*Updated: 01 May 2012 Tuesday · 6:30pm.*

FINAL COURSE GRADES AND BREAKDOWN BY CATEGORY FOR PHYS-1000 Spring 2012. Estimated Pre-Finals Grades can be found here.

Reminder that ICES Student Course Evaluations are available now online via GoWMU .

Monday 4/23: Office Hours.

Tuesday 4/24: FINAL EXAM (2:45pm-4:45pm)

Wednesday 4/25: Office Hours.

Thursday 4/26: Dr. Phil does not plan on coming in today.

Friday 4/27: LAST DAY TO MAKE UP EXAMS.

Monday 4/30: Office Hours.

Tuesday 5/1: Grades due at Noon.

Monday 1/9: Class begins. Why are you here? "They" made you take this -- or at least a science course with a lab. Why? Science literacy. The nature of studying Physics. Science education in the United States. HOW THINGS WORK -- Macro/Gross versus Micro/Detailed analytical model. We're looking at the bigger picture. Much of what we know is Black Box stuff. (We can drive a car without knowning what those dark greasy shapes under the hood are.) (We can use a computer or a cellphone without knowing how to build a computer chip or program it.) "Speed Limit 70" -- what does it really mean? First Equation: Speed = Distance / Time. v = d/t . Physics - Numbers - Equations - Calculations. We can use the equations in Physics to (a) Predict the future (how far will this go?) or (b) "Predict" the past (where was this when it started? how fast was it going?) These are Powerful Tools

Wednesday 1/11: Distribute syllabus. Speed = Distance / Time. v = d/t . What is measurement? Systems of units need to have a Standard. Why the metric system? Because the old units don't make much sense in turns of numbers and conversions. In the metric system, once you've defined something, like The Meter is the standard unit of length, you can make larger or smaller units by the use of prefixes. A centimeter (cm) is 1/100th of a meter, while a kilometer (km) is 1000 meters.

- Quiz 1 will be in-class on Friday 13 January 2012. It will be for attendance purposes. If you miss class on Friday, you will be able to get some of the points by downloading Quiz 1A from the website and turning it in.

Friday 1/13: **The Simplest Types of Motion: **(1) No motion. (v = 0) ;
(2) Moving at a constant speed. (v = constant) ; (3) Moving with a changing
speed. (v is not constant) **What is "1 m/s"?** We need a few
benchmark values to compare English and SI Metric quantities. **Converting
Units:** Multiply a number by "1", where the numbers in the top and
bottom of the fraction represent the same quantity, just in different units,
hence the fraction equals 1. So... 60 m.p.h. = *( 60 miles/hour ) × ( 1
hour / 3600 sec ) × ( 1609 m / 1 mile) = *26.8 m/s. **A Table of m/s
Comparisons: **1.00 m/s = slow walking speed. 10.0 m/s = World Class sprint
speed (The 100 meter dash -- Usain Bolt is the current
Olympic (9.683 seconds) and World (9.58 seconds) record holder.) 26.8 m/s = 60
m.p.h.. 344 m/s = Speed of sound at room temperature. 8000 m/s = low Earth
orbital speed. 11,300 m/s = Earth escape velocity. 300,000,000 m/s = speed of
light in vacuum (maximum possible speed). Remember PTPBIP! Q1 and your PID
number. *Quiz 1 was given in-class on Friday 13 January 2012, for attendance
purposes. If you missed class on that day, you will be able to get some of the
points by downloading Quiz 1A from the website and turning it in.* (Click
here for a copy.) Topic 1 assigned. (Updated
Searchable booklist available online here .)

NOTE:Monday 16 January 2012 is Dr. Martin Luther King, Jr. Day and while WMU holds no classes, there are many MLK Day activities going on around campus.

Monday 1/16: **MLK Day to Honor Dr. Martin Luther King, Jr. **-- Classes
Do Not Meet at WMU -- University-wide activities.

Wednesday 1/18: Textbook example of Skating. Moving at a constant speed.
INERTIA = Momentum. "A relentless quality of motion that it the result of
an object having mass." External Forces push or pull on objects. Internal
Forces hold objects together. Some stories about Sir Isaac Newton. Newton's
Three Laws of Motion: **Zeroeth Law** - There is such a thing as mass. The
Zeroeth Law represents the underlying assumption that the Three Laws require,
in this case, that objects have mass, a measure of how much "stuff"
(matter) they contain. **First Law** - An object in motion tends to stay in
motion, or an object at rest tends to stay at rest, unless acted upon by a
__net external force__. In real life, "an object in motion tends to
slow to a stop" -- that's because there ARE external forces, such as
friction, in play. If there is a change in speed, then we have an acceleration.
**Second Law** - F=ma. Physics Misconceptions: Things
you think you know, are sure you know, or just assume to be true in the back of
your mind... but aren't true. Aristotle was sure that heavier objects always
fell faster than lighter objects, but we did a demostration on Tuesday which
showed that wasn't always true. Example: You're driving a car. To speed up, you
need to put your foot on the accelerator (gas pedal), so YES, you are
accelerating -- True. To drive at a constant speed, you must still have your
foot on the accelerator, so YES, you are accelerating -- Not True because
constant v means a = 0. To slow down, you must take your foot off the
accelerator and put it on the brake pedal, so NO, you are not accelerating --
Not True because v is changing, so a < 0 (negative).

Friday 1/20: Acceleration a = delta-v / delta-t -- a change in speed divided
by the time. If we have an acceleration, then we must have an external force
and *vice versa*. F=ma allows us to think about what is happening. If we
want a larger acceleration, we need a bigger force. If you apply the same force
to a smaller mass, we get a bigger acceleration. If we want the same
acceleration for two objects, then the force will be larger or smaller if the
mass is larger or smaller. Etc. **Comparisons:** What do we mean by a = 1
meter/sec² ? You cannot accelerate at 1 m/s² for very long. **Types
of Motion**: No Motion (v=0, a=0), Uniform Motion (v=constant, a=0), Constant
Acceleration (a=constant). We generally cannot accelerate for very long.
**Free-Fall:** If we ignore air resistance, all objects near the surface of
the Earth fall towards the Earth at the same rate. *a _{y} = -g* ;

