Phys104 - How Things Work
University of Maryland, College Park
Fall 2010, Professor: Ted Jacobson

Notes, Demos & Supplements

Please refer to notes from 2008 and 2009 for many details about the material.
Here I will try to only indicate roughly what topics were covered in class,
and I will elaborate topics not adequately covered in my previous notes or
in the textbook. (Actually, I will often get carried away and write much more...)

Friday 12/03


- discussed the optical system of a CD/DVD reader

- wavelength and minimal focusing/beam waist

- discussed the table showing CD/DVD/Blu-ray disc wavelengths and distance parameters---
  see table in notes for 12/01.

-  Showed how one can "see" the spacing distance between tracks using diffraction. The smaller the
spacing between the tracks, the larger the spacing between the diffraction maxima. I first shined the
green laser through the clear plastic diffraction grating, then reflected it off of a CD, a DVD, a blu-ray
disc, and a vinyl LP. You could see diffraction maxima in all cases except the blu-ray. I explained what
determines the angle these maxima occur at: the path length difference between adjacent tracks must be
a whole number of wavelengths of the light. In the case of blu-ray, the track separation is only 320 nm,
and the laser wavelength was 532 nm, so the path length difference is always less than a whole wavelength,
even at a 90 degree angle.

- optical fibers: covered as in the textbook. A few more things I mentioned:

- in a simgle mode fiber, the indices of refraction of the core and cladding are quite close: n_core=1.48,

- billions of bits per second are how far apart in space are the pulses of light at any given instant?
Well, if it were one billion bits per second, that would be one bit every nanosecond. Light travels 30 cm in
a nanosecond in vacuum, and 20 cm in a nanosecond in a material with index of refraction 1.5 (close to that
of the fiber). So the pulses are closer than 20 cm apart.

Wenesday 12/01


- discussed further how helium-neon laser works: accelerated electrons collide with helium atoms,
exciting them. The helium collides with neon and transfers the excitation to neon, placing it in
it's upper level state. 

- LED's (light emitting diodes)

- run "backward" these are "photodiodes", which convert light to electrical current or voltage.

- laser diodes

- digital storage of information, music, etc.

- how a vinyl LP encodes music. The question came up whether the groove variations are vertical or
horizontal. Turns out they are both: the two channels of the stereo are encoded in opposite 45 degree
tilt variations. See:

- structure of CD or DVD

- size of one pit or spot on the disc is set by how tightly the laser light can be focused,
which is no smaller than the wavelength of the light.

- writable and re-writable discs: on a disc that you "burn" the disc is coated with
a dye that changes from a crystalline, transparent material to a cloudy one when exposed to a
laser light of a certain kind. On rewritable discs the dye can be restored to its transparent state
by raising the temperature and then cooling it.

- disc formats, laser wavelengths, and capacities:

capacity per layer
wavelength in vacuum
wavelength in plastic
length of pits
between tracks
700 MB
780 nm (IR)
503 nm
830 nm
1600 nm
4.7 GB
650 nm (red)
420 nm
400 nm
740 nm
25 GB
405 nm (violet)
261 nm
140 nm
320 nm

Monday 11/29


- fluorescent bulb: showed that the Tesla coil will also light up a compact fluorescent bulb.
Discussed again how fluorescent bulbs work, in some more detail.

- "black light": this is the same as a fluorescent bulb, but with a coating that fluoresces in the near UV
around 360-380 nm. (The UV photons emitted by the mercury in the tube have wavelength 254 nm.)

- "plasma displays": each pixel is a little fluoresent lamp.

- laser:  acronym for "Light Amplification by Stimulated Emission of Radiation"

- characteristics of laser light: the photons have nearly the same (i) wavelength, (ii) direction, (iii) phase
(i.e. the oscillate in step with each other). These properties alow light to travel in straight lines and be narrowly

- how lasers work explained more or less as in the textbook.

Wednesday 11/24

Independent study:

a. Read "Reperesenting Sound: Analog & Digital" on pp. 405-406.
b. Read "Soap bubbles" on pp. 451-452.
c. Read the introduction to Section 15.2 and "Digital Recording" on pp. 489-490.

Try to answer all three
"Check your understanding" in these sections, and then look up the answers.

Then answer the following three questions (this does not need to be turned in; I will post the answers after the break):

1. Write the answer to life the universe and everything as a binary number.
[Use Google to find the answer to life the universe and everything. Binary numbers explained on p. 406 and in class notes.]

Answer: in base 10: 42 = 1x32 + 1x8 + 1x2; in binary: 101010.

2. Explain why you see colors reflecting from a CD or DVD.

Answer: This is explained briefly on p. 489. The spiral track of pits forms parallel lines. Seems to me it's the
reflective parallel lines between the lines of pits that matters. Light reflected from these lines into a given angle
interferes destructively (see p. 451) unless the path length difference for adjacent lines is an integer
multiple of the wavelength of the light. Hence at a given reflection angle, a given color of light is strong and the
rest are suppressed. The distance between the parallel lines is not much longer than a wavelength of visible light,
so this
angle is fairly large for visible colors.

3. The encoded surface area of  a CD is about 86 square centimeters. Given that the shortest pit is
0.83 microns long, and that the sideways spacing is 1.6 microns (see Fig. 15.2.2), the area needed per bit
is roughly (0.83)(1.6) = 1.33 square microns.
(a) Calculate how many bits of information can fit on the CD. (Be careful dividing square centimeters by square  microns!)
(b) Using the fact that there are 8 bits in a byte, calculate how many bytes can fit.
[Your answer should come out to about 800 million, i.e. 800 MB of data.]

Answer: 1 cm = 104 microns, so 1 square centimeter = (1 cm)2 = (104 microns)2 = 108 microns2 = 108 square microns.
Dividing the total area of 86 square centimeters by the area per bit, 1.33 square microns, yields 
(86 x 108 sq. microns)/(1.33 sq. microns)=  64.66 x 108 bits = 64.66/8 x 108 bytes = 808 MB.

Monday 11/22


- A bit more about RealD 3D glasses: As explained in last Friday's notes the lenses have two layers,
a linear polarizer in back and a layer that converts circular to linear polarization in front. You can demonstrate
the fact that the front and back are different by holding up the glasses in front of an LCD display (which emits
linearly polarized light). If the back of the glasses faces the display, then by rotating the lens you can block
out all the light since the polarizers are crossed. If the front of the glasses faces the display then you can rotate
all you want but you'll never block all the light. (When held at a certain angle the light is bluish and when
held perpendicular to that it is yellowish. I don't yet know why this is... I asked the company and they
told me it is considered proprietary information.)

- Color perception: as described on pp. 454-455. Besides that, I noted the following:

- the names of the cone cells, "red", "geen" and "blue", only indicate the location of their peak sensitivity;
they are sensitive to many colors of the spectrum. The "red" cone even has some sensitivity to blue and

- we are much less sensitive to violet than to blue light.

-  in a sense, we are all color blind: there is an infinite variety of different mixtures of colors of the spectrum,
and our eyes filter all that into some combination of the three cone cell responses. In fact, the overall response
level is just "brightness", so there are actually two color variations we sense. You can think of these as the
proportion of "red" vs. total cone response, and the proportion of  "green" vs. total cone response. The
proportion of "blue" is whatever is left so is not an independent feature. This two-dimensional color space
is illustrated here:
color gamut
(Diagram taken from here:
The spectral colors are around the boundary of this shape, labeled by their wavelength in nanometers. The line
of purples along the bottom consists of colors that are not in the spectrum. The different shapes and triangles inside
show what region can be faithfully recreated with a given display type. Here's a short article about a 5 color per pixel
display that Sharp is developing, to improve color reproduction:

- Atomic Spectra - started with the great demo:
Students viewed these light sources though a hand held plastic sheet diffraction grating.
the mercury and cadmium lamps emit in a few discrete colors/frequencies. These are characteristic of
the electronic structure of the atom. We also saw how the spectra of fluorescent lights have a few distinct frequencies.
These come from different components of the coating of the tubes, which emit visible light when bombarded by
ultraviolet photons from mecury vapor in the tube.

- Explained this more or less as in the book. I emphasized how surprising it is that an atom has a "ground state"
in the first place: why don't the electrons radiate electromagnetic waves and spiral into the nucleus? If it weren't
for quantum mechanics, they would do so in a nanosecond. But the Heisenberg uncertainty principle keeps them
from doing that:
The uncertainty in velocity is inversely proportional to the uncertainty in position.  If the electrons
became too localized near the nucleus, their velocity and hence their kinetic energy would become very uncertain,
in particular it could be very large. So if their energy is strictly limited, they cannot get too close. In the ground state
of the atom, they are in their lowest energy configuration, as close as they can get. If an electron absorbs some energy
by colliding with another electron, or absorbing some light, for example, then it has extra energy, and since it is
accelerating can radiate, shaking off the extra energy and settling back into its lowest energy state in the atom. 

Each kind of atom has its own characteristic patterns of electron vibrations, with corresponding energies.
When an electron changes from one pattern to another of lower energy it gives off the energy difference in the form of a
"packet" of light, called a photon. The energy of the photon is equal to the frequency of the photon times Planck's constant,
E = h f, with h = 6.6 x 10^-34 J‧s. Hence, each atom has its own characteristic frequencies of light it emits. 

-So a UV photon with frequency 10^15 Hz has energy 6.6 x 10^-19 J. So 10^19 of these per second
would only make a power of 6.6 watts!

- Fluorescent lights explained. (See textbook also for more detail than I had time for.)
Explained phosphorescence using an energy level diagram:

E3 --------

E2 --------

E1 --------

A photon of energy E3 - E1 can excite an atom from the E1 level to the E3 level. Then the atom can "decay" in two steps,
from E3 to E2 and then from E2 to E1. Each of these steps has less energy than the original excitation, hence lower frequency.
It can be that E3 - E1 is an ultraviolet energy, but E3 - E2 and perhaps E2 - E1 correspond to visible photon energies.

- I showed a fluorescent bulb lit up by the electric field induced around the Tesla coil. The field accelerates stray
charges in the bulb, which either strike mercury atoms, exciting them and causing them to emit a UV photon, which
then hits the phosphor coating and makes it fluoresce.

Friday 11/19


- sunlight: emitted by the surface of the sun, which is hot thanks to the nuclear fire within.
I explained the various features of the following graph which shows the energy flux of sunlight, in units of watts
per square meter per nanometer of wavelength interval, vs. wavelength on the horizontal axis.
solar spectrum

- why the sky is blue, sunsets red, and clouds white. This is all explained in the book.
An interesting point: as mentioned in the book,  atoms and molecules are too small to
be efficient antennas for light, and they are better antennas for shorter wavelengths.
That's why they scatter blue more readily than red.  But how big is the wavelength
of visible light compared to an atom? It is several thousand times longer!

- Someone asked why the sky is not violet, since that would be scattered even more than
blue. I conjectured that it is because our eyes are less sensitive to violet, and I found
a statement online to the same effect. I was also asked why we don't see green
in the sunset, and answered that we do occasionally: here's a nice picture.

