coupled with its willingness to be attracted to the earth will alwaysbalance one another out making the object accelerate at the same rate asall other objects (again, assuming you ignore air friction).

Note: Close to the surface of the earth, that acceleration in the MKSsystem of units is 9.8 m/s2. In our system of units, it's 32.2 ft/s2. Kindly notethat the MKS system of units is not something that only pointy-headedscientists use (thank you, Sterl Phinney for that turn of phrase), it is what THEENTIRE REST OF THE WORLD USES OUTSIDE AMERICA! In other words,

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we are the oddballs for using things like inches and pounds as our system ofunits.

12.) What we have been looking at in this section has been an oddphenomenon, but it is perfectly reasonable if you understand how your universeis built. That is what we will be doing in this class this year. Trying tounderstand how the universe works.

E.) Energy:

1.) I've been having such a good time, let's do just one more bit ofamusement. Visualize an object sitting motionless out in space. Once you'vegot it, mentally apply a constant force to it. What changes?

a.) Most people will say that the body's position will change.

b.) Most people will say that the time will change.

c.) Most people will say that the body's velocity will change.

d.) And although it is wrong, at least some people will say that thebody's acceleration will change (this is wrong because a constant force willproduce a constant acceleration, and a constant acceleration doesn'tchange . . . )

2.) WHAT MOST PEOPLE WON'T SAY, but what happens to be true, isthat the other thing that changes is the body's inertial mass.

3.) That's right, folks. As the body's velocity increases, so also will it'sresistance to changing its motion--its inertial mass. And for those of you who arestill awake, YES, THIS IS VERY WEIRD.

4.) If you wanted to do an experiment in which you observed thisphenomenon, you would have to come up with a device that measures the massof an object that is in motion, relative to you (actually, if the mass was charged,observing how the mass acted as it passed through a known magnetic fieldwould do the trick). Let's assume you have done that. You have this cleverdevice that measures a body's resistance to changing its motion--it's inertialmass--as it passes you by. With that device, we are almost ready to do aninteresting experiment.

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5.) First, though, there is one more minor bit of information you need toknow. It has to do with the idea of energy.

a.) In a very loose, hand waving, conceptual way, a body is said tohave energy if it has the ability to affect (i.e., do work on) other objects.

i.) A speeding bullet, for instance, can affect a target when ithits. A speeding bullet, therefore, is said to have energy.

b.) If the energy exists as a consequence of the object's motion, it issaid to have kinetic energy.

i.) Kinetic energy is sometimes called the energy of motion.

ii.) Kinetic energy is numerically equal to (1/2)mv2, where m isthe object's inertial mass and v is its velocity. (This expressionassumes that the object is not going close to the speed of light.)

c.) So now we are ready for the big experiment.

6.) You are sitting still out in space. You have your mass detectiondevice with you. You also have sitting next to you an object whose inertial restmass is exactly 1.0 kilogram (the bar over the zero means the zeros repeatforever, and the term rest mass alludes to the inertial mass of the object as itsits still next to you in your frame of reference).

a.) A friend takes the object and applies a constant force to it. Indoing so, your friend does work on the object. The object accelerates to100 miles per second.

i.) Observation #1: I should point out how absurdly fast this is.The Space Shuttle in space only goes 17 miles per second, so we aren'ttalking about normal speeds, here. Still, let's assume you could dothis.

ii.) Observation #2: Another way to frame this situation is tosay that by doing work on the object (i.e., your friend was pushing it),she put energy into the system. That energy will show itself as an

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increase in the body's kinetic energy--its energy of motion--as the bodyspeeds up.

b.) You are still sitting still, so as the object comes whistling by andyou point your inertial mass measuring device at it, what will your devicemeasure?

c.) Common sense suggests that the mass will still be 1.0kilograms. Unfortunately, that isn't what you would read. In fact, as thebody passed by at 100 miles per second, the mass measuring device wouldmeasure the body's mass to be 1.000000145 kgs. In other words, the masswould have increased.

i.) Observation #1: Think about what this means. At 100 milesper second, there is, evidently, inherent within the structure moreresistance to changing its motion--more inertia, more mass if you will--than there was when the body is sitting still.

ii.) THIS IS VERY, VERY FREAKY.

d.) Put enough energy into the system to get the speed up to 10,000miles per second and the mass will measure 1.00145 kg.

e.) Put enough energy into the system to get the speed up to 170,000miles per second and the mass will measure 2.46 kg.

f.) Put enough energy into the system to get the speed up to 185,999.9999miles per second and the mass will measure 30,496 kg.