- Due to Windows taking 17 minutes to save a file, I was unable to distribute Q2 as planned. (You can get an advanced copy of the quiz here.)
- For a = 1.00 m/s², we created a table with 3 columns:
*t, v = at, x = ½at²*, with*t*. We then found_{0}= 0, v_{0}= 0, x_{0}= 0*v*and*x*for t = 1, 2, 3, 4, 5, 10, 25 and 100 seconds. - The Apollo 15 Hammer and Falcon Feather Drop webpage. QuickTime movie: (low res 8MB, higher res 80MB)

Monday 1/23: **Free-Fall:** If we ignore air resistance, all objects near
the surface of the Earth fall towards the Earth at the same rate.
*a _{y} = -g* ;

Wednesday 1/25: **Two kinds of numbers:** Scalars (magnitude and units)
and Vectors (magnitude, units and direction). Velocity is the vector version of
speed. Combining motion in the *x* (costant speed) and *y* (free
fall) gives us **Projectile Motion**. The ojbect moves in a parabolic arc.
High and low trajectories: (1) 45° gives the maximum range for a given
initial velocity and (2) that all other angles have a complementary angle
(90° - theta) that gives the same range (but a different time and height).
**Example**: Cannon shot at 100.m/s @ 30°. Same Range if launched at
60°, but the time of flight is longer for the 60°. **Newton's Three
Laws of Motion: Zeroeth Law** - There is such a thing as mass. **First
Law** - An object in motion tends to stay in motion, or an object at rest
tends to stay at rest, unless acted upon by a __net external force__.
**Second Law** - F=ma. **Third Law** - For every action, there is an
equal and opposite reaction, __acting on the other body__. (Forces come in
pairs, not apples.) *What keeps a book from free falling when it comes in
contact with the table?* There is a Support or Normal Force from the table
on the book -- leaving us with no net external force. (1st Law). *Why should
there be a Normal Force?* Because the book is pushing on the table and the
table is pushing on the book. (3rd Law). The Normal Force is NOT automatically
present -- you have to be in contact with a surface. The Normal Force does NOT
automatically point up -- F_{N} is perpendicular to the surface. The
Normal Force is NOT automatically equal to the weight. F_{N} = mg only
if there are no other forces in the y-direction. **Ramps or Inclined
Planes** support some but not all of the weight of an object. So it takes
less force to move an object up a ramp of height *h*, than to lift an
object directly to a height *h*. How things move (constant speed, constant
acceleration) and Why things move (Forces, momentum). Now we want to talk about
the Effort to make things move. **Work: A Physics Definition **(Work = Force
times distance in the same direction). Work = Energy. For the object on the
ramp, if we ignore friction, then while the force applied to slide the object
up a ramp is less than the force to lift it, the force for the ramp must be
applied for a longer distance -- in this case the total work being done is the
same.

Friday 1/27: **Work: A Physics Definition **W = F d. (Work = Force times
distance in the same direction). Work = Energy. SI Units are (N)(m) = (Joule) =
(J). English Units for energy include the footpound and the Calorie. There are
4196 J in 1 food Calorie. **Graviational Potential Energy** PE = mgh.
Location of h=0 is arbitrary choice. If I do work on an object to raise it to a
height h above the ground, the object gains a PE which is then available to
turn into falling motion when I let it go. If I want something to go higher, I
must do more work on it. **Rotational Motion** -- In a sense, rotational
physics is just like linear (straight-line) physics. Have a version of Newton's
Laws of Motion. The rotational force is the Torque. There is a "rotational
mass", as we have to worry about not just the mass, but how it is
distributed about the axis of rotation. Q3 Take-Home quiz due Monday 30 January
2012 in class or by 5pm.

- Sample Exam 1 Page (10 questions -- the actual Exam 1 will have 30-50 questions).

Monday 1/30: **Review** of what we have done so far. Just a few equations
-- v = d/t , x = vt , a = delta-v/delta-t , x = x_{0} + v_{0}t
+ ½at² , F = ma , w = mg , g = 9.81 m/s² , W = Fd , PE = mgh .
More concepts, including Newton's 3 Laws -- always watch out for the 3rd Law,
which involves equal and opposite forces *acting on the other object*,
rather than the same object.

- If you are using the Testing Center for Exam 1, you must (a) make an appointment at the Testing Center AND (b) send me an e-mail saying that you are taking your Exam 1 at the Testing Center at such-and-such a time, so that I know to send an exam over there.
**IMPORTANT NOTE FOR EXAM 1:**You cannot use your cellphone, tablet or computer as a calculator. Such devices and any study papers must be put away before you start your exam. Any such materials left out during the exam may result in your paper being scored as a zero. (See Dr. Phil if you are using a language translation device.)

Wednesday 2/1: Exam 1.

Friday 2/3: **Translating Linear physics to Rotational physics** (as
"easy" as changing Roman/English variables to Greek), because we
already know the Physics of Chapter 1. 360° = 2 pi radians. We are
building a table with two columns: Linear Physics on the left, Rotational
Physics on the right. Angular position, angular velocity, angular acceleration,
angular force = torque. Newton's 3 Laws of Motion applied to rotations.
"Rotational Mass" Moment of Inertia, I. Angular momentum.

Monday 2/6: Why is it important that the wind turbine blades used as the
first example in Chapter 2 be balanced? If balanced, then the
**center-of-mass** is at the rotation axis. Otherwise, the center-of-mass
will be moving as the blades turn -- wobbling and shaking -- which will require
a force -- this force adds stress to the bearings and the support structure,
weakening it and eventually causing it to fail. Note that center-of-mass and
center-of-gravity are not the same thing. The c.m. is based on how the mass is
distributed, the c.g. requires gravity. Rotational mass (moment of interia), I,
has units of kg·m². Angles in degrees or radians are
"quasi-units", which can be "wished" away as opposed to
meters or seconds -- radians and degrees are really talking about how much of a
fraction of a circle you're dealing with. Force versus Torque. Torque = radius
arm × force, but the force must be perpendicular to the radius arm or
lever arm. Torque has units of N·m. Work = torque × theta (angle),
which still has units of N·m or Joules. As with the work from a force, you
do know work unless there is (a) a torque and (b) a change in angular position
in the same direction. **Mechanical advantage**, pp. 59-60. Pulling a nail
out with a claw hammer -- the curve in the claw provides the pivot point, the
long handle gives you the mechanical advantage. Next up: Wheels. But before we
can go rolling along, we have to talk about friction...