- polarizing filters: I started with polarizing sunglasses. They block horizontal
polarization and pass vertical. This is useful because light that reflects off horizontal
surfaces tends to be horizontaly polarized, as explained in the book. I depmostrated this
by reflecting a laser beam off a horizontal glass plate, and placing a polarizing filter
in the path of the reflected beam. When the filter was oriented to block horizontal
polarization, the beam was dimmer. At a certain angle, the reflected beam is 100% horizontally

A polarizing filter is made of a stretched material that has long molecules oriented so that
charge can flow easily in one direction, and not easily in the perpendicular direction. Light
that is polarized in the direction charge can flow is either absorbed or reflected more
than the perpendicular light. Placing two of these filters perpendicular to each other
blocks all light, because what gets through the first doesn't get through the second.
that waxed paper radomizes the polarization, so when placed between crossed polarizers,
allows light to get through. A beautiful demo: M8-01 POLAROIDS AND KARO SYRUP
showed that sugar syrup rotates the polarization of light though an angle that depends on
the frequency. So when a bottle of the stuff is placed between two polarizers, different amounts
of different colors get through, resulting in a mix of colors that is quite lovely. The mix you get
changes when you change the relative angle of the two polarizers. You could demonstrate this
at home using a pair of polarizing sunglasses and a bottle of karo syrup. Don't forget to
rotate oneof the sunglasses to change the color mix!

- Liquid Crystal Display (LCD): Showed first that the display emits polarized light.
(It's polarized at 45 degrees.) Explained how it works: The display is made of a bunch of "pixels",
each of which is made of three different colored light pixels (if it's a colored display). Each colored
pixel has a sandwich of two crossed polarizers, with the light behind (backlit screen). Light that makes
it through the first polarizer would be blocked by the second, except that in the sandwich there is a
"liquid crystal" (composed of long chain molecules that like to line up parallel to each other) which
rotates the polarization by 90 degrees, so when the light reaches the second polarizer, it can pass.
To make a patch of the display appear black, a voltage is applied across the gap between the two polarizers,
which reorients the liquid crystal molecules in that patch so that they no longer rotate the polarization.
In a wristwatch type display, the illumination comes from ambient light, and a mirror is placed
behind the second polarizer. Otherwise the idea is the same.
Here is a schematic diagram, with explanation below:
In the set-up shown here, the two polarizers P1 and P2 are crossed. The liquid crystal medium LC is aligned
with etchings on the plates E2 and E1, which are oriented perpendicularly to each other, making the LC twist
as shown in the panel on the left. When light passes through, its polarization is also twisted, so it can pass the
second polarizer. When the voltage V is turned on, as in the panel on the right, it creates an electric field that
orients the LC molecules along the electric field, because they have electric dipoles (separated + and - charge).
In this configuration the polarization of incoming light is no longer rotated, so the light is blocked by the
second polarizer.

circular polarization: to get an idea what it is, see this model:
In a circularly polarized electromagnetic wave, the electric field vector spins around in a circle. It can go clockwise
or counterclockwise, also called right circular and left circular. Circular polarization can be thought of as a
combination of horizontal and vertical linear polarization, offset from each other by one quarter of a wave cycle.

3D movies: The projector projects a different image for the right and left eye, the images differing by the angle
of view due to the separation of the eyes. Old technology used two different colored images and two colored
lenses, on for each eye, so select the image. Linear polarizing filters were later used. This required the two images
to be projected with opposite polarizations, and it required that the screen surface preserve polarization upon
reflection of the light. This worked much better since all colors were treated equally for both eyes, but is
not ideal because when the head tilts the eyes see some of the wrong image, and also the polarization of
wider angle parts of the screen is (I think) thrown off. New "real D 3D" technology, like that used in the
movie Avatar, uses circular polarization. One image is projected in right circular polarization, the other in
left circular, and the glasses you wear pass one of these through the right eyepiece and the other through the
left eyepiece. The eyepieces are made of two layers, the front one converts circular to linear polarization, and
the back one is a conventional linear polarizing filter that passes vertical polarization and absorbs horizontal.
The right eyepiece converts right circular to vertical and left circular to horizontal, so only what starts as
right circular gets through. The left eyepiece does the opposite.

Wednesday 11/17

exam 2

Monday 11/15

for exam 2

Friday 11/12


- Visible spectrum: note that blue light has higher frequency and shorter wavelength than red

- When electromagnetic radiation travels through a "transparent" material, it interacts with the material but is not
absorbed or reflected. The interaction makes it slow down. The slow-down factor is called the index of refraction,
which generally depends on the frequency of the radiation.

- In normal air the index of refraction is 1.0003 for visible light, in water 1.3, in glass 1.5 (depends on the glass),
in diamond a whopping 2.4. So for example in glass the speed of light is (3 x 10^8 m/s)/1.5 = 2 x 10^8 m/s.
Light travels only 2/3 as fast in water as it does in vacuum.

- Why does light travel slower in a medium? It's because the electric field polarizes the charge in the material.
The wave continues to oscillate with the same frequency, but it doesn't travel as far in one cycle, so its wavelength
is shorter. (I don't claim that this is a complete explanation.)

- refraction: bending of light at an interface between two materials. I showed this by shining a laser at an angle
through a rectangular block of lucite. See picture at this demo: L4-01 OPTICAL BOARD - RECTANGULAR SLAB
The reaon the light bends is explained in the book. Refraction can be used to focus light, which is exploited to make
lenses in eyeglasses, telescopes, microscopes, etc.

- dispersion: the index of refraction depends on frequency, since the material resonates more at a particular frequency
The effect is just a little bit for visible light, e.g. in water red travels abut 1% faster than violet. We showed this using
a glass prism that separates white light into the component colors. We also showed that there is an ultraviolet (UV)
component to the spectrum of the lamp I was using. We showed this by placing a phosphorescent sheet there, which
absorbs UV light and re-emits the energy partly as visible light.

- rainbow: This is explained briefly in the book, but that explanation misses a crucial point: the light coming out of a
spherical droplet emerges more at a particular angle than at other angles. This is called the "rainbow angle", and it
depends on the color, ranging from 40˚ to 42˚ in the visible spectrum. The reason for it is that as the illumination point
goes upward from the center of the droplet to the top, the angle of refraction reaches a maximum and then decreases again.
This is hard to explain in words here but is nicely illustrated by this applet. (It only seems to work with some browsers
so try another one if it's not working for you.) Sometimes you can see a fainter, secondary rainbow, which comes from double
reflection inside the water droplets. We also discussed that you can see a 360 degree rainbow sometimes from an airplane.
Another way I did it once was to go outside on a bright sunny summer day in a bathing suit, holding a garden hose,
with my thumb over the end of the hose so it created a spray of water droplets all around me. Looking in the direction opposite
to the sun, I could see a beautiful 360 degree rainbow at an angle of 40-42˚. Try it!

- polarizers - just started this, showed crossed polarizers and that a computer display emits polarized light.

Wednesday 11/10


- polarization of em wave: direction of the electric field vector

- model of wave, direction of magnetic field, plane wave

- most efficient length of a dipole antenna for emission or absorption is one fourth of a wavelength.

- electromagnetic waves can be "added together" without disturbing each other: at each point in space at
each time, the total electric field vector is sum of the electric field vectors of the individual waves, etc. This is
how for example space can be filled with radio transmissions of many stations, and many cell phone channels, etc.
To pick out one of them, a receiver can orient in a certain direction, but more importantly it can have a resonant
circuitry that is tuned to be sensitive to signals in a particular frequency range.

- AM (amplitude modulation) and FM (frequency modulation).
AM and FM
AM and FM both require a range of frequencies to transmit a given signal; this range is called the bandwidth.
FM is more robust since frequencies are more stable under the distortions of strength than is AM.
Also the bandwidth of FM is much greater, so it can transmit much more information about the sound.

- cell phones convert analog to digital, then transmit the binary digits (0 or 1) by alternating
between two frequencies (so this is a discrete form of FM)

- microwave ovens: generate 2.45 GHz waves with a magnetron. See picture here:

Explanation (of sorts) in the book. The question came up about the aging of magnetrons.
I found this assertion online, which makes sense:
"The maximum output of a magnetron tube drops about 1-3% a year in
average use, probably because the coating on its cathode wears out and
its permanent magnet weakens (sometimes even cracks)."

- visible light: another form of electromagnetic wave, generated by the accelerated motion of atomic electrons
(usually). Covers a tiny range of frequencies, not even an octave (factor of two) in frequency. Just below visible
frequency is near infrared. I showed with the digital camera that a remote control emits a flashing infrared light.

- Electromagnetic waves cover a huge range of frequencies, essentially an infinite range:

Monday 11/08


- This website explains much about the "Hybrid synergy drive" used in the Toyota Prius and other
   Run your cursor up to the words "Control panel" at the top and you get a list of topics.

- Showed applet explaining the concept of electromagnetic radiation from accelerated charges.
  The key idea is that the change of the electric field travels at the speed of light.
  The applet illustrates the concept that when a charge accelerates, distortions in the electric field
  lines propagate outward at the speed of light. These distortions amount to the electric part of
  electromagnetic waves. Try setting the demo button in the upper right on "inertial", with v=0.
  Then suddenly slide the slider to nonzero velocity, and watch the shift in electric field lines
  propagate outward. Notice that the kink becomes more and more perpendicular to the direction
  of propagation as it goes out. The kink represents a "sideways" electric field vector, showing
  the polarization of the wave. Next, set the button to "SHO", simple harmonic oscillator, and
  put the velocity slider on, say v = 0.7. (This is the speed in units of the speed of light, i.e. v = 0.7 c.)

- The moving charge creates a changing magnetic field which induces a changing electric field
which indeuces a changing magnetic field, etc.

- K8-45 shows radio waves from spark, and J3-23 shows that those are electromagnetic waves,
shielded by the conducting "Faraday cage".

- K8-42 shows radio waves, and how radiation intensity is greatest in the direction perpendicular
to the antenna, and how the electric field of the wave is parallel to the antenna. It also shows,
since the light bulb lights up, that these waves carry energy. This means that it takes energy to drive
the current back and forth in the antenna. I gave the example of WAMU transmitting at 17,000 W of
power. Cell phone batteries are (I think) mostly used up transmitting the waves from the phone
to the cell towers.

- EM waves have equal energy in the electric and magnetic fields, The magnetic field is perpendicular to
the electric field, with field strength B = E/c, where c = speed of light = 3 x 108 m/s = 300,000,000 m/s.
Also (wavelength)(frequency) = c. Light travels 30 cm in one nanosecond (billionth of a second, 10-9s.
It goes around the circumference of the earth about 7 times in a second, to the moon in about a second,
and from sun to earth in about 500 seconds.