7.) Conclusion: Evidently, if you do work on and put energy into a system(i.e., our object) in this way, it isn't just the energy of motion--the kinetic energy--that increases. The mass increases, also. And its right about this point in thelecture that the classroom rebel gets a wild hair, stands up on the desk, andshouts at the top of his or her lungs, "WHAT THE HELL ARE YOU TALKINGABOUT? THIS MAKES NO SENSE AT ALL!!!"

8.) Before we respond to the disruptive hooligan on the desk, though,there is just one more question I'd like to ask. "Looking at the data trend, whatdo you suppose the top speed of the object might be?"

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a.) If asked in class, someone usually notices that as the object'svelocity got closer and closer to the speed of light (i.e., c = 186,000 milesper second), the mass edges toward infinity.

b.) In fact, this is the reason Einstein concluded that no massiveobject can ever be made to go the speed of light. To reach that speed, theobject would end up infinitely massive and you would have had to haveput an infinite amount of energy into the system.

9.) So what are our conclusions?

a.) At low velocities, when energy is put into a system as outlinedabove, the energy shows itself in the system by increasing the object'skinetic energy--it's energy of motion. Very little of the energy shows itselfas an increase in the body's resistance to changing its motion (i.e., itsmass).

i.) As you only experience low velocity phenomenon in the "realworld," this characteristic of matter will never be evident to you ineveryday life . . . unless, of course, you happen to be a nuclearphysicist.

b.) At high velocities, when energy is put into the system as outlinedabove, the energy shows itself in the system by increasing the object'skinetic energy very little. Most of the energy shows itself as an increase inthe body's resistance to changing its motion (i.e., its mass).

10.) How do we know all of this?

a.) Our best particle accelerators--Fermilab, for instance, outside ofChicago--can accelerate protons up to .9999995 times the speed of light.It can do this because the mass of a proton is only 1.67x10-27 kilograms,which is to say small, and because we have access to enormous amountsof energy. In fact, to do one run, a typical accelerator uses somewherearound the amount of energy that the city of San Francisco burns in aday.

Note: Go to http://www.fnal.gov/ for information about Fermilab.

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b.) And for you Stanford fans, Stanford has a smaller linearaccelerator that runs an entire mile long. They use electric and magneticfields to accelerate subatomic particles like protons and electrons tonearly the speed of light, then deflect the particles off-track. At the endof the run, they crash the particles either into an unsuspecting piece of,say, gold foil, or into other particles.

c.) This is how we first "split the atom." High speed, high energyparticles were crashed into gold foil smashing apart the gold's atomicstructure as they collide, spewing nuclear bits and pieces of atoms outthe other side into a Bubble Chamber.

i.) Bubble chambers were used as late as 1975. In them, asaturated gas would produce a trail of bubbles as subatomicparticles spewed into it. (I'm telling you about this because you willbe seeing a very small version of one in class)

ii.) As magnetic fields make negative charges circling in onedirection and positive charges circling in the opposite direction,magnetic fields could be used on the tracks produced in the chamber.From these, we were able to deduce things about the "stuff" thatcame out of the atom's inner structure when split.

iii.) At this stage of the game, scientists need to ignore thebillions of common interactions that occur in today's particleaccelerators in favor of the rare interaction. As such, refresh timehas become important. What are now used are spark chambers,scintillators, and CCD's (coupled charge detectors). In fact, some ofthese particle detectors are the size of the nine story MillikanLibrary on Caltech's campus.

d.) The important point is that when particles accelerated in thisway collide with whatever it is they have been aimed at, they hit withconsiderably more umph than they should have (yes, umph is a scientificterm--you need to know its definition for the test . . . not). Why does thishappen? Because the inertial mass of the speeding particles is soenormous in comparison to their rest mass, their impact carries a wallopthat is considerably larger than would have been the case if therelativistic phenomenon hadn't been in evidence.