- Why are there different kinds of screwdriver tips? A slotted screwdriver is simple, but the Phillips head pattern is designed to slip out of the slots if you apply too much torque, thus keeping you from overtightening or damaging the screwhead.
**Study note:**After requiring you to memorize the basic terms and equations for Exam 1, you should know that for Exam 2 and later, Dr. Phil will give you a short list of the equations we are using, so you don't get lost or confused.

Wednesday 2/8: To understand wheels and how they work, we have to look at
friction. **Two kinds of Friction:** Static (stationary) and Kinetic
(sliding). For any given contact surface between two materials, there are two
coefficients of friction, *µ*, one for static (µ_{s})
and one for kinetic (µ_{k}). Static is always greater than
kinetic. If I push on a book lying on a table with a small force, it does not
move -- static friction will oppose the attempt to move up to a maximum value.
After that, kinetic friction will oppose the motion. If I push on a book and it
moves across the table at a constant speed, it is not accelerating. The postive
work I am doing on the book (force and movement in same direction) is exactly
canceled by the negative work that kinetic friction does on the book (force and
movement in opposite directions). Hence the total or net work done on the book
is zero, which makes sense because the book is not accelerating. **On An
Inclined Ramp**, a book will not slide until the angle is steep enough.
Static friction can vary its value up to a maximum -- kinetic friction is a
single value. **Traction** is the available friction force. **Rubber on
concrete. **Tires rolling with friction on good roads -- this is static
friction not kinetic friction because the tires aren't sliding on the pavement.
**Anti-Lock Brakes and Traction Control.** ABS works by monitoring the
rotation of all four wheels. If one wheel begins to "lose it" and
slip on the road while braking, it will slow its rotation faster than the other
tires, so the computer releases the brake on that wheel only until it is
rolling without slipping again. This can be done many times a second, much
faster than the good old "pump your brakes to stop on ice" trick
older drivers are familiar with. Traction control uses the ABS sensors to
monitor the wheel slip during acceleration -- keeps the wheels from spinning.

- The development of the wheel, or the use of rollers under things, to move is a major advancement in human history. Though it also required the development and construction of better roads.

Friday 2/10: Return X1. **Friction and Traction and Wheels:** If your
wheels are rolling without slipping, that is you are in control and have good
traction, then a there is a connection between the rotational motion of the
wheels and the linear motion of the vehicle. Position: d = r × theta.
Speed: v = r × omega. Acceleration: a = r × alpha. A computer hard
drive might spin at 3600 RPM. An RPM is a revolution per minute. 3600 RPM is 60
revolutions per second. Each revolution is 2 pi radians. So... omega = 2 ×
pi × 60 (rad/sec) = 377 rad/sec. You can end up with very large speeds
very quickly with rotating systems. Q4 Take-Home quiz on Rotational Motion, due
on Monday 13 February 2012, in class or by 5pm.

- A early computer hard drive with 14" diameter platters, spinning at 3600 RPM or omega = 377 rad/sec. The radius r = 7" = 0.178 m. The linear speed at the edge is v = r × omega = (0.178 m)(377 rad/sec) = 67.1 m/s. This ends up being 150 mph.

Monday 2/13: Q4 questions. Inertia = momentum. Linear momentum, p = m v .
Angular momentum, L = I × omega . It takes a force to change linear
momentum, or a torque to change angular momentum. Kinetic Energy is the energy
of motion. K.E. = ½mv² . Note that if you double the speed of an
object, say a car goes from 25mph to 50mph, the linear momentum is doubled, but
the K.E. is quadrupled. This is one of the reasons why it is so hard to
increase speed -- it takes much more work to put in that kinetic energy.
Likewise, if you want to slow down, you have to do negative work and remove the
K.E. Brakes typically turned the K.E. into heat energy. Unfortunately that
means you can burn out your brakes, especially if you're driving a big rig.
Example of Runaway Truck Ramps on mountain roads to stop trucks speeding
downhill with no brakes safely. **Conserved Quantities in Physics:** linear
momentum, angular momentum and energy (K.E. + P.E.) are examples of quantities
which must be conserved in Physics. This means we have to account for them.
Collisions are very complicated, for example, but the total momentum of
"the system" must be conserved in a collision. "The system"
is the combined momentum of two vehicles, for example. If two identical cars
traveling at identical speeds are heading towards each other, then they have
p_{total} = +mv - mv = 0 before the collision, and after a head-on
collision where they form one wreck of mass (m+m), the system still has 0
momentum, so the wreck does not move. To change the total momentum or energy of
a system, one much do work from an external force.

- Q4 due date extended to Wednesday 15 February 2012.
- Exam 1 Fixes: Scantron questions #19 (coded wrong) and #33 (allowing + answer as well) have been automatically fixed.
- Exam 1 Curve available here.
- "First Look" course grades are available via the Mid-Term Grades on GoWMU. Please note that these are very rough estimated grades only.

Wednesday 2/15: A System is a group of objects taken together. So while two
cars are two objects, in order to understand what happens in a collision we can
take the two cars as a system. Now any forces doing any damage to the two cars
are *internal* to the system and don't change the motion of the system.
**Two extremes in collisions:** Totally Elastic Collision (perfect rebound,
no damage) and Totally Inelastic Collision (stick together, take damage). The
Linear momentum of the system is conserved in all types of collisions.
**Totally Inelastic Collisions: **Two identical cars heading towards each
other at the same speed, while each have momentum, the total momentum of the
system is zero. So when they smash into one wreck, the wreck has the same
momentum as the system, which is zero, so the wreck's speed is zero. **Totally
Elastic Collisions:**-- perfect rebound, no damage, conserve both momentum
and K.E.** Two special cases**: (1) same mass , v_{2i} = 0, so
v_{2f }= v_{1i} and v_{1f} = 0. All the momentum and
K.E. transfer from object 1 to object 2. (2) same mass, v_{1i} = -
v_{2i} , so they just bounce off each other and go the other way.
**Close approximations:** The Executive Time Waster. **Why you want
inelastics collisions in a wreck.** 5 mph versus 3 mph impact bumpers.
**Impulse:** Instead of writing F=ma for Newton's 2nd Law, we can change it
to F = delta-p/delta-t, and talk about the change in the initeria (momentum).
The Impulse equation is delta-p = F × delta-t. So you can get the same
change in motion by applying a large force for a short time, or a short force
for a long time. Hooke's Law (Spring
force) -- Springs exhibit a linear restoring force if you don't stretch them
too far. It's linear, so that means stretching the spring twice as far will
give you twice the force. It's a restoring force, which means the force points
back to the original position. Example: A meter stick supported on two
chalkboard erases. Like a floor, if you push down on the middle, it will bend.
Release it and it will spring back to its original position.