- AM, FM, and cell phone (and more) frequency bands, wavelengths, and bandwidths:

AM radio
FM radio
Cell phone
Microwave oven
550-1600 kHz
87-106 MHz
870-895 MHz
2.45 GHz
450-800 THz
300 m (1 MHz)
3 m (100 MHz)
 30 cm (1 GHz)
12 cm
0.6 microns (500 THz)
10 kHz
200 kHz
30 kHz

Friday 11/05


- tesla coil demo: the outer coil is the primary and has maybe 10 turns.
The inner coil has very fine wire and many turns, I'll guess 1000 but I could be off...
The primary volatage is alternating at about 200 kilohertz. A voltage around 200,000 V
develops across the inner coil, which is plenty to break down the air and cause a
spark to jump the gap between the aluminum rods. I think the spark rises because
it's hot.

- AC power transmission: To minimize power losses due to resistance of electrical
transmission lines, one should operate them at the lowest possible current. As we saw
before, the resistive power loss is proportional to the square of the current: power loss =  I2R.
So cutting the current by a factor of 100 cuts the loss by a factor of 10,000!
But for a given power delivered to the users, if the current is lowered, the voltage
must be raised: As we saw before, the power delivered to the "load" is VI.
Transmission lines operate at a voltage of something like 500,000 V. This is
extremely high, and is only practical for transmission, but not for generating the
power in the first place, nor for using it. This is where transformers come in...
the power plant generates, say, at 5000V. This is stepped up to 500,000 V for
transmission, stepped back down to 5000V at a substation, and delivered to neighborhoods,
where it is stepped down to 240 V by numerous transformers for delivery to
individual buildings or groups of buildings. How is voltage stepped up and down?

- AC voltage transformer: By exploiting electromagnetic induction an AC voltage
can be stepped up to a higher voltage or stepped down to a lower voltage.
See diagrams and explanation in the textbook for some details. Here I'll summarize the essentials:

1. Two coils, the primary and the secondary, are wrapped around a ring shaped iron core.
2. When a current passes through the primary it creates a magnetic field, which magnetizes the core.
3. The magnetic field is contained inside the core and directed around through the other coil.
4. When the primary voltage is alternating, it creates an alternating current in the primary, which
    creates a magnetic field that is changing in time, which induces a voltage in the secondary.
    Note this ONLY happens when the magnetic field is CHANGING in time. That's why
    you need to use AC voltage to make a transformer (with DC, nothing is changing).
5. Each loop of wire in a coil feels the force from the induced electric field, so the total voltage
    in the coil is proportional to the number of turns of wire in the coil.
6. The same amount of changing magnetic field affects the primary and secondary, so the
    ratio of their voltages is just equal to the ratio of the number of turns N in their coils:
    V_s/V_p = N_s/N_p. This way, the voltage is stepped up if the number of secondary turns is
    higher than the number of primary ones, and stepped down if the secondary has fewer turns.
7. The transformer transfers power from the primary circuit to the secondary one. If the transformer
    is ideal, it doesn't lose any power to resistance, vibration, field leakage, etc. In that case the power
    in the primary circuit V_p I_p is equal to the power delivered to the secondary circuit V_s I_s.
   Therefore I_s/I_p = V_p/V_s = N_p/N_s.
8. Since the core is a conductor, the alternating magnetic field would induce eddy currents in it,
    heating it up and wasting energy. To prevent this, the core is built from a bunch of thin layers,
    separated from each other by an insulating coating.
- I demonstrated the transformer with K3-04. Wrapping the wire around different number of times
changed the voltage which was diplayed on the screen. I noted the following: there is no magnetic field
where the wire is located! However, the changing magnetic field makes an electric field that circulates
around the core. The wire feels this electric field and that's what induces the voltage across the wire.
I pointed out a remarkable thing: it doesn't matter how the wire is arranged, only the total number of
turns around the core matters. The reason can be traced to the fact that if you move the wire further
away from the core, the electric field it feels gets weaker, but a correspondingly longer length of
wire feels that field. The way it works out, the compensation is perfect, and the shape of the wire loop
is completely irrelevant. This has a beautify mathematical explanation that I can't go into here (but if
you happen to know vector calculus, suffice it to say that this can be traced to Stokes' theorem).

- Changing electric fields make magnetic fields - I mentioned that Maxwell proposed that, much like
changing magnetic fields make electric fields, changing electric fields will make magnetic fields.
His reason for thinking this was actually incorrect, but the conclusion was right. (He thought that
empty space was filled with a polarizable medium, the ether, and a changing electric field would
make a changing electric polarization of the ether, which would entail currents in the ether that would
generate magnetic fields.) This electric induction effect means that electric and magnetic fields can
create each other, with no need for charges to support them: a changing magnetic field makes a changing
electric field which makes a changing magnetic field, etc. The result is an electromagnetic wave. 

Wednesday 11/03


- eddy currents

- why you "swipe" a credit card (magnetization of strip on card generates induced current)

- older hard drive read heads worked the same way. Now they use the "giant magnetoresistance effect".
This is an effect some materials have where their electrical resistance is extremely sensitive to magnetic
fields. (It happens because the field flips some spins which ends up liberating more free charge to carry the
current.) When a magnetized region sweeps by the read head, it changes the resistance and a current
flows that can be detected.

- More example applications of electromagnetic induction:
Magnetic induction is used in cordless toothbrushes, for example, to charge up the battery without
any electric contact. The toothbrush sits on a base which has an alternating electromagnet, and the
toothbrush also has a coil in which a current is induced and used to charge the battery. Another use
is in induction stovetops (which are not very common - yet). The stovetop has electromagnetic coils
instead of burners. The coils generate an alternating magnetic field that heats the pan in two ways:
(i) it generates currents in the cooking pan or pot, which heat the pan by resistance, and more importantly
(ii) the pan is ferromagnetic, so its magnetization is rapidly alternated, which generates heat in the
pan. With a stovetop like this, no heat is transferred to the stovetop or the surrounding air. Rather the
energy goes directly into the pan in which the food is being cooked.

- SI unit for magnetic field can be read out of the Lorentz force law equation:
F_magnetic = q v B_perp. The units of B are the units of F/qv, that is, N/(C(m/s)) = N/(A-m).
This is called one tesla, 1T = 1 N/(A-m). The magnetic field in a completely magnetized
ferromagnetic material is around 1 T. The field of a very strong electromagnet used in
an MRI machine is around the same. The field between the poles of the demo magnet we looked
at is 3.5 kilogauss. One gauss = 10-4 T, so this is 0.35 T. The field of a small bar magnet might be
around 0.01 T, and the field of the earth is 30-60 microteslas = 0.3-0.6 gauss.

Monday 11/01


- force between current carrying wires - K1-02: parallel currents attract, anti-parallel currents repel.
I explained this in terms of the magnetic field circulating around the wires, and the Lorentz force.

- how a simple DC motor works, using K4-21, the "St. Louis motor". Explained the role
of the "commutator".

- This website illustrates very nicely how a "3-phase AC brushless motor" works:
Under the "Motor Type" tab at top in the middle, select "Asynchronous motor (indcution)".
Then use the green arrow buttons in the lower left to step through the demonstration.
The three electromagnets generate a magnetic field vector that rotates in a circle.

- Moving a wire in a magnetic field makes a current flow, because the Lorentz force
acts on the charges moving in the wire, and they can then flow in the wire. Demonstrated
with K2-2. This is an example of an induced current. This is an elementary generator:
mechanical work is converted into electric current. 

- Demonstrated with the motor-generator pair: K4-41, that a generator is a motor run
in reverse, and vice versa.

- Electromagnetic induction is more general: suppose instead of moving the wire
we move the magnet. Because motion is relative, all that matters
is the relative motion, so again current will flow. But now the wire is not moving, so the
cause of the current cannot be a magnetic Lorentz force, since that acts only on moving charges.
So what is it? Answer: an electric force!! Really, when a magnetic field is changing in time that
entails also having an electric field. But notice: this electric field only exists in the frame
of reference in which the magnet is moving --- so we learn that the presence or absence of an
electric field can depend on the frame of reference.

- Lenz' law: "Effects oppose causes". Or, the direction of an induced current always is such as
to oppose the change of magnetic field that produced it. This is to be expected, otherwise one might
get something for nothing, like a perpetual motion machine. I illustrated Lenz' law with K2-43, and
a spectacular demo, K2-62, the can crusher. My explanation of the can crusher is that, according to Lenz' law,
the induced current in the can is opposite to the rising current in the coil, and these opposite currents
repel. The can is therefore pinched inward, and blown out the ends.

random notes i might mention wednesday:

IBM website describing and animating mechanism of modern
hard drive read technology.

Note about attraction to a magnet: A magnetic dipole, is oriented in a magnetic
field so that it aligns with the field. This happens becasue the field pushes away
the north pole and attracts the south pole. This orientation by itself does not explain
the fact that a dipole is pulled toward a magnet. That happens because the magnetic
field is stronger closer to the magnet, so once the dipole is aligned, the pole that is
closer to the magnet is attracted more strongly than the farther pole is repelled.

Friday 10/29


- Showed dipole pattern of magnetic field of a spining charged sphere, like an electron.
Every electron is a little magnet.

- Explained more about the nature of ferromagnetic materials (see Wednesday notes),
specifically, ferromagnetic domains and domain walls. If the domain walls move
easilt the material is called "soft", and while it strongly magnetizes when placed in
an external magnetic field, it loses that magnetization as soon as it is removed from
the external field. If the domain walls "stick", then is is called "hard", and it retains
its magnetization. This is what distinguishes permanent magnets from materials
like iron (or steel, which is mainly made of iron) that are attracted to permanent magnets.

- I demonstrated how a steel rod, once attracted to a magnet, becomes magnetized itself
and then attracts another steel rod. Also, the steel rod is attracted to the magnet regardless
of its orientation. The reason is that in the presence of an external magnetic field, its
domains will tend to align with that field, whatever the direction.

- The demo J7-14 CURIE POINT OF DYSPROSIUM showed that when dysprosium
is cooled to liquid nitrogen temperature, it undergoes a phase transition and becomes
ferromagnetic as shown by its attraction to the strong magnet.  Then it absorbs heat from
the room air and eventually goes above its Curie point and loses its ferromagnetism
and drops back to the liquid nitrogen bath. It just keeps going up and down and up and down.
As one student pointed out after class, it's like a little motor. The source of energy for the
motor is the heat in the room, which can partly be converted to work because it is
deposited into the colder liquid nitrogen bath. So this is a simple heat engine!

- A loop of current makes a dipole, and a stack of loops, or a coil of wire with
many turns, multiplies the strength of the field.

- Explained how the electromagnetic bell works: when the current flows in the coil of
wire it makes an electromagnet turn on, which launches the bell hammer toward the bell.
But when the hammer is pulled away it breaks the circuit, turning off the electromagnet,
and the hammer snaps back, makes contact, reconnects the curcuit, and is launched again toward
the bell, etc. 

- Demo of low power high force electromagnet: The magnetic field from the current in the
coil magnetizes the iron core which creates a super strong magnetic field, much stronger
than the field created by the current in the coil of wire alone.