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11.) So now its time to quiet the heckler and find out what's going on. Infact, you've had the key to this mass/energy problem ever since you were weesmall.,,

a.) What is the first (and probably only) equation you ever learnedhaving to do with Einstein and his Theory of Relativity?

That's right, it's E=mc2.

b.) What Einstein was really saying with E = mc2 was that massand energy are two forms of the same thing.

v.) Put a little differently, Einstein maintained that at its mostfundamental level, material is nothing more than "congealed" energy. Infact, he even called mass frozen energy.

12.) Nature exhibits this mass/energy characteristic in some prettyspectacular ways.

a.) Take a single deuterium atom (hydrogen isotope with one protonand one neutron) and put it on a scale (OK, we are being silly here--playalong). Assume we find the mass of the atom to be x. Do the same thingwith a second deuterium atom. Its mass will also read as x.

b.) Now, take those two atoms and forced them together to make asingle entity. This will take close to a billion atmospheres of pressureand temperatures up around 10,000,000 degrees Centigrade, but do itanyway.

c.) When you are done fusing the two deuterium atoms into onesingle entity, you will end up with a helium atom. Now put that Heliumatom on the scale.

i.) What you will find is that the mass of this new atom will notequal the sum of the two deuterium atoms that made it up (i.e., themass will not equal 2x).

ii.) What you will find is that the helium atom's mass will beshy by 0.7% of that sum.

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d.) So where did the missing mass go? It was turned into pureenergy all ′a E = mc2.

13.) So when we fuse small atoms to make bigger atoms, we get energygiven off. This is the heart of the hydrogen bomb--small deuterium atomsmaking larger helium atoms.

14.) Do we get a lot of energy or a little energy from the fusion process?

a.) Take one gram of hydrogen and fuse it into as much Helium asyou can.

i.) How much Helium will that be? It will be .993 grams worth.

ii.) The missing .007 grams will have been converted to pureenergy.

b.) How much energy is released when .007 grams of matter isconverted into pure energy?

i.) The conversion of the .007 grams of matter into pure energy,according to E = mc2, will produce enough energy to send 350, four-thousand pound Cadillacs 100 miles into the atmosphere. That'show much energy is released with the fusion of one gram of hydrogen.

c.) The Sun, our star, converts six hundred and fifty-seven milliontons of hydrogen (that's 657,000,000 TONS) into six hundred and fifty-THREE million tons of helium every second.

i.) Put a little differently, our star converts four million tons ofmatter into pure energy every second.

ii.) This is part of the reason our star does such a nice job ofheating the little bit of nothing we call our planet, even though we are93,000,000 miles away from the sun.

Note: One out of every 10,000 hydrogen atoms is deuterium left overfrom the Big Bang. What's more, the average time it takes two deuteriumatoms to combine at the core of the sun is around 1010 years. There aredeuterium atoms fusing right now in the sun (remember that 657,000,000 tons

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of deuterium that fuses to make 653,000,000 tons of helium with 4,000,000tons of stuff being turned into pure energy every second), but they are doing thisway before coming to the average time. In fact, assuming the sun poops outwhen it gets done with its deuterium fusion, this means the sun's age will bearound 1010 years when it dies.

15.) So what is energy?

a.) Feynman, a Nobel Laureate in physics from Caltech, was askedthat question several years ago at a California Association of IndependentSchool meeting by mo ′i .

b.) Cool dude that he was, his answer was simple and to the point.He said, "I have no idea." And in so answering, he spoke for physicistsaround the world.

c.) We know when a body has energy. We know how to produceenergy. We know how to store energy. We know how to use energy. Weknow how to transfer energy long distances. What we don't know isexactly what energy is.

d.) Having made that unsettling remark, it should be pointed outthat there is a very useful approach used to analyze certain kinds ofsituations that incorporate the idea of energy into a model you are goingto come to know and love. But that will come a little later.