Friday 2/17: **Striking a Baseball with a Bat: **If you apply a force to
the center of mass, then you will cause a change in the bat's linear motion.
Apply a force away from the center of mass and you will be applying a force a
distance away from a pivot point and it will change its rotation. About 7"
from the end of the bat is the **center of percussion**, a place where the
linear force and rotational torque effects cancel each other out -- this is
much more comfortable. In addition, a baseball bat isn't perfectly rigid. Since
it can bend, it can vibrate if struck. In a vibrating object, a **node** is
where there is no apparent vibration and an **anti-node** is where there is
maximum vibration. If one holds the bat at a node near the handle, there will
be another node right by the center of percussion. This "sweet spot"
not only provides the best force on the ball, but puts less stress on the bat
and on your hands. Hit the bat away from the sweet spot and it is possible to
break a wooden bat. Conservation of Total
Mechanical Energy (T.M.E. = K.E. + P.E.). We can change height for speed
and vice versa. Conservation of T.M.E. (P.E. + K.E.) on a **roller
coaster**. Total energy limits maximum height. If speed at top of the first
hill is about zero, then this P.E. is all we have. Cannot get higher, but we
can change height for speed. **Sample Exam 2** page. (Click
here for a copy.) Q5 Take-Home quiz on Total
Inelastic Collisions, due on Monday 20 February 2012, in class or by 5pm.

Monday 2/20: **Uniform Circular Motion** -- speed is contant, velocity is
not. The velocity vector is always tangent to the circle, the centripetal
acceleration, a_{c} = v²/r, and the centripetal force,
F_{c}, are always radial inward. For a car driving around a corner on a
flat road, the centripetal force comes from the static friction between tire
and road. Best case, the centripetal acceleration is limited to a_{c} =
g. For any given radius curve, there is a maximum safe speed.
Potential Energy: Storing energy from applied
work for later. Gravitational P.E. = mgh. Location of h=0 is arbitrary choice.
Conservation Laws are very important in Physics. Conservation of
Total Mechanical Energy (T.M.E. = K.E. +
P.E.). Lose angle and directional information because energy is a scalar, not a
vector. We can change height for speed and vice versa. Conservation of T.M.E.
(P.E. + K.E.) on a **roller coaster**. Total energy limits maximum height.
If speed at top of the first hill is about zero, then this P.E. is all we have.
Cannot get higher, but we can change height for speed. **The Loop-the-Loop**
on the roller coaster requires that there be sufficient speed v (or K.E.) such
that we meet the conditions of Uniform Circular Motion at the top. The minimum
speed occurs when the downward pointing normal force from the track on the
upsidedown cars goes to zero, and the centripetal force, F_{c} =
ma_{c} = mv²/r , comes only from the weight, w = mg.
**Stability:** Some things easily fall down and some things are hard to
knock over. An object is in Stable Equilibrium when any small shift raises its
P.E. (Trying to tip over a chair will raise its center of mass, raising its
P.E. -- let it go and it tends to fall back into position.) An object is in
Unstable Equilibrium when any small shift lowers its P.E. (Trying to stand up
my cane on the desk, results in it falling over, due to lowering its center of
mass, lowering its P.E. -- the center of mass is unsupported by the bottom of
the cane if moved very far from vertical.) Examples: Rollovers,
"J-Turns" (a U-turn with a rollover), Jeep CJ vs. Jeep YJ. The
HUMVEE, which replaced the Army Jeep, is much wider and has a low center of
gravity -- very hard to rollover -- as opposed to a person on a riding
lawnmower.

- Q5 now due on Wednesday 22 February 2012.

Wednesday 2/22: What's the opposite of a collision? An explosion. Or recoil.
Example: When a gun is fired, the bullet goes one way and the gun barrel goes
the other way. Example: A pitcher on ice skates at rest -- when he hurls a
fastball to the right, he goes to the left. Total momentum of the system
remains constant (in this case, zero). The Rocket
Equation -- uses conservation of momentum: A mass of burning fuel moves one
way at an exhaust speed while the remaining mass goes the other way. **Orbital
mechanics**: Each radius of circular orbit has a different value of g(r). As
*r* increases, *v* decreases and *T* increases. For Low Earth
Orbit, such as the International Space Station, about 250 miles up, the orbital
speed is about 17,000 mph (8000 m/s) and the orbital period T is about 90
minutes. For the Moon, the period is around 28 days at a quarter of a million
miles away. Geosynchronous orbits occur *T = 1 day* exactly, and for
geosynchronous communications sattelites, the orbit must be directly over the
equator -- hence all sattelite dishes in the U.S. face south

- Solution to first Sample Exam 2 is posted here.
- Wikipedia discusses The New York Times and Robert Goddard in 1920 (and 1969).

Friday 2/24: **Dr. Phil has canceled today's classes
due to weather / illness. Updates later today**.

- Two handouts have been emailed to the dept. for copying and handing out at Noon. (This apparently did not happen on 2/24 -- handouts given on Monday 2/27.) You can download them here now:
- Second Sample Exam 2 questions. (Click here for a copy.)
- Topic 2 worksheet -- instead of the next quiz -- more points for you! (Click here for a copy.)
- Additional comments on Topic 2 worksheet will be posted here later today.