- Force on a current: not only do electric currents create magnetic fields, but a current feels
a force in a magnetic field. We demonstrated this with
The force is perpendicular to the current, and perpendicular to the magnetic field.
This is a special case of the magnetic force on ANY moving charge. I demonstrated this
with a "cathode ray tube", a.k.a. electron gun, showing that a beam of electrons moving
though space is deflected by a magnetic field:

The magnetic force on a moving charge is called the Lorentz force:
the magnitude is F_magnetic = q v B_perp, where q is the electric charge, v is the speed of the charge,
and B_perp is the component of the magnetic field strength perpendicular to the velocity.
The direction of this force is perpendicular to both the velocity and the magnetic field, in the direction
the palm of your right hand faces when your thumb points along v and your fingers point along B_perp.

Wednesday 10/27


A student asked an interesting question: why is the coulomb not an SI "base unit",
whereas the ampere is a base unit? The answer is that so far it has been easier for
experimentalists to make an accurate, reproducible measurement of current than of
charge. In the future, I expect this will change (soon). One day the standard unit of electric
charge may well be defined in terms of the elementary unit of charge, which is carried
by electrons and protons. In fact, it seems that day may be imminent. A Coulomb would
then be equal to exactly (i.e., by definition) 6.241 509 629 152 65 ◊ 1018 positive elementary charges.


- Magnetism was initially discovered by the ancient Chinese and Greeks (and probably others,
of course) via lodestone, a naturally occurring magnetic material, and the earth's magnetic field.
People made compasses that oriented towards the north pole.

- a magnetic field line shows the direction a compass needle would point at each point.
The pattern of the
earth's magnetic field lines is shown at this link. This is similar to the
pattern that we could see with the demo J5-05 MAGNET MODEL - FIELD LINES.
It is as if there is a giant bar magnet inside the earth.

- A common "bar magnet" has two "poles". Like poles repel, opposites attract. They
are called north (N) and south (S) poles. What we call the "North" pole of a magnet
by definition points toward the North pole of the Earth...which actually means that the
North pole of the earth is a South magnetic pole!

- Magnetic poles are similar to positive and negative electric charges, with a
big difference: you never get one magnetic pole alone. They always come in pairs, called a
dipole. If you break a bar magnet in half, the result is not just two single poles, but a pair of dipoles.
(Theoretical physicists have explored theories that allow for exotic objects in the universe that are
in fact isolated magnetic poles. So far none have been discovered...)

- Bloomfield advocates pretending up to a point that there are isolated magnetic poles, but I can't
bring myself to do that. The real story is more interesting, as we'll see. But if we allow this fiction
for a moment, we can define a magnetic field by analogy with an electric field:
magnetic field = force per unit magnetic pole charge. In symbols, Fmag= p B, where p is the pole
strength and B is the magnetic field vector. (I'll talk about the SI units later.)

- electromagnetism: In 1820 Oersted, a Danish physicist, discovered that an electric current
will make a magnetic needle deflect. (See demo J5-20). This turns out to be the key to a complete
understanding of magnetism and its relation to electricity. It shows that magnetism is an electrical
effect of moving charges...

Oersted found that the magnetic field around a long straight wire forms circles around the wire,
and the magnetic field of a circular loop of wire makes a pattern that looks like a magnetic dipole.
You can see a picture here, which comes from this website. A coil of several loops of wire will make
a magnetic field similar to that of a bar magnet. Notice that a loop of current creates a magnetic
dipole field, since the loop has a top and a bottom side. It can't create just one pole.

Not only does a current create a magnetic field, it responds to a magnetic field. The
K1-05 FORCE BETWEEN CURRENT-CARRYING COILS shows this in action. We can
even reverse the poles of these "electromagnets" by reversing the direction of the current.

- The earth's magnetic field comes from electric currents in the liquid outer core of the earth,
which is made of molten iron and nickel. This field changes in direction and strength over time,
and periodically reverses over geological times. Maryland Professor Daniel Lathrop has constructed a
model of the earth's core in a lab on campus and is using it to try to understand the behavior of
the Earth's magnetic field.

- What is a "permanent magnet" material?  Quite astoundingly, it is made of a bunch of microscopic
magnets all lined up. These magnets are nothing but spinning electrons! Being a charged body, when an
electron spins it is like a tiny circulating current, and the electron behaves like a tiny magnetic dipole.
Why do the electrons keep spinning? It's not "thermal" motion - they spin at zero temperature. They
spin because they have to. They can't stop spinning. They always spin the exact same amount, no matter
what happens to them. This is a property of, you guessed it, quantum mechanics! So why aren't all
materials magnetic? Because their electron spins are pointing every which way and their magnetic
fields cancel each other out. In just a few types of material, called ferromagnetic, the total energy of the
material can be lowered if some of the spins line up parallel. The most common of these materials are
iron and nickel, and various compounds made of them. The lined up spins are "frozen" into alignment,
sort of like water molecules in an ice crystal. And, like ice, the magnetic alignment can melt if the
temperature is high enough. I demonstrated this by raising the temperature of a Canadian nickel above
its magnetic melting point, called the Curie point:

Monday 10/25


Alessandro Volta's pile
The voltage of a battery is determined by the chemical potential energy difference of the
substances that react chemically in the battery. To make a larger voltage difference, you
can stack one on top of another. Volta's pile had many stacked layers of zinc and copper
plates, separated by cardboard soaked in sulfuric acid or brine (salt water).

Electrical resistance is determined by (1) the number of free charges, and (2) the
average drift velocity of the charges. The number of free charges is determined by the nature
of the material and, e.g. the thickness of the conductor. The average drift velocity is
determined by the number of collisions the charges experience, which is determined
by the nature of the material, the temperature, and the length of the conductor.

Many materials obey Ohm's law: current is proportional to voltage drop.
Resistance R is defined by V = I/R, equivalently V = IR. The SI unit of
resistance is V/A =
Ω = "ohm" (that's the greek letter Omega).

R of a material depends on temperature T. For conductors,
R increases with T, because electrons are deflected more often by
vibrations of the material. For semi-conductors, R decreases as T increases,
because more
electrons are liberated to participate in the current
(see demo K5-36).
For superconductors, the resistance is ZERO below some critical
temperature. So far the highest such temperature is 138K.


Here are some notes that might help you understand the material:

Relations between voltage, current, resistance, and power

voltage: electrostatic potential energy per unit charge at a given location; SI unit: J/C = V = "volt"
current: charge per unit time flowing past a given point; SI unit: C/s = A = "ampere"
resistance: opposition to flow of current; SI unit: V/A = Ω = "ohm"
power: energy per time; SI unit: J/S = W = "watt"

Ohm's law, holds approximately in many situations: 

V= IR,

where V = voltage drop, I = current, R = resistance

Power: If charge q moves through potential drop V it loses energy qV. The energy might
wind up as heat, or might do work. If this happens in time t then the rate of energy use is
qV/t. Since q/t is the current I, the power P is

P =VI.

We can use Ohm's law to get different expressions for the power, in case it is being dissipated
by a resistance R:

P = I2 R = V2/R.


A100W bulb generates more light than a 40W bulb at the same voltage (120V),
so evidently it has a lower resistance (since P=V2/R). If you connect these two bulbs
in parallel, so they have the same voltage across them, then the smaller
resistance bulb will be brighter. But if they are connected in series,
i.e. so the current goes through one and then the other, they have the same current.
Since P = I2 R,  the the 100 W bulb will be dimmer!

Friday 10/22

Figure 10.2.1 - photocopying machine
Figure 10.2.3 - photocopying process


- shielding of electric fields: "Faraday cage": in a region surrounded by a conducting material,
the electric field is always zero.

- photocopy machines and printers

- electric current: nature at SI unit 1C/s = 1A = 1 ampere. Nickname: = 1 amp.

- Example: current in a lightning bolt, 5 C in 100 microseconds gives a current of 50,000 A.

- current in a wire: each charge collides over and over with the material in the wire.  The "drift velocity" -
average velocity down the wire - is very slow, eg 1 mm/s. The amount of current depends on the number
of charges and the average velocity of the charges. Thicker wires carry more current for the same applied
voltage, longer wires carry less.

- bulb filament: a very long (coiled) very thin wire: has lots of resistance to current. Heats up to extremely
high temperature and emits visible (and infrared) light.

- power expended when a current I flows through a voltage drop V is P = VI.

- Example: A small bulb connected to a 1.5 V battery carries a current of 2 A. How much power
is consumed: 1.5 V means an energy difference of 1.5 J for every 1 C of charge. 2A means 2 C/s of charge
flows through, hence 1.5 x 2 J/s = 3W is consumed. The energy goes into heat and light coming out of the

Wednesday 10/20

Video about lightning (watch from 3:30 to 5:20)
National Weather Service Info on Lightning
More technical info on lighning from National Weather Service

lightning research lab video


- Air breakdown 30,000 V/cm = 3 x 106 V/m. Electric field in an atom is more
like 1010 V/m. So the field in air breakdown does not pull electrons out of atoms,
rather it accelerates particles until they have enough energy to knock out electrons
when they collide with air molecules.

- Corona discharge discussed in detail. Strong electric field at a sharp point on a conductor: 
charge gets backed into the
corner and concentrated, producing large nearby electric fields
that can lead to
corona discharge.

- Lightning - see links above

- Piezoelectricity- "piezo" means havign to do with pressure. Certain crystals, for example quartz,
have the property that when you squeeze them, their charge polarizes, and they develop a voltage
difference across them. I demonstrated this with the above demos. Moreover, conversely, if you
apply a voltage difference across one of these crystals, they will squeeze or stretch. They are terrifically
useful therefore, since they can be used to convert mechanical motion into electrical signals, or vice versa.
Examples of things that use this: clock crystals (vibrations generate readout signal, and electrical
voltage pulses keep crystal vibrating), acoustic instrument "transducer" pickups, microphones,
speakers, inkjet printer "pumps", ... 

- didn't get to photocopying machines. will do that next at the beginning, then section 10.3: current, circuits,
batteries, voltage, and power...

Monday 10/18


- Discussed structure of molecules and matter: how even though everything is neutral
overall, it can stick together by arrangement of charges. There are two qualitatively different
ways this canhappen: one is spontaneous correlated fluctuations of charge distribution,
they other is when the molecule already has a "permanent" electric polarization, like a
water molecule. This polarization explans how water molecules are held together in
water and in ice. (See pictures below.)

- electrostatic induction of charge

- electric field, voltage, and their relation:

electric field E = electric force per unit charge (N/C)
voltage V = electric potential energy per unit charge (J/C = V, "volt")

- Relation between field and voltage comes from force x distance = work

e force that must be exerted to move the charge against the electric field
has magnitude (charge)(electric field), force x distance =
(charge)(electric field)(distance).
On the other hand, the work
is equal to the change of potential energy, which is (charge)(change of voltage).
(charge)(electric field)(distance) = (charge)(voltage change).
So electric field = (voltage change)/(distance). The direction of the electric field is the direction
of steepest drop of voltage. Another way to say this: E = gradient(V). Units of this are V/m,
which is equivalent to N/C.

- Analogy between voltage and altitude: higher altitude, higher gravitational potential
energy, and the direction of the net force at a point on a mountain, taking into account gravity
(downwards) and the reaction force of the mountain (perpendicular to the ground), is in the
steepest downhill direction. This force per unit mass is analogous to the electric field.