16.) For now, it is sufficient to simply marvel at how remarkable andsurprising your physical universe is.

F.) So What's This Class Going to Do For You?

1.) The goal of this class is to prompt you to think about the question,"What do I know about my universe?"

2.) In all probability, you will find that the answer to that question is,"Not very much . . . " That shortfall will hopefully be remedied as the yearproceeds and we delve more and more into the world of physics.

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G.) The World of Physics--Background:

1.) Physics is the study of the dynamics of the physical world.

2.) There are a number of ways we can go with this study. We could, forinstance, take a physics for poets approach and talk qualitatively about what weknow of the physical world. At least for test preparation, this approach is fairlyeasy because it primarily requires memory work.

a.) Example: The atom is 10-10 meters across.

b.) The speed of light is c = 3x108 m/s.

3.) An alternative is to take a conceptual approach. Moving in thatdirection would see us talking qualitatively about the underlying "laws" uponwhich the mathematical models are based. This is more challenging than theplain physics for poets approach because it means the student has tounderstand the conceptual side of the theory, then use that understanding toqualitatively predict what would happen in unknown situations.

a.) Example: Consider the following physics concept: "If you want tochange the magnitude (i.e., size) of the velocity of an object moving in aparticular direction, you must exert a force in that direction."

b.) The above statement is a conceptual "fact," often referred to as a"law." So let's assume you start with that law. What might you beasked to do with it?

c.) Consider the following: You are walking horizontally (i.e., not onan incline) with a constant velocity. As you walk, you hold a ball in yourhand next to your body. You release the ball and it falls. When the ballhits the ground, does it hit behind you, next to you, or ahead of you?

d.) Completely ignoring any kind of preconceived notions you mighthave about the situation, what does our law suggest the answer should be?

i.) Note first that if your velocity magnitude in the horizontaldoesn't change (i.e., you just keep walking), and if the ball's velocitymagnitude in the horizontal doesn't change (i.e., it doesn't slow down

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or speed up in its horizontal motion), you and the ball should still beside by side when the ball hits the ground.

ii.) Does the ball's velocity magnitude change in the horizontal?According to our law, "If you want to change the magnitude of thevelocity of an object moving in a particular direction, you must exerta force in that direction."

iii.) Is there a force on the ball? Sure, there is gravity. But gravityis a force in the vertical--gravity is what makes the ball fall. In thehorizontal, there are no forces acting, assuming you are ignoringfriction and assuming there isn't a big wind blowing.

iv.) In short, the ball's velocity magnitude in the horizontal shouldnot change, so it should land right next to you as you walk.

Note: A friend pointed out that this is the reason low flying bombersbank after dropping their payloads. If they didn't, they would be right on top ofthe explosion when the bombs hit the ground.

e.) This is typical of a conceptually based analysis of a situation.

f.) The point here is that doing "conceptual" problems requires thestudent to take a "law," then apply it to an everyday situation todetermine what should happen in that situation. This requires a certainamount of thinking on your feet, which is to say that it requires somethingthat most people aren't overly crazy about doing (myself included).

This is one reason why conceptual questions are often deemed moredifficult to do than are straight math problems in physics classes.

g.) Minor note about the question, itself: A lot of people incorrectlysay that the ball would hit behind the dropper. Why? Probably becauseexperience suggests that may be the case. How so?

i.) You are speeding down the freeway and you drop the wrapperfrom your In and Out burger out of the car window (bad student!).Where does the wrapper land? It doesn't land next to your car, itlands way behind your car. You can see how someone mightmistakenly extrapolate from this situation to the "falling ball"situation even though the two situations are not the same.