Monday 2/27: Review for X2. A rocket uses conservation of momentum: A mass
of burning fuel moves one way at an exhaust speed while the remaining mass goes
the other way. For our typical rocket in the Topic 2 worksheet, 90% of the mass
is fuel/oxidizer and 10% is the structure and engines and tanks and payload.
**Why multi-stage rockets? **Because even 10% of the mass of a single-stage
"big dumb rocket" can be a lot of dead weight to try to lift into
space. So by breaking up the rocket into pieces, each one with 90% fuel and 10%
structure, we can throw away an empty stage and start with a smaller, lighter
rocket. Even the Space Shuttle was really a multi-stage rocket -- you had the
spaceplane itself, an external fuel tank so that we didn't have to carry the
fuel tank into orbit, plus the big external solid rocket boosters that only
burn for the first few minutes. **The deLaval Nozzle:** It seems so simple
at first. Just burn the fuel and convert it into flame and thrust, and away the
rocket goes. But if you have a converging-diverging engine nozzle, you first
compress the exhaust to make it go faster, then let it expand and push away
from the rocket -- you get much better performance. The shape of the engine
bell -- the cone where the exhaust comes out -- can be optimized for use in the
lower, thicker atmosphere or out in the vacuum of space. So the different
engines of a multi-stage rocket can be tuned to work better in their
environments. **Newton's Universal Law of Gravity** (or
Newton's Law of Universal Gravity). We have
been using w=mg to find the force of gravity(weight) near the Earth's surface.
But once you are no longer near the surface, gravity weakens. It turns out that
gravity requires two masses, either *m _{1}* and

- The purpose of the Topic 2 worksheet is to simulate what happens to a rocket, by calculating what happens to the burnt fuel (thrust) and the remaining mass of the rocket in small chunks of time. Because the mass of the rocket decreases while the force remains the same, the acceleration increases. We can calculate the average acceleration over each 10 seconds by finding the change in the speed v from one time to the next, divided by 10 seconds.
- If we used the Rocket Equation, we would get this value for the final speed. Your answer in the worksheet will not quite be the same.
- The Topic 2 worksheet is NOW DUE: Wednesday 14 March 2012 -- after Spring Break.
- NOTE: Winter Ice Storm Warning from Tuesday 10pm to Wednesday 7pm. Plan accordingly, keep track of the weather.
**NOTE:**It was just pointed out to me that there was an error in the Answers: 17 should be C – the speed is constant, though the velocity is not constant., not D.

Wednesday 2/29: Exam 2.

Friday 3/2: WMU SPIRIT DAY -- No Classes.

- WMU Spring break next week. Our next class will be Monday 12 March 2012.

SPRING BREAK -- NO CLASSES.

- IF YOU MISSED EXAM 2 Send Dr. Phil an email as soon as possible -- Make-Ups are scheduled for Monday 12 March 2012 after 2:30pm, Tuesday 13 March 2012 at 11am, Noon, or after 2:30pm.
- REMEMBER Topic 2 Worksheet is due on Wednesday 14 March 2012.
- Mid-Term course grades are available via the Mid-Term Grades on GoWMU. Please note that these are still rough estimated grades only. If you haven't yet taken Exam 2, then your Exam 1 grade was used for an estimated grade.

Monday 3/12: Reset. **Demo: The Cartesian Diver** -- we need to
understand the Physics to know why I can make the "diver" in the
bottle sink or rise at my command. (We'll come back to this later.) **Or
Balloons: **You can buy a helium filled balloon and it will want to rise up
in the air, but a balloon filled with air from your breath will want to sink to
the floor. **Three Classical States of Matter**: Solid, Liquid, Gas. Gas
molecules are free to move around, having totally elastic collisions with other
atoms and molecules. When they bounce off the walls of a container or a
balloon, they are applying a force. All those forces are extended over the
area. And Pressure = Force ÷ Area, so the gas applies a pressure outward.
Meanwhile the outside air and the elastic material of the balloon apply an
equal pressure inward. Heating the air inside the balloon makes the gas
molecules move faster and expands the balloon. **Extended Objects:** Mass
occupies a volume and shape. Mass-to-Volume
Ratio (Density). NOTE: Do not confuse the Density of the Materials with the
Mass-to-Volume Ratio of the OBJECT. It's not what the object is made out of,
it's the mass and volume of the whole object. A ship made be made of steel, but
a ship is also mainly just air, like our lecture hall -- otherwise you couldn't
get inside the ship. Density of Water built into the SI metric system (1
gram/cm³ = 1000 kg/m³). Floating on the Surface: Mass-to-Volume Ratio
of the boat < Mass-to-Volume Ratio of the Liquid. Or for a balloon to rise,
the Mass-to-Volume Ratio of the balloon < Mass-to-Volume Ratio of the air
(typically 1.29 kg/m³). So using helium, instead of air, inside the
balloon lowers the Mass-to-Volume Ratio of the whole balloon (less mass). Or
heating air inside the balloon expands the balloon and increases the volume.
From a question is class -- the pressure of the air is lower at higher
altitudes and the air gets thinner. That's because the air pressure is based on
supporting the weight of the air above you. Less atmosphere above you the
higher you go, so lower pressure. A balloon will rise at first, but eventually
it will reach an Equilibrium -- a balance -- where the Mass-to-Volume Ratio of
the balloon equals the density of the air at that altitude. To go up further
you have to either lower the mass or heat the balloon and expand it.

- Remember Topic 2 Worksheet. Due Wednesday 14 March 2012, in class or by 5pm.
- Remember Topic 1 paper. Due on Friday 30 March 2012 --OR-- Monday 2 April 2012 -- your choice.
- Optional Draft Topic 1 paper review, if you are interested. Last day to turn in a Draft is Monday 26 March 2012, but you can turn in a Draft any time before then.
- Battle Creek Field of Flight Air Show and Balloon Festival. Hot air balloons warming up:

- NOTE: There are
__no labs__for PHYS-1000 the rest of this week (12-16 March 2012). If you*had*lab on Tuesday, then you won't have lab next week.

Wednesday 3/14: (Happy Pi Day! 3.14...) **Three Classical States of
Matter**: Solid, Liquid, Gas. Combinations: Condensed Matter (covers both
Solids and Liquids) and Fluids (covers both Liquids and Gasses). **Two Extreme
States of Matter**: Plasma (electrons stripped off, high temperature),
Cryogenics (extreme cold, odd behavior). Pressure
= Force / Area. SI unit: Pascal (Pa). **Example**: Squeezing a thumbtack
between thumb and forefinger. 1 Pa = 1 N/m², but Pascals are very small,
so we get a lot of them. One Atmosphere standard air pressure = 1 atm. = 14.7
psi = 101,300 Pa. (The book rounds this off to 100,000 Pa.) **Buoyant
Force** = Weight of the Boat = Weight of the Water Displaced by the Submerged
Part of the Boat. (Similar for a Balloon in Air.) Because the Mass of the Boat
= Mass of the Water Displaced, we can use the equation for Mass-to-Volume
Ratio(rho) and explain why for a boat to float that rho_{Boat} <
rho_{Water}. **Archimedes and Eureka!** (I found it!) **Absolute
(total) Pressure vs. Gauge Pressure** (difference between two readings).