- Electrical breakdown of dry air occurs at around 30,000 V/cm.

hydrogen bonds in
picture from Wikimedia Commons

water and ice
Picture from here.

Friday 10/15


- SI unit of charge = coulomb = C; value of Coulomb constant k_B, magnitude of
force between two charges of 1 C at 1 m (about 1010 N), or between two 10-7 charges
at 1 cm (about 1 N).

-  elementary unit of charge

- why a rubbed balloon sticks to the wall (polarization of charges in the wall)

- why neutral atoms attract to form molecules, for example H_2 : correlated fluctuating polarization

- why Gecko feet stick to walls: like attraction of neutral atoms, acting macroscopically,
at the ends of zillions of tiny fibers

- American Scientist article about
Gecko feet

Artifical gecko tape:

movie of loading and unloading gecko tape

- van de Graaff generator

- electrical discharge - breakdown of air, corona discharge, lightning rod

Wednesday 10/13


- v = wavelength x frequency applies for standing waves as well as for travelling waves
(in fact standing waves can be viewed as a superposition of two oppositely
moving travelling waves). This can also be expressed as frequency = v/wavelength.
For example, apply this to the vibrating string of length L.
The wavelengths of the modes are 2L,2L/2,2L/3,2L/4, etc.
The frequencies of these modes are v/2L, 2v/2L, 3v/2L, 4v/2L, etc.
In terms of the fundamental frequency f_1 = v/2L, these frequencies are
f_2 = 2f_1, f_3=3f_1,  f_4 = 4f_1, etc, i.e. they are multiples of the fundamental.

- vibration of drum head, as discussed in the textbook.

- other examples: Liquids or gases can support only longitudinal, compressional waves,
because transverse motions of a liquid or gas have no restoring force. But a solid
supports both longitudinal and transverse waves. This is used in seismology,
the study of ground/earth vibrations. These waves travel at different speeds in the
rock, and one can infer from the difference in arrival times how far away the
source of an earthquake or explosion is. Also, the presence of a liquid outer core
inside the earth is inferred from the fact that transverse waves are observed, by
seismometers placed on the surface of the earth, to reflect from the outer
boundary of the liquid core, since they cannot propagate within it.

- human hearing is incredibly sensistive - see Monday notes.

- Electric force: so far we've discussed the force of gravity, which is a fundamental
force, and other forces like string tension, gas pressure, friction...these are not fundamental -
since they have to do with how large numbers of atoms act together. But they can be traced
to the electrical force acting at the level of individual atoms, and the electrical force is
one of the fundamental forces.

- I covered much of the material that appears in the textbook on pp. 305-309, except
electric polarization. I'll get to that Friday.

- In addition, I spent some time discussing the structure of an atom: a nucleus consisting
of protons and neutrons, packed close together, and electrons, spread out very far.
The mass of each proton or neutron is around 2000 times the mass of one electron,
so virtually all the mass of an atom is in the nucleus. But the atom is about 100,000 times
larger than the nucleus! To picture this, if we scale the nucleus up to 1 cm across, the atom
would be 1 km across!!! This large space is taken up by the electrons, which are
"delocalized" over this volume, as, according to quantum physics, they have no definite position.
(Yes, that's obscure and weird and we don't have time to properly go into it here...)
The protons in the nucleus repel each other, and they are really close so the repulsive
force is huge, but they stick together nevertheless since neutrons and protons attract each other
via the nuclear force, another fundamental force. As a student pointed out (or asked), the energy
of nuclear fission reactors or bombs comes from this electric repulsion when a nucleus is split apart.

Monday 10/11

H4-41 DRUM

- crystal oscillator in my wristwatch - as explained in book. Additional info:
Apparently I overstated their accuracy. I don't recall where I got that number but I said
these are accurate to 0.1 s per year. Actually they are accurate to about 10 s per month -
much worse! That's about 100 s per year, out of about 30,000,000 s per year.
So one part in 300,000 accuracy. Still not bad!

- reviewed nature of string oscillation and harmonics, octaves and fifths,
with guitar strings as an example. I played the strings and demonstrated these things.
Control pitch with tension and mass, as well as choice of harmonics:
In particular, I showed how one can select to sound the harmonics of a string by
touching the string lightly at the desired node while plucking the string, then
removing the touch point immediately. I demonstrated that the nodal points are not
vibrating, and that if one touches the string there it keeps vibrating, while
if touched anywhere else it stops immediately. A string vibrating freely
contains simultaneously many harmonic modes, all added together.
This is called superposition of vibrations. I showed an applet that demonstrates
this: choose "display modes", set the "number of loads" all the way to the right,
and pluck the string in different places to see the different combinations of
modes that are present.

- reviewed nature of sound waves, pressure nodes, and sound harmonics in the twirl-a-tune
demo, and in the open and closed pipes demo. A key idea about harmonics in pipes
is that at (near) an open end the pressure must match the ambient atmospheric pressure,
so it does not vary there. Hence an open end is a pressure node. At a closed end on the
other hand the pressure may certainly vary, as the air is alternately compressed and dilated
there. In fact at a closed end the pressure must have an anti-node. (This can be explained by
the fact that the air at that end cannot move and further in one direction, but I won't give
the explanation here.) 

- A student asked a good question: if the ends are pressure nodes, how is the sound transmitted
through the ends out to the room? The answer is that the ends are not quite nodes. I gave an
analogy with the guitar string: if the ends didn't actually vibrate a tiny bit, the face of the guitar would not
vibrate, and the guitar would not generate an audible sound wave. The ends don't have to vibrate much
for this to work, since the guitar is constructed to effectively transfer sound energy to the air.
The book has a more extensive discussion of this on pp. 284-5.

- speed of sound in air is the same for all frequencies within the range of human hearing.
[I didn't say this in class, but this is a special proprty, true for many but not all types
of wave. For example, it isn't the case for water waves.]
The speed of sound in dry air is 331 m/s, plus 0.6 m/s for every degree celsius above 0˚C (at sea level).
So it's 343 m/s at 20 ˚C.

A student asked if altitude affects the sound speed. Indeed it does, but apparently only
because of the temperature being lower. (I didn't explain this in class.)
The lower pressure, which reduces the restoring force, is compensated by the lower density,
which reduces the inertia. [The speed depends only on the ratio pressure/density, which
according to the ideal gas law is proportional to the temperature.]

- speed = wavelength/period = wavelength x frequency, so wavelength = speed x period = speed/frequency
A 440 Hz thus has a wavelength at 20 ˚C of (343 m/s)/(440 Hz) = 78 cm. 10,000 Hz sound has a
wavelength of about 20 times smaller, so about 4 cm.

- The speed of sound is related to the speed of the air molecules, but is also determined by the number
of motions those molecules can make, that is, translations and rotations for nitrogen and oxygen molecules.
Helium is much lighter, so has a smaller inertia, and it also has a stronger restoring force since the atoms
are spherically symmetric so cannot rotate like air molecules. So the speed of sound in helium is higher,
in fact about three times higher: 972 m/s at 0 ˚C.  I demonstrated this by breathing some helium and speaking!
The cavity of my voice box resonates at a much higher frequency with helium in it than with air.
Here's a funny recording:
The decompression chamber Scott Carpenter is speaking from is at high pressure, but mostly helium
gas. At that pressure, even a small fraction of oxygen is still a high enough density of oxygen to breathe safely.

- Here's some interesting material I didn't get a chance to cover:
  Human hearing: When variations in pressure hit your ear drum, they shake it, and it sends the sound on to your
   inner ear where it is picked up by the movement of tiny hairs connected to nerves.
      + Human hearing is extremely sensitive. An ear can pick up variations of pressure as small as one part in a
         billion. In terms of energy, the quietest sound that can be heard carries a power (energy per unit time) of
         10^(-16) watts  per square centimeter. An ear opening is smaller than a square centimeter, but then the ear
         itself probably gathers sound and funnels it in, so probably the minimum power you can hear is around
          10^(-16) W. That's really tiny. For instance, compare it to the power to raise one gram 1cm in 1 s,
         mgh/second = 10^(-3)kg (10 m/s^2)(10^(-2)m) = 10^(-4) W. So you can hear sound with a power that is
         one TRILLIONTH (10^(-12)) of this tiny lifting power rate!

      +  Humans can hear sound from 30 Hz to 20,000 Hz. Some other animals can hear much higher frequencies.
           Elephants can hear lower frequencies:

Friday 10/8   Exam1

Wednesday 10/6   review

Monday 10/4


Prof. Orozco taught the class. He covered:

Sound as density waves. Being waves these can go around objectes (as opposed to
particle that travel in straight lines). These are longitudinal waves of compression
and dilation of air in the direction they are travelling.

Frequency = 1/period = number of cycles per second f = 1/T.
The SI unit of frequency is 1/s, or Hz (hertz).

Human hearing range: 30 Hz - 20,000 Hz (only young people can hear above 10,000 Hz or so...)
Vocal ranges: bass: 80-300 Hz, soprano 300-1100 Hz. 

Compared the sound of sine waves, which are pure harmonics, and saw-tooth and
square waves of the same frequency. Thus they have the same pitch, but sound
different because of the higher harmonic components.

Transverse waves on a string: as explained in textbook.

Friday 10/1



Oscillation: repeating motion around an equilibrium configuration, i.e. a configuration
in which the system will remain at rest.  The system is pulled back towards
its equilibrium configuration by a restoring force. It overshoots because of inertia.
The combination of restoring force and inertia determines its period, i.e. the time
to complete one cycle of oscillation. When the restoring force is increased, the
period decreases. When the inertia is increased, the period increases.

The amplitude is the magnitude of the largest displacement from equilibrium.

Harmonic oscillator: An oscillator whose period is independent of its amplitude.
This property is equivalent to the statement that the restoring force is proportional to
the displacement.

A pendulum is nearly a harmonic oscillator, for small amplitudes:
graph illustrating how the period of a pendulum depends on the amplitude
The restoring force is tangent to the arc of the swing, and comes from the component
of the gravitational force in that direction. (The component along the string is cancelled
by the string tension force.)  The period of a pendulum is independent of the mass!
This is because the restoring force, being due to gravity,
is proportional to the mass,
so the acceleration is independent of the mass
(just like for a falling object).
The period of a pendulum of length L is 2pi times the square root
of L/g, (where g is
the acceleration due to gravity).

Clocks: explained as in textbook.

Wednesday 9/29


Wankel engine: wikipedia article
Video: How a rotary engine works
Wankel engine animation

- Heat pump/AC unit: Using the fist link above, I showed a diagram of a house heat pump
arrangement and its parts, and described how it operates. I explained that when it is cooling,
the outside coils are the condensor and the inside ones are the evaporator, wheras when it is
heating, it's the opposite. As one student said, when it's heating the house, it's cooling the outside
air (which is already colder but gets even colder). In order to switch between heating and cooling
modes, you have to be able to redirect the fluid so that when it comes out of the compressor it
goes to one or the other of the coils. To accomplish this there is a movable valve. The first
link above has a diagram showing how such a valve can be designed.

- Heat engines: convert heat flow to work.