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ii.) Still, does the outcome of the "falling wrapper" situationmake sense in light of the physics force concept laid out above? Yes!For the wrapper situation, our law completely supports the outcome.

iii.) How so? The concept says, "If you want to change themagnitude of the velocity of an object moving in a particulardirection, you must exert a force in that direction.."

iv.) When you drop the wrapper out the window, the relativemotion of the air through which the car travels produces whatappears to be wind. In the vertical, the wrapper begins to pick upvelocity due to gravity (i.e., it's falling), but in the horizontal (i.e., inthe direction associated with the car's motion) that wind force beginsto slow the wrapper's motion. As such, you would not expect thewrapper to land next to you in the car. You would expect it to landtoward the rear of the car . . . which is exactly what it does.

3.) A third approach is to focus on the mathematics that are used tomodel the concepts that underlie physics. Ignoring the first option, andassuming there is no conceptual trickery going on, this is often the easiest thingto do in physics. Learn the equations, learn how to use them, then use them.

a.) Example: According to Newton's Second Law, the relationshipbetween the force F on an object and the acceleration of the object is F =ma, where m is the object's mass.

b.) Given Newton's Second Law, what is the acceleration of a 2 kg massunder the influence of a 12 newtons force (where a newton is a kg.m/s2)?

c.) Solution:

ΣF:

F1 = ma

⇒ a = F1

m

⇒ =12 kg • m / s2

2 kg

⇒ = 6 m / s2 .

Ch. 1--A Little Bit of Magic

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d.) Easy, eh?

4.) We will start out in the first pew, then go traipsing into the otherareas. Buckle up. This is going to be fun.

H.) A Big Note About Tests and Studying:

You will find at the end of this chapter two lists of content-ladenquestions.

The first list reflects the information you should have gleaned fromlistening in class and from reading this manual.

The second list is last year's summary of information to know for Test 1.It reflects material covered in lecture and the manual, and the informationtaken from the assigned chapters in Hewitt's Conceptual Physics.

In some instances, the lists will overlap one another. In some chapters inthis manual, the two lists will have been combined into one. None of thesevariations should be a problem. Whether presented in single or multiple lists,the chapter-end questions are there solely to give you, the testee, a feel for whatI, the tester, feel you should understand from the material presented within thesection.

For a given section, it is up to you to read (but not answer) all of thechapter-end questions as homework right after taking the previous test. In thatway you will know what to look for in the "upcoming" material. Studying in thisclass is going to very much resemble doing research. You need to start thatprocess at the immediate beginning of every section.

As your tests will be oriented more on research based questions thananything else (the answers are all found in your notes, this manual, or Hewitt),you will not find "solutions" to these questions at the end of the manual.

Sorry about that (life's tough . . . and then you die).

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QUESTIONS

1.01) What is the "elementary building block of matter?" Is it the smallestentity in existence? Explain.

1.02) What is an angstrom? Also, what is the diameter of an atom?

1.03) What are atoms made up of (OK, this is really dumb--think of it as mercypoints if I put it on the test)?

1.04) What determines the kind of atom you are looking at (i.e., whether it ishydrogen or lithium or what)?

1.05) How fast do electrons travel inside the nucleus?

1.06) If an atom was expanded up so that it's volume was thirty-five trillioncubit feet, what part of its whole would be made up of solid matter?

1.07) If you had to put a word to the reality of the physical world, what would itbe?

1.08) What is time?

1.09) Assuming you are observing from a frame of reference that is locatedsomewhere "out there," what will the watch of a hiker do as the hiker descendfrom the top of a mountain to the bottom? (the effect might be small--be anallytechnical, here)?

1.10) Who is Ruth Buzzie?

1.11) According to Einstein's view of the world, how is time related to thespace?

1.12) What is inertia? What is inertial mass (be complete)? How, technically,is inertial mass measured?

1.13) What is gravitational mass, and how is it measured?

Ch. 1--A Little Bit of Magic

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1.14) Do bodies of different mass has different gravitational forces on them,and if so, why do they accelerate at the same rate if allowed to freefall (ignoringfrictional effects)?

1.15) What is the MKS system of units?