- Water is unusual in that the mass-to-volume ratio of ice (solid) is LESS than liquid water, so ice floats. Ice which floats doesn't add to volume of water when it melts, but grounded ice (non-floating) does. This is one of the reasons why people worry about what global warming might do to the great ice sheets around the world.

Friday 3/16: Return X2. (Lecture notes coming...) **Temperature &
Heat.** Heat = Energy. Two objects in thermal contact, exchange heat energy,
Q. If net heat exchange is zero, the two objects are at the same temperature.
**Temperature Scales**: °F, °C and
K (Kelvins).

- Quiz 6 is a Take-Home quiz on Floating, handed out Friday 16 March 2012, and due on Wednesday 21 March 2012.
**There was a question about a possible conflict between a Sample Exam 2 question and one from the actual Exam 2.**I believe it was question 16 on Exam 2 (Sample Exam 2 question 12). -- There is no conflict, the answers in both solutions are correct, because they are NOT the same question.

Monday 3/19: Recall (1) Pressure = Force ÷ Area, (2) Conservation of
Energy (PE+KE), (3) mass-to-volume ratio = mass ÷ Volume. **Smooth Fluid
Flow: **Pressure from a column of liquid looks like P.E. Create a Kinetic
Pressure term which looks like K.E. and add in the base pressure for total
pressure to create Bernoulli's Equation and the
Continuity Equation. Using a column of liquid to make a **barometer** to
measure air pressure. Switch from water to mercury (Liquid mercury (Hg)
mass-to-volume ratio = 13,600 kg/m³) changes h at 1 atm. from 10.33 m to
0.759m. The **aneroid barometer**. Water Tower
and the Faucet Problem. Why the water tower needs a vent. Want Smooth
Continuous Flow, not Turbulent Flow or Viscous Flow. *Flow rate = Volume /
time = Cross-sectional Area × Speed*.

Wednesday 3/21: Bernoulli's Equation and the
Continuity Equation. Want Smooth Continuous Flow, not Turbulent Flow or
Viscous Flow. *Flow rate = Volume / time = Cross-sectional Area ×
Speed*. The faster the fluid flow, the lower the Pressure. **Example**:
The aspirator -- a vacuum pump with no moving parts. **Example**: Air flow
around a wing. (Faster air over top means lower pressure on top, so net force
is up -- Lift.) **Spoilers** -- doors open in wing to allow air to pass
between upper and lower surfaces, thus "spoiling the lift" by
eliminating the pressure difference. Why the Mackinac Bridge has grates on the
inside north- and soundbound lanes. **The Cartesian Diver Revisited:** The
diver is open at the bottom, closed on top, and has a bubble of air in it.
Squeezing the sealed bottle increases the pressure inside the bottle, driving
more water into the diver, raising its mass-to-volume ratio (density) and
causing it to sink.

- If you want to read about turbulent or viscous fluid flow, you can read Chapter 6 of your textbook -- otherwise we are skipping Chapter 6.

Friday 3/23: **Heat Energy (Q)** and Temperature Change & Phase Change. Heat
energy can move by Conduction (contact), Convection (transport of material,
typcially gas or liquid, in a heating/cooling, rising/falling cycle) and
Radiation (light). When you feel the warmth of the Sun, you're really detecting
the invisible Infrared (IR) light from sunlight. Block the IR light and the
remaining visible light does not feel warm. Add/remove Heat Energy Q will
raise/lower the temperature of a material using the **Specific Heat**
(J/kg·°C) for objects of mass *m*. Add/remove Heat Energy Q will
change its phase between solid-liquid-gas using the **Latent Heat of
Fusion**, *L _{f}*, between solids and liquids, or the

- Not giving you a Take-Home quiz over the weekend, so you can read your book or write your Topic 1 paper...

Monday 3/26: **Latent Heat of Fusion** versus **Latent Heat of
Vaporization** in water. "A watched pot never boils". Water will
boil in a pan for a long time. Indeed, the latent heat of vaporization of
water, 2,260,000 J/kg is huge and important for cooking and putting out many
fires. Those bubbles in boiling water are in some ways similar to the bubbles
in carbonated water -- they require a **nucleation site** (seed) to form on
. If you have a really smooth glass container and heat water in a microwave,
you may get superheated water -- any disturbance will cause the water to
suddenly and violently erupt and change phase. **The Whistling Tea Kettle:**
The white cloud is condensing water vapor as the steam expands and is cooled in
the air. The actual steam (gaseous water) is invisible, like air, and is in a
small jet coming out of the hole -- it will give you a severe burn injury!
**Thermal Conductivity** -- depends on the material. Heat Flow = (Thermal
Conductivity × delta-T × Area) ÷ (gap distance) =
(k)(delta-T)(A) / d . Heat flow is in J/sec = Watts, the same as power. Some
materials, like gold, conduct heat very well -- gold "feels" nice on
the skin because it quickly gets warm to the touch. Some materials don't
conduct heat well -- some of these insulators may use air to bulk up the volume
and decrease the amount of material that can conduct heat. For example, warm
thermal blankets and quilts, or down or fiberfill winter coats.
**Thermodyanmics (Heat + Motion)** -- Moving heat energy Q around. The
Laws of Thermodynamics. Zeroeth Law -- There
is such a thing as temperature. First Law -- Conservation of energy. Second Law
-- One cannot extract useful work from a cyclic mechanical system without
wasting some energy. Entropy examples -- It takes work to clean or restore
things. Left to themselves, everything falls apart.

*Note the gap between the whole for the whistle and the white cloud of condensing water vapor.*

Wednesday 3/28: The Heat Engine and
Three Efficiencies (Actual, Carnot and 2nd
Law). Fuel Economy (miles per gallon) is not an Efficiency. There is no
conspiracy to keep big 100 m.p.g. cars out of our hands. To use less fuel, do
less work. Reverse the arrows in the Heat Engine and you get a
**Refrigerator**. **Sample Exam 3** page. (Click
here for a copy.) Q7 Take-Home quiz on Heat
Engines, due on Monday 2 April 2012.