- Ideal efficiency: the 2nd law of thermodynamics implies that the
entropy can't decrease: Q_c/T_c ≥ Q_h/T_h. The minimum heat that can be
dumped to the cold reservoir is thus Q_c,min = Q_h (T_c/T_h). The maximum
work that can be obtained is Q_h - Q_c,min. The engine is called "ideally efficient"
in this case.

- The efficiency can be increased by decreasing T_c or increasing T_h.

- Example: steamboat engine operating with 500K steam and dumping the
heat to river water at 300K. Starting with 1000 J of steam heat, the minimum
heat that can be dumped into the river is (1000 J)(300K/500K) = 600 J. So the
maximum work that can be obtained is 1000 J - 600 J = 400 J.
(The entropy decrease of the steam as 1000 J leave it is - (1000 J)/(500 K) = -2 J/K.
So the entropy increase of the river water must be at least + 2 J/K.
I.e., Q_water/T_water = Q_water/(300 K) = 2 J/K.
Multiplying both sides by 300 K yields Q_water = 600 J.)

- Internal combustion engines - I covered this just as it it discussed in the book.
The only additional things: I showed how the camshaft works to control the timing of
openng and closing the valves (see link above). Also I showed how a rotary (Wankel)
engine operates (see links above).

Wednesday 9/27



- reviewed entropy, second law, and why work must be added to pump heat from a colder to a hotter system.

- explained operation of a refrigerator using a working fluid and a pump:
Evaporator: extract heat by evaporating working fluid
Compressor: compress gas. This takes work, and heats gas.
Condenser: liquify gas, give off heat.
Expand: pass through thermal expansion valve to drop pressure in evaporator.

If you just open a fridge and run it, then you will just heat up the room. A refrigerator can be used to cool a
room (i.e. as an air conditioner) only if you put the heat rejection coils out the window. This is how a window
AC works.

- You can pump heat from outside to inside even when it's colder outside. In effect, you are air conditioning
the outside, and dumping the heat inside! Alternatively, you can pump the heat out of the ground.

- Entropy change: Q/T (see 9/24 notes). An ideally efficient fridge wastes no heat, which means the
entropy stays the same, does not increase. This also means the process is reversible.

- Example: How much work must an ideally efficient refrigerator with inside temperature 270 K (-3 celsius) 
do to pump 900 J of heat out of the fridge, if the room temperature is 300 K (27 celsius)? Answer: Since the
fridge is ideally efficient, that means that the next entropy change is zero. This allows us to figure how much
heat must go into the room:  the entropy increase of the room must equal the net entropy decrease of the 
Q_room/300 K = 900 J/270 K, hence Q_room = 900 J (300 K/270 K) = 1000 J.  So 1000 J goes into
the room, but only 900 J of that originated as thermal energy in the fridge. Energy is conserved, so the remaining
100 J must have come from somewhere, and that somewhere is the work done by the fridge condensor pump motor.
That is, 1000 J = 900 J + W, hence W = 100 J.

- Using a heat pump to heat a house: reconsider the previous example, but let the outside of the house in winter
play the role of the inside of the refrigerator. Then an ideal heat pump can transfer 900 J of heat from the outside 
air at 270 K into the house, provided the pump consumes 100 J of work, and dumps a total of 1000 J into the 
house.  This is really striking: instead of paying for 1000 J of heat coming directly from electric, gas or oil heaters,
one can (ideally --- not in the real world) get 1000 J for the price of 100 J of work, by moving the remaining 900 J 
of thermal energy from the outside to inside. 

- Efficiency and temperature difference: the greater then temperature difference, the more work must be done to
move a given amount of heat "uphill" to a higher temperature. That's why the most efficient heat pumps for 
heating houses use not the thermal energy of the air, but the thermal energy of the ground. Even in dead of winter,
the ground a few feet down below the surface stays at around 50 Farenheit, or 10 celsius, or 283 K. Re-doing the
above calculation, with 270 K replaced by 283 K, we get Q_room = 900 J (300/283) = 954 J. So it only takes
954 J - 900 J = 54 J of work to pump the heat, rather than 100 J as before.

- Supplementary note added: I explained that to move heat from T_c to T_h >T_c some work must be done,
converted into extra heat added to the hot reservoir, otherwise entropy would decrease. (In a standard refrigerator
this extra work is done by the compressor.) A student remarked in class that instead of
doing work one might just add heat. This is indeed possible. But if the heat is drawn from a yet hotter temperature
reservoir at T_hotter, then the entropy decrease of that reservoir will require even more entropy to go into the T_h
reservoir, so the fridge wouldn't be ideally efficient. "Absorption refrigerators" have no compressor, and use heat
from a burner rather than work from a compressor. Here is an explanation (somewhat obscure, to me at least)
of absorption refrigerators.

Friday 9/24

mythbusters video of superheated water boiling instantly
supercooled water freezing "instantly"

- boiling explained some more

- sound just before water boils? Bubbles of vapor form near the bottom of the container where it is
hotter, then they rise and start to cool, whereupon their pressure drops, and the surrounding water
implodes them. The collective sound of all these implosions is the "roaring" sound one hears just
before water boils.

- superheated water

- heat spontaneously flows from hot to cold, but not vice versa. WHY? It's because disorder
increases: the average thermal energy of a particle of the hot material is greater than that of the colder material.
When they randomly exchange energy, on average more evergy will be transferred from hot to cold than vice
versa. The general statement of this is:

Second law of thermodynamics: the total amount of disorder (entropy) of an isolated system never decreases.

Entropy: is a measure of disorder - we will quantify it next class.

Entropy, heat, and temperature: A given amount of heat placed added to a lower temperature system increases
the entropy more than the same heat added to a higher temperature system. WHY? Because the higher temperature
system is already more disordered, so the additional thermal energy has less impact on the total amount of disorder.

- refrigeration: if heat Q_in is removed from a freezer at temperature T_in, the entropy of the freezer goes down. 
The second law of thermo tells us that the entropy of the room must go up by at least this much. If this same heat Q_in
is put into the surrounding room at the higher temperature T_out, the entropy of the room increases, but this increase
is LESS than the entropy decrease of the freezer (see previous paragraph). So the second law tells us that, in fact, MORE
heat must go into the room, Q_out > Q_in. Monday we'll discuss just how much more. But in the meantime, we can ask,
where does the extra energy --- the difference between Q_out and Q_in --- come from? Answer: from the work done by the
compressor pump that runs the freezer! Monday I'll explain just how a freezer works, and why the compressor pump is

Supplement for Chapter 8:
Entropy change as a quantitative concept, and the efficiency of heat pumps and engines
See 2009 notes for and expanded treatment.

As discussed in the textbook, entropy is a measure of disorder. When heat Q goes into a system in equilibrium
at a temperature T, the disorder increases. If the system is already very hot, it is already very disordered, so the
disorder increases less than it would if the same heat went into a colder system. Entropy gives a way of quantifying
the disorder: when heat Q goes into (or out of) a system at absolute temperature T, the entropy increases (or decreases)
by Q/T,

(1)     Entropy change =  Q/T = (heat into system)/(temperature of system)

This entropy change for a given heat transfer is inversely proportional to the temperature. For example, at double
the temperature, the entropy change is half. With Q in Joules, and T in degrees Kelvin, the units of entropy are J/K.
The concept of entropy was originally formulated (by Clausius in 1854) purely using the concepts of heat and temperature in this way.
The connection to disorder, which can be quantified using probability theory, came a little later.
Since T is a measure of
the average thermal energy per particle motion, the entropy basically measures how many units of thermal energy there are.
Since the "unit of thermal energy" grows with temperature, the same heat has less entropy at a higher temperature.

Entropy increases when heat flows from a hotter body at temperature T_h to a colder one at temperature T_c < T_h, since then
Q/T_c > Q/T_h. The reverse direction, flowing from cold to hot, would decrease entropy. The "Second Law of thermodynamics"
states that the total entopy of an isolated system never decreases.

The maximum possible efficiency of a heat pump or heat engine is governed by the Second Law: to move heat from a cold
system to a hot one without decreasing entropy, a certain minimum amount of work must be done, which winds up as extra
thermal energy delivered to the hot system. Similarly, to generate work using heat in a hot system, a certain minimum fraction
of the initial heat must be discarded as heat in a colder system. 

If a heat pump (refrigerator) moves heat Q_c from a cold system (the refrigerator) to a warmer system (the room),
that would violate the second law of thermodynamics unless the heat Q_h dumped into the room is greater than the
heat taken out of the fridge. Specifically, in order not to decrease entropy, it must be that

(2)     Q_h/T_h  ≥  Q_c/T_c,


(3)     Q_h  ≥  Q_c (T_h/T_c).

The amount of heat is dumped is minimized when the entropy does not change at all, in which case the ≥ is replaced by =.
When the entropy does not increase, the heat pump is called ideal. In this case, since entropy did not increase, it
can also be run backwards without violating the second law, so it is reversible. Thus the most efficient heat pump is a reversible one.
The difference Q_h - Q_c is, by virtue of conservation of energy, equal to the work done on the system.

Similar reasoning can tell us how much work W can be done if heat Q_h is provided to a heat engine (like a car motor),
if the motor heat is at temperature T_h and the engine dumps heat Q_c into the environment at the colder temperature T_c.
The dumped heat can't be zero, since that would mean entropy decreased, but it can be smaller than the suppled heat Q_h,
since T_c is less than T_h.
Since we're starting with Q_h, and entropy must increase, the opposite of (2) must be satisfied,

(4)     Q_c/T_c ≥ Q_h/T_h,


Q_c ≥ Q_h (T_c/T_h) .

Notice that if the environment is at absolute zero of temperature, T_c = 0, then for an ideal engine, Q_c = 0, i.e. all the heat
goes into work! But in any other case, some of the input heat is inevitably lost as dumped heat.

Wednesday 9/22


- hot plate viewed with video camera nightshot: this is sensitive to the infrared radiation
  and it shows up as a bright white light.

- thermos: suppresses conduction, convection, and radiation

- phases of matter: solid, liquid, gas; transitions between these

- melting: It takes energy to pull a molecule away from the ice crystal and put it into
liquid form. The "latent heat of fusion" of water/ice: 330,000 J/kg at 0 celsius.
This is huge: compare this to heat capacity: 4190 J/kg per degree celsius.
So the latent heat of fusion could raise the temperature by 330,000/4190 = around 80 degrees celsius!
As heat flows into a glass of water, it goes into melting more ice, not raising the
temperature of the water & ice. The faster heat goes in, the faster the ice melts,
absorbing the heat in the heat of fusion/melting.

- evaporation: It takes energy to pull a molecule away from the liquid and let it escape as vapor.
The "latent heat of evaporation" (vaporization) of water/steam: 2,300,000 J/kg at 100 Celsius.
This is REALLY huge: this much heat could raise temperature by 2,300,000/4190 = about 550 degrees celsius!!
example: cooking by steaming: when steam condenses on vegetables it releases this huge heat of vaporization.
Conversely, evaporation has a cooling effect: the molecules that evaporate have more energy
than the average molecule, needed to supply the heat of vaporizations, so when they leave, the average
energy of the molecules they leave behind is lowered.