1.16) What is the acceleration of gravity in the MKS system of units?

1.17) If a body has energy, what does that mean?

1.18) What do you have to do to change a body's energy content?

1.19) What is kinetic energy? What is work? What is the difference betweendoing positive work and negative work?

1.20) At very low velocities (like the velocities you and I experience in our dailylives), what happens to a body when work is done to it?

1.21) At very high velocities (i.e., close to the speed of light), what happens to abody when work is done to it?

1.22) If you accelerated an object to 170,000 miles per second, by how muchwould it's mass have grown?

1.23) Why did Einstein claim that you can never motivate an object to go thespeed of light?

1.24)What relationship did Einstein come up with that explained all of thisweirdness concerning energy? What do the symbols in the relationship mean?

1.25) What kinds of temperature and pressure are required to effect fusion ofhydrogen atoms?

1.26) When hydrogen fuses, what percent is converted to pure energy?

1.27) How much energy is released when 1 gram of hydrogen is fused intohelium?

1.28) To what speeds can the Fermilab accelerator accelerate protons?

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1.29) How much mass is converted into pure energy in the sun every second?

1.30) So what is energy?

1.31) If you had to use one word to describe the physics universe, what wordwould that be?

PHYSICS EXAM SUMMARY2004-2005

The following was given out last year as a test summary. Some of thequestions are duplicates of the questions outlined above. Some of thequestions concern material that will not be discussed in class, but that residesin the assigned chapter(s) in Hewitt.

01.) How many distinct elements (types of atoms) are there.02.) Of the elements alluded to in #1, how many exist in a stable sense in nature?03.) What is the simplest element?04.) What does atomic number measure?05.) What makes one type of atom different from another type of atom. Thatis, what is the defining characteristic that allows us to differentiate?06.) What process is the primary energy source in the core of the sun?07.) Know the difference between fusion and fission.08.) Approximately how many atoms are there in a thimble full of water?:09.) What makes neutron stars so unusual?10.) What four elements comprise living things?11.) What is the diameter of an atom?12.) Have some idea as to the relative size of atoms. Have we ever seen an atom. Ifso, how so?13.) What American is known for having experimented with static electric charge?14.) What are alpha particle?15.) Spatially, how are atoms built? That is, are they densely packed and, if so, howdensely packed . . . or are they mainly space?16.) Why are normal atoms electrically neutral?17.) Atoms that are not electrically neutral--what are they called?18.) Relative to an electron, how massive are protons?

Ch. 1--A Little Bit of Magic

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19.) What is a charged atom called?20.) An atom with an unusual number of neutrons, relative to the norm, is calledwhat?21.) What is the name for an atom with one proton and two neutrons?22.) What is the specific difference between the elements that are named deuterium,hydrogen, and tritium?23.) What is the atomic mass unit? What is its abbreviation?__________________________________________24.) How would you describe a molecule? That is, if you had two molecules, whatwould be the uniting characteristic?25.) What is sublimation? Freezing? Boiling?26.) Who came up with E = mc2? What do the symbols mean in that equation?27.) What is "pair production." When it happens, what do you end up with?28.) What is 90% of the mass of the universe made up of?29.) What is an element?30.) The first six elements are hydrogen, helium, lithium, beryllium, boron, andcarbon. What would you end up with if a neutron in, say, the beryllium, converteditself to an electron and a proton,?31.) How fast do electrons move in their orbit around the nucleus of a typical atom?32.) In reality, does time run at the same rate everywhere?33.) What is a cesium clock?34.) Drop an eraser and an anvil. Assuming both had the same contour (i.e., the sameair friction characteristics), both should reach the ground even though the anvil wasfeeling a larger force (it is more massive). How can this be?35.) What is "a resistance to changing one's motion" called?36.) According to Einstein, mass is simply another form of what?37.) By approximately how much would an object's mass increase if you couldaccelerate it to around 170,000 miles per second?38.) The sun's core converts how much mass into pure energy every second?39.) What is the speed of light?40.) What is Newton's Second Law?

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