- The actual efficiency turns out to be low. One way to raise the efficiency
is to change the temperatures of the reservoirs -- the Carnot effciency
(theoretical best case) can be raised by either raising T
_{H}or lowering T_{C}. - Reminder: Topic 1 Papers can be turned in without penalty on Friday 30 March 2012 or on Monday 2 April 2012, up until 5pm in the Physics Office.

Friday 3/30: **Final thoughts about Heat Engines and Refrigerators:**
When an engine is cold, T_{H} = T_{C}, and the Carnot
efficiency is zero. You have to establish a temperature difference between the
hot and cold reservoirs in order to extract useful work, W. Especially with the
larger blocks of truck diesels -- have to warm up the engine to get anything
out of them. Glow plugs -- heating elements used to prewarm the cylinders in
diesel engines and soon to preheat catalytic converters in your anti-pollution
system to reduce the pollution from the first 60 seconds of engine running.
**End of Exam 3 material**. Waves: **Single Pulse vs.
Repeating Waves**. The motion of the material vs. the apparent motion of the
wave. For Repeating Waves, we have a Repeat
Length (wavelength) and a Repeat Time (Period). Frequency = 1/Period. Wave
speed = frequency × wavelength. The speed of sound in air: 334 m/s @
0°C and 344 m/s @ 20°C. **Waves and Resonance.**
Standing Waves on a string.
Fundamental, First Overtone, Second Overtone, etc.

- On Monday we'll do a series of demos of waves and resonance -- and you'll see that you'll actually SEE what Dr. Phil put on the board today!
- Note that some of the material in Chapter 9 on ocean tides and gravity, we've already talked about.

- Solution to Sample Exam 3 Set here.

Monday 4/2: **DEMO DAY:** Waves: Single Pulse vs. Repeating
Waves. The motion of the material vs. the apparent motion of the wave. For
Repeating Waves, we have a Repeat Length
(wavelength) and a Repeat Time (Period). Frequency = 1/Period. Wave speed =
frequency x wavelength. **Demonstration**: the Slinky shows both
longintudinal (string type) and transverse waves (sound type). Waves and
Resonance continued. Standing Waves on
a string. Fundamental, First Overtone, Second Overtone, etc.
**Demonstration**: First and higher overtones on a string driven by a saber
saw. (Can't see the Fundamental on the saber saw demo, because the tension
required usually breaks the string.) Standing Waves in a tube. **Demo:
**Getting Fundamental and overtones from twirling a plastic tube open at both
ends. **Demo**: Variable length organ pipe -- Fundamental and First Overtone
(overblowing), varying pitch (musical note) by changing length of tube open at
only one end. Tuning forks, resonance boxes. **Demo**: Tuning forks require
both tines to work -- the "sound of a tuning fork with one tine" is
that of silence. Musical instruments: Accoustic string instruments have a
resonance box. Brass instruments start from the "natural trumpet",
which can only play the fundamental and overtones for the pipe. Woodwind
instruments get more complicated. **Beat frequencies** occur when two sounds
have almost the same frequency -- get a distinctive *wah-wah-wah *sound,
whose *beat frequency = | f _{1} - f_{2} |* .

- Monday 2 April 2012 is the last day to turn in your Topic 1 Book Report without penalty. Papers turned in on Tuesday or later will be subject to a 10,000 point/day deduction.
- Reminder: If you had Dr. Phil evaluate a Draft Paper, (a) you'll have to about Wednesday to get your Final Paper turned in and (b) you need to turn in the Draft Paper that was marked up as well. If you forgot about the Draft Paper, you can turn that in at any time in the next couple of days. Thanks!
- UPDATES: (1) Second Sample Exam 3 and its solution are posted; (2) Solution to Quiz 7 is posted.

Wednesday 4/4: Exam 3.

**PHYS-1000 LAB:**If I understand it correctly, this was the last week of labs for PHYS-1000. So that should free up some time in your schedule -- a welcome relief this time of the semester!- YES -- We have class on both Friday 6 April 2012 and Monday 9 April 2012.

Friday 4/6: The speed of sound in air. **Sonic Booms** and other
shockwaves. Bullwhip stories. Waves take
time to travel. Sound takes time to travel. The speed of sound in helium is
greater than the speed of sound in air. When you talk, you make sounds using
the vocal cords which are based on wavelength. But your hearing is based on
frequency. So when you talk in helium, it sounds high pitched and squeaky. The
perils of SCUBA diving. The Realization that **Electricity and Magnetism**
were part of the same Electromagnetic Force was a great triumph of 19th century
physics. Greeks knew about static electricity -- build up charge and get
sparks. ~~Demo: Static electricity~~. The Two-Fluid Model of
Static Electricity (A & B), to account for the two types of behavior noted.
Franklin's One-Fluid Model of Electricity. Occam's Razor: If you can't decide
between two competing ideas for how Nature works, take the simpler model.
Real Electric Charges. Two charges: like
charges repel, unlike (opposite) charges attract. Coulomb's Law looks like
Newton's Law of Universal Gravity. **Four
Fundamental Forces in Nature:** Gravity, E & M, Weak Nuclear Force,
Strong Nuclear Force. **The Hydrogen Atom**. Gravity loses to Electric Force by a factor of 200
million dectillion (!!!). Likewise, the two
protons in the nucleus of the Helium Atom require the Strong Nuclear Force to
overcome the 231 N electric repulsion. **Isotopes** are the same element
(proton number Z), but with different numbers of neutrons (N). Some isotopes
are stable, some are unstable and undergo radioactive decay. Protons repel
protons, neutrons ignore neutrons -- but protons WILL stick to neutrons with
the Strong Nuclear Force. If we didn't have the Strong Nuclear Force making the
Electric Force irrelevent inside the nucleus, then the only element in the
universe would be hydrogen.