- example: cooling by sweating.

- example: A spectacular demo of this is the Cryophorus (see above): we saw that water can be made to
freeze just by letting a bit of it evaporate quickly (by condensing the vapor on the other end of the
tube in the LN bath).

- relative humidity = (landing rate)/(leaving rate);
:  cooling by sweat less effective on a humid day.

- saturated vapor pressure: at a given temperature, it takes a given presssure to have 100% relative humidity.
At room temp, saturated pressure for water is a few percent of atmospheric pressure. At 100 ˚C it becomes
an atmosphere of pressure. At this stage, a bubble of vapor in water can be stable, i.e. not collapse by the
ambient pressure. If more heat is put into the system, the bubble will expand and rise, and
more bubbles will form. This is called boiling. Demonstrated LN boiling at room temperature...

Monday 9/20


- thermal expansion (for a metal, fractional change of length ~ 1/100,000 per degree K.

- Heat: thermal energy in transit...or sometimes just thermal energy. Forms of heat:

    conduction: by vibrations & collisions in stationary material
    convection: by movement of fluid or gas
    radiation: by electromagnetic waves

- heat flows spontaneously from a hotter body to a colder one.

- Feel the plastic and metal parts of the chair you're sitting in: the metal feels colder
  even though the parts of the chair are all at room temperature (in thermal equilibrium).
  Why? Heat flows more rapidly our of your hand into the metal, and you sense that flow.
- metals are generally good heat conductors because their free electrons, which also conduct electricity,
  can efficiently spread thermal energy by collisions.

- heat flow per unit area measured in (W/m^2); thermal conduction depends on the
temperature gradient, i.e. on the degrees K change per meter. To find the heat flow, you multiply
the heat conductivity by the temperature gradient. The SI unit of heat conductivity is
(W/m^2)/(K/m) = W/m.K. The conductivity of threee common metals, using cm instead of m
as the unit of length, W/cm.K: copper 3.98, aluminium 2.37, brass 1.23.

- convection: often driven by buoyancy of hotter air or liquid.

- radiation: "red hot" glows in visible red. "white hot" is higher temperature, higher frequency radiation
  colder might be "infrared hot", but you can't see infrared radiation. 

Friday 9/17


- hot air balloon

- ideal gas law:
p = k rhoparticle T = k (N/V) T

  where p is pressure, k is Boltzmann's constant k = 1.381 x 10-23 Pa m3/K, rhoparticle is the particle
  density (number per unit volume), T is the absolute temperature in kelvin, N is the number of particles,
  and V is the volume occupied.

- A nice applet illustrating the ideal gas law.

- absolute temperature scale (kelvin):
absolute zero
N2 boils
H2O freezes
room temp
H2O boils
0 K
77 K
273 K
295 K
373 K
-273 ˚C
-196 ˚C
0 ˚C
22 ˚C
100 ˚C

- One degree increment kelvin is the same as one degree increment celsius. The two scales just differ by the zero point.
  To define one degree the interva between freexing and boiling points of water is divided into 100 equal parts.

- [A student asked (or seemed to ask) what does it mean for two temperature intervals to be equal? That's an important question.
  The deepest way to answer would be to say they correspond to equal increments of average kinetic energy. In practice,
  though, one could use properties of a physical system. For instance, the ideal gas law, with a gas that is almost ideal, shows
  that equal temperature intervals correspond to equal pressure intervals at fixed volume, so one could use pressure measurements.]

- The ideal gas law explains buoyancy of balloons: Archimedes' principle says the buoyancy force is equal to the weight
   of the displaced air. We can compare this to the weight of the same volume of gas in the balloon. The pressure inside and outside
   the balloon is the same, otherwise the balloon wall would accelerate in or out. (Actually a small part of the inward force comes from
   the streched skin of the balloon, so the pressure inside must be a little more than atmospheric pressure in order to balance this
   extra force of balloon tension. But let's ignore this small discrepancy.) So both p and V are the same, so the product NT must be the
   same.  Let's apply this to three cases:
   hot air balloon: p and V are the same, and T is greater inside, so N must be smaller inside.
  That is, there are fewer air molecules inside than in the displaced air;
   in other words,density of air in the hot air balloon is smaller than that of the surrounding air. Hence, its weight is less than the
   buoyant force, so the balloon floats. How much less? For the hot air balloon demo (which didn't work great because of open seams)
   let's say the temperature of the air inside is on average 5 K (= 5 ˚C = 9 ˚F) higher than the room temp of 295 K, i.e. inside it is 300 K.
  This corresponds to a fractional difference of 5/300 = 1/60, or around 2%. In this case the air inside would be about 2% lighter than
  the air it displaces.
  helium balloon, room temperature: p, V and T are the same so N is the same! This is called Avogadro's principle: at fixed pressure
  volume and temperature, the number of gas molecules is the same for all types of gas. (Avogadro's principle was crucial in the
  development of chemistry, since it allows the proportional number of molecules before or after a reaction to be assessed by measuring
  the macroscopic quantities: volume, pressure and temperature.)

  Since a helium atom is much lighter than an air molecule, the weight of the displaced air is much greater than the weight of the helium.
  How much? One helium atom has atomic mass 4 (two protons, two neutrons - the electrons have negligible mass compared to those).
  One nitrogen atom has atomic mass 14 (7 protons, 7 neutrons), and a nitrogen molecule has two nitrogen atoms, so the mass of the
  molecule is 28, which is 7 times that of a helium atom. (Oxygen, which comprises 21% of the air, is even more massive: 32.)
  So the displaced air is around 7 times heavier than the helium in the balloon.

  helium balloon, LN temperature: p and V are the same as that of the displaced air, T is less at liquid nitrogen (LN) temperature,
  so N is more. How much more?
   N_in/N_out = T_out/T_in = (300 K)/(77 K) = approximately 4 times more molecules. This is not enough to compensate the smaller
   mass of a helium atom (which is 7 times smaller per molecule), nevertheless the cold helium balloon sinks because the buoyancy force
   must also support the weight of the skin of the balloon itself. Another interesting comparison is the volume before and after we
   cool the balloon. For a fixed helium balloon, at room temp and at LN temp, p and N are the same (no helium atoms enter or leave the
   balloon), so the ratio T/V must be the same. If we lower T by a factor of 4, we must lower V by a factor of 4, so the balloon shrinks.
   This is another way to see that the density of the helium inside increases. By the way, then how much does the radius R shrink?
   If the balloon is a sphere its volume is proportional to R3, so (RLN/Rroom)3 = TLN/Troom = 1/4. Hence RLN/Rroom =  (1/4)1/3 =~ 0.6.
  That is the radius of the balloon on LN is only 60% of the warm balloon radius.  

- reaction to buoyant force demo.

Wednesday 9/15


- typical faucet pressure: 30-80 psi
    1 psi = 1 pound per square inch = 6894 Pa, so 60 psi ~ 414,000 Pa. Note this is about four atmospheres
     of pressure. Makes sense that water pressure had better be more than atmospheric, otherwise water
     wouldn't come out of the faucet! Monday we showed one atmosphere of pressure supports about 10 m
     of water, so 60 psi is produced by a column of water roughly 40 m high. So water towers need to be something
     like this height.

- helium balloon floats because of buoyancy in atmosphere: the helium is lighter than the displaced air.

- Gas: molecules separated by distance much greater than the molecules.

- example: air, 78% N_2 (diatomic nitrogen), 21% O_2 (diatomic oxygen), 1% Ar (argon), 0.03% Co_2 (carbon dioxide)...
  At STP (standard temperature and pressure) two air nitrogen molecules are roughly 20 times further apart than the size of
  the molecules themselves. Each molecule is around 0.15 millionths of a millimeter across, and they are moving fast,
  on average 500 m/s. To get some intuition, if a molecule were one centimeter in size (I used 10 centimeters for illustration
  in class so you could see it on the board), the separation would be 20 cm. Each molecule would occupy a volume around
  (20 cm)^3, so it would sweep out this volume on average before colliding. Since its own cross-sectional area would be
  around 1 cm^2, it would have to travel 8000 cm = 80 m, i.e. 8000 times the size of the molecule. But for real air molecules,
  this is still a very short distance: 8000 x 0.15 millionths of a millimeter= 1.2 thousandths of a millimeter = 1.2 microns.

- Liquifying air: I put an air balloon in liquid nitrogen and condensed the air inside. The volume of the balloon shrank to nothing,
  because all the air molecules became a liquid, and were 20 times closer, so they occupied 8000 times less volume! Once they
  quickly evaporated, they re-inflated the balloon.

- How does gas exert pressure? By myriads of collisions. Why do the air molecules keep moving, instead of coming to rest
  after dissipating their energy like a superball? Because they keep getting energy from the environment. Why doesn't all
  the energy just spread out and dissipate completely?
Because of the influx of energy from the sun's radiation.

- Absolute temperature: can think of it, for a gas, as proportional to the average kinetic energy 1/2 mv2 of a molecule.

- Ideal gas law: pressure ∝ (particle density) x (absolute temperature) ∝ (particle density) x (mv2)
  We can understand why this would be true: pressure comes from the force of collisions with the walls. The
  number of collisions per unit area per unit time is proportional to the number of molecules per unit volume (particle density),
  and proportional to the speed v of the molecules. The average force in each collision is proportional to the mass times
  the average acceleration, which accounts for the factor of m. The acceleration is proportional to the change of velocity
  when a molecule bounces off the wall, which is proportional to v itself, which accounts for the second factor of v.

- Temperature scales: Absolute zero corresponds to no kinetic energy, and is labled as 0 K (degrees kelvin). One degree kelvin
  is the same increment size as one degree celsius. 0 celsius is the freezing point of water and 100 celsius is the boiling point.
  0 celsius = 273 kelvin.

Monday 9/13


- friction: I said some more about the nature of sliding friction, then talked about static friction.
As an example I discussed the fact that the horizontal friction force of the road on the tires supplies the
external horizontal force that accelerates a car.

- applying Newton's laws to fluids.

- pressure: force per unit area. SU unit "pascal": 1 Pa = 1 N/m2

- explained why pressure is the same everywhere at the same depth, how "water seeks it's own level",
how pressure increases with depth in the fluid in order to support a greater mass above it.

- A student asked about tides: these seem to contradict the fact that water always seeks the same
level. The answer is this: the fact that water seeks the same level only applies when the gravitational
force is the same everywhere (think about how we inferred that it was true). The tides are caused by
the fact that the gravitational pull of the moon (and to a lesser degree the sun) is stronger on the side
facing the moon (or sun) than on the opposite side. This causes the water in the oceans to bulge
outward on the sides facing the moon and the opposite side. The earth rotates under these bulges
once per day so there are two high tides and two low tides. When the sun and moon are lined up
with the earth at new moon or full moon, the tides are larger. These are called "spring tides".
At the quarter and three quarter moons, the tides are lower, and are called "neap tides".
For more info, see our textbook, section 9.3, or the Wikipedia article on tides.

- example: atmospheric pressure at sea level is around 100,000 Pa.

- example: How much pressure increase with depth in water? A cubic meter of water has a mass
of 1000 kg, and therefore a weight of about 10,000 N. So the pressure to support it is 10,000 N/m2,
that is, 10,000 Pa. So the pressure increases by 10,000 Pa for every meter of water. How high a
column of water could atmospheric pressure (100,000 Pa) support? Answer: 10 m.
That's why we don't use water in barometers, it would take a huge barometer!

- example: Water towers for distributing water (see textbook for more discussion).

- buoyancy: upward force on objects immersed in a fluid or gas, caused by the pressure being
greater at the bottom than the top.

- Archimedes' principle: buoyant force = weight of displaced fluid. To see why: if the occupied space
were filled with more of the same fluid, the fluid would just remain at rest, unaccelerated. So the
net force due to the surrounding pressure must be just enough to support it.

example: Illustrated with the F2-5 demo, boat and rock.
The puzzler at the end: if you take the rock out of the boat and put it in the bottom
of the tank, will the water level go up or down? The answer: it will go down. The reason: when the
rock is sitting on the bottom of the tank it displaces only its own volume in water. But to support it
floating in the boat, the extra displaced water must have the same weight as the rock. Since the "rock"
(really a lead slug) is much more dense than water, the required volume of water is much greater
than the volume of the rock.

- Demonstration of the force of atmospheric pressure: I13-12 - can crusher demo.

- regarding the question of what would happen to a human body exposed to the vacuum of space
googling will bring up many links. Here's one from NASA.

Friday 9/10


- Work that gives an object kinetic energy: Satchel Paige pitching, Sandy Koufax pitching

- Derivation of kinetic energy: if a constant force F acts over a distance d in the direction of the force,
the work done is W = Fd = mad. If the initial speed is 0, and the final speed is v, the acceleration is a = v/t.
The distance traveled is d = v_avg t = (v/2)t, the average speed times the time. So W = m(v/t)(vt/2) = 1/2 mv2.
We learn that kinetic energy is 1/2 mv2. Given the work, we can find the speed. Given the speed, we can find
how much work it takes. Note that since the energy depends on the square of the speed, twice the speed
has FOUR times the energy.

- Mechanical advantage: do same work with less force acting over more distance.
Examples: ramp, lever, hydraulic press, block & tackle.

- For the lever, work at one ened is transferred to work at the other end. The work at one end is equal to the
work at the other end, F1 R1 = F2 R2, where R1 and R2 are the distances from each end to the fulcrum,
and F1 and F2 are the forces applied at the ends, perpendicular to the lever. Hence F1/F2 = R2/R1. 

- For the block and tackle, the demo had four loops of rope over the pulleys. Each rope holds 1/4 of the weight
of the buck of lead bricks. To hold the bucket I need to exert a force only 1/4 of it's weight on the end of the
rope. When I pull the rope and the bucket goes up a distance d, I must pull the rope over a distance 4d.
One fourth the force over four times the distance gives the same work as just lifting the bucket directly.
It must be so, since the bucket ends up with the same increase of gravitational potential energy.

- For the hydraulic press, I gain mechanical advantage both because I'm using a lever, and because the
hydraulic pump has oil cylinders with different cross sectional areas. When I press the piston on the
narrow side, the piston on the wide side moves through a smaller distance. I didn't measure it, but say
I moved my hand through 50 cm and the press moved by half a centimeter. The ratio is then 100 to 1,
so the force I could exert is "amplified" by a factor of 100, which is why I could easily break the
2x4 peice of wood.

- friction: work done "against" friction results in thermal energy: it heats up the surfaces that are rubbing.

- rollers, wheels, and bearings

Wednesday 9/8


- example of ISS and astronaut orbits around earth. Speed around 17,000 mph.
Velocity changing, acceleration toward center of earth, same for ISS & astronaut,
caused by gravitational force, force different on ISS and astronaut, proportional
to their masses.

- I mentioned that this special propoert of gravity, that all things fall with the
same acceleration, regardless of their mass, is the cornerstone of Einstein's
reformulation of gravity theory, "general relativity" (GR). According to GR,
there is no gravitational "force", and things fall because of the curvature of
space and time. Under normal circumstances the theory makes almost identical
predictions as Newton's theory of gravity. But there is an example in practical life
where GR makes a significant difference: in the GPS (global positioning system).
The clocks on the GPS satellites run at a different rate both because of their motion
(that's an effect of "special relativity" - nothing to do with gravity) and because
of their altitude: a clock runs slower at a lower altitude. The difference between GR
and Newtonian gravity can become extreme, for example near a black hole, where
gravity is so strong that it traps light. I didn't say this in class, but in fact at the
"horizon" of a black hole, where light is first trapped, a clock stops running
altogether...which is directly related to the fact that it must actually be moving at
the speed of light in order to sit there!

- vertical acceleration due to gravity at surface of the earth; increase of velocity with
time v = gt. After 1 s, v = 9.8 m/s; after 2 s, v = 19.6 m/s, etc. 

- thrown object: gravity acts only vertically at teh surface of the earth;
horizontal motion unaffected. I illustrated this with the funnel cart demo.

- circular orbit of ISS is also just due to falling toward the center of the earth. At that
altitude, the acceleration of gravity is nearly the same as at the surface of the earth,
and accounts for the orbit: I showed that the angle of the ISS on the circular orbit
changes in one second by an amount approximately equal to (9.8m/s)/v, where v is
the speed of the ISS orbit. (Actually the gravitational acceleration is a little smaller
at the altitude of the ISS orbit (~ from 278 km to 460 km). Using this and the fact that
the same angle is equal to the distance traveled during that second divided by the radius
of the orbit, one can work out the relation between the speed v, the radius of the orbit R,
and the centripetal acceleration a. At the altitude of GPS orbits, or communication satellite
orbits, or the moon, the acceleration is even smaller. In fact it is inversely proportional to
the square of the distance to the center of the earth.

- [Supplemental - not required: For those who are interested in a quantitative treatment,
in a short time interval t with centripetal acceleration a, the centripetal component of
velocity is at, so the angle is close to at/v. But the angle is also the distance traveled vt
divided by the radius of the orbit R,  that is vt/R. The angle traveled in the orbit and the
angle by which the velocity vector is rotated are the same, so at/v = vt/R. This implies
a = v2/R, or equivalently v = (ar)1/2 . Putting in a = g = 9.8 m/s^2 and R = 6400 km
(radius of the earth) yields around v = 8000 m/s which is around 18,000 mph.]

- Weight: at the surface of earth, the gravitational force on an object of mass m is mg downward.
This force is the object's "weight". For 1kg, the weight is (1kg)(9.8 m/s^2) = 9.8 N. Note the unit N!
The weight is 9.8 newtons of force.

- WORK - energy transfer. Examples:
1. lift mass: positive work done on mass, increase gravitational potential energy of mass
2. lower mass: negative work done on mass, decrease gravitational potential energy of mass
3. move mass sideways at constant speed: zero work
4. throw mass horizontally: positive work on mass, increase kinetic energy of mass

Work = (Force) x (displacement in direction of force)

The displacement is counted negative if it is opposite to the force.

Example: lift a mass a height h, the work is (mg)(h) = mgh, which is equal to the increase
of gravitational potential energy of the mass.

Example: throw a mass: the kinetic energy is 1/2 m v2. I will derive this from the work formula next time.

Friday 9/3

Newton's laws:
I. If no force then no acceleration.

II. acceleration = force/mass; in vector notation: Ftotal = ma

III. Force of B on A has equal magnitude and opposite direction to force of A on B; in vector notation: FB on A = - FA on B

 - vector addition, negative of a vector.

- measurement units: we'll use the SI (Systeme Internationale) units;
For some history and current definitions of these units see:



N = kg m/s2

- 1 kilogram = 1000 grams, 1 gram = mass of 1 cubic centimeter of water (at a standard temperature and pressure). Actually the
  kilogram is defined today in terms of a particular object: One day it will be defined in terms of the mass of some type of atom,
  once our ability to measure such things improves some.

- Fundamental forces of nature: gravitational, electromagnetic, weak, nuclear. All other forces we see, like the pull of a string,
  or the table pushing up on my coffee cup, result from collective behavior of matter, and can be traced mostly to electric forces
  of attraction and repulsion of electrons and protons.

- Gravitational force: any two masses attract each other along the direction joining them. The gravity we feel from the earth
  pulls toward the center of the earth because the earth is spherical, and when you add up all the pull vectors toward all the different
  bits of the earth, the total winds up pointing toward the center of the earth. The force is weaker when the two masses are farther

- Strange property of gravity that is different from all other forces: the acceleration it produces is the same for all objects, independent
   of mass. This was illustrated by dropping a bean bag and a crumpled piece of paper. Also swinging a pendulum with different amounts
   of mass bu tthe same length: the time to swing stayed the same. And finally I illustrated it with a video of an astronaut taking a spacewalk.

-  For example, at the surface of the earth the acceleration due to gravity is 9.8 m/s2, which is usually denoted by the letter "g".
   Why is the acceleration the same for all masses? According to Newton's second law, this can only happen if the force of gravity itself
   is proportional to the mass of the body it is acting on. In particular, at the surface of the earth, it is mg, downwards. This force is
   called the weight of the object, W = mg. (Then F = ma reads mg = ma, which implies that a = g, no matter what m is.)

Wednesday 9/1


- note: the reading for this week is Chapter 1.

- inertia, velocity, acceleration, force, and mass

- vector quantities: have both magnitude and direction. Note: the textbook denote
  vector quantities by boldface letters. On the board in class I will instead denote
  vectors by a letter with an arrow on top.

- vector addition: two add two vectors, place the tail of the second arrow at the tip
  of the first; the arrow from the tail of the first to the tip of the second is the sum of
  the two vectors.

- Newton's second law: acceleration is proportional to applied force. More precisely,

        F = ma

where F is the total applied force vector (add all the force vectors), m is the mass,
and a is the acceleration vector. So doubling the force doubles the acceleration for
a fixed mass. Doubling the mass halves the acceleration for a fixed force.

Monday 8/30


- course logistics & policies

- energy as key concept of physics
         - conservation of energy
         - fundamental types of energy: kinetic (energy of motion), potential (configurational)
         - other forms of energy:
                 - chemical (microscopic kinetic and potential energy stored in structure of atoms and molecules)
               - nuclear
(microscopic kinetic and potential energy stored in structure of nuclei)
                 - thermal, "heat": (random, microscopic kinetic and potential energy)

- entropy: a measure of disorder
         - second law of thermodynamics: total entropy of the world cannot decrease (but always increases)

In class I discussed the decrease of entropy of water freezing to ice (the water molecules are more ordered in
the froen crystalline form than in the liquid form), and how that is compensated by the extra entropy due to
the heat given off when ice freezes (heat of fusion). A simpler example is a refrigerator: the inside is cooled
so its entropy decreases, but this comes at the expense of heat transfer to the outside which increases the
entropy of the room more than the decrease of entropy of the inside of the fridge. We will come back to this
example later, and treat it quantitatively.