- The old party trick of breathing in helium from a helium balloon can be very dangerous, because you are displacing breathable oxygen from your lungs. Likewise, pure oxygen at high pressure is very dangerous. So to avoid nitrogen bubbles in the blood while Scuba diving, you either need to make a timed-and-delayed ascent or switch to a gas mixture with some oxygen and no nitrogen. But helium-oxygen mixtures must be carefully regulated by a trained person.
**Catastrophic Resonance Video:**The Tacoma-Narrows Bridge Disaster. Page down to see the video -- it has NOT been speeded up. (Note: The Mackinaw Bridge cannot do this.)

Reminder that ICES Student Course Evaluations are available now online via GoWMU .

Monday 4/9: Real Electric Charges. Two
charges: like charges repel, unlike (opposite) charges attract.
Coulomb's Law looks like
Newton's Law of Universal Gravity. 1 Coulomb
of charge is an enormous amount of charge. Two 1.00 C charges separated by 1.00
meters have a force of nine-billion Newtons acting on each other. **How does
q _{1} know that q_{2} is there?** -- "Action at a
Distance" -- Gravity and the Electric Force are not contact forces. The
mathematical construct of the Electric Field. E is not an observable quantity.
(Side example: Methods of measuring speed v, do not directly measure speed v.)
Electric Fields, E = k q / r² (E-field from one point charge) and
F

- I got a correction to what I'd been told -- PHYS-1000 Lab DOES meet this week (9-13 April 2012). -- Dr. Phil

Wednesday 4/11: Return X3. Update on remaining class time, discussion of
format of the Final Exam. **Black Box devices** -- whether electronic or
mechanical (iPad to new car) -- often make it difficult to see "How Things
Work". Using Static Charges with Xerox copiers, laser printers, inkjet
printers.

- Reminder: Apr. 24 Tue - Final Exam 2:45-4:45pm (2 hours)

Friday 4/13: **D.C. Electrical circuits.** Ohm's Law. V=IR form. **The Simplest
Circuit:** Battery, wires, load (resistor). Power dissipated by Joule heating
in a resistor. P = I V . Series and Parallel
Resistors. Two devices connected together in a circuit can only be
connected two ways: series or parallel. In **Series**, same current, share
voltage. Equivalent resistance is always larger. In **Parallel**, same
voltage, share current. Equivalent resistance is always smaller. **Resistor
Network Reduction.** The battery only "sees" an equivalent
resistor, which controls its current. So we could (but won't) reduce a resistor
network to a single equivalent resistance, go back and fill in the table for V
= I R and then P = I V. In the example sketched in class, Resistor
R_{1} sees the largest current and dissipates the largest amount of
energy per second (Power in Watts). This means it is also the most vulnerable.
Story of radio "repair" call from 4,000,000,000 miles. Topic 3 is a
worksheet on looking at Real World Data, due on Friday 20 April 2012. (Click
here for a copy.) Q9 Take-Home quiz on
Electrical Circuits, due on Wednesday 18 April 2012.

**Note**: If Q9 had the two light bulbs mounted in Series, instead of Parallel, they would both glow much dimmer than usual, because neither would be operating at full voltage. Also, although we didn't talk about it, the resistance R of light bulbs is not a constant -- it changes as the bulb heats up. So it makes a huge different to a light bulb whether it is hooked up in series or parallel.**Reminder about The Last Quiz:**Quiz 10 will be a Check-Out Form that you will fill out when you turn in your Final Exam -- you won't have to study for this one.**Regarding Topic 3**: Remember that 2 hours and 20 minutes is 2.20 hours, but 2 20/60 hours or 2.33 hours. So calculate accordingly. Also, although this is real world data, I actually simplified the time info for the four trips to make it easier to see. I don't really have a gas station in my driveway. (grin) And for the record, yes, I do spend a lot of hours on the road every day, and I do go get the gas tank refilled about every other day. And yes, that's a lot of money for what is supposed to be a part-time teaching job. What can I say? I really am interested in teaching Physics to you.**NEED TO KNOW THE EXAM 3 CURVE?**Click here.

Monday 4/16: The Great 19th Century Debate: **Is Light a Particle or a
Wave**? The answer is "YES" -- the "wavicle" is both a
wave (with a frequency and wavelength) and a particle (the photon is a discrete
bundle of energy, E = h f, where h = Planck's constant = 6.626 × 10^{ -34} J·sec and f =
frequency in Hz.) Wave-Particle Duality did not seem obvious at the time. The
**Electromagnetic Wave** travels at the speed of light. c = 300,000,000 m/s
= 186,000 miles/sec. **Electromagnetic Spectrum**: Visible light
(ROYGBIV=red orange yellow green blue indigo violet). Visible light is 400nm to
750nm (4000 angstroms to 7500 angstroms). Cannot "see" atoms with
visable light, because the atom is about 1 angstrom across (1.00E-10 meters).
The visible light wave is too large to see something that small. Frequences
LOWER and wavelengths LONGER than visible light (IR infrared, Microwave, Radio
waves, ELF extremely low frequency). Microwave ovens have metal screens in
their windows -- the centimeter-range sized EM waves cannot see the
"small" holes in the screen, so they bounce off the window as if it
were just like the metal in the other five walls. Discussion of how microwave
ovens "cook" food. Frequencies HIGHER and wavelengths SHORTER than
visible light (UV ultraviolet, X-rays, Gamma rays). UV-A and UV-B, tanning and
the problem of cheap sunglasses. Images inside object using X-rays passing
through or scattering or being absorbed by the object. Why Superman's X-ray
vision cannot work -- because everyday situations are "dark" in the
X-ray band, thankfully!

- With a double-rainbow, the second one is fainter and the color order is reversed, because there are two reflections inside each raindrop and not one. We see the spectrum of pure colors because of dispersion -- the tiny differences in the index of refraction with each different wavelength of light.

Wednesday 4/18: **Optics**: When a straight light ray hits a boundary
between one material and another, three things can happen: Reflection,
Absorption, Transmission. The Law of
Reflection. When light rays strike a rough surface, you get Scattering,
which is reflections off many different angles. People tend to not like
photographs of themselves, because they are used to seeing their mirror image
-- their normal image, which the rest of us sees, looks "wrong".
**The Optical Lever **-- move a mirror by 10° and the reflected ray
moves by 20°. (Dr. Phil's theory on the origin of "seven years of bad
luck for breaking a mirror".) The speed of light in vacuum is c =
300,000,000 m/s. The speed of light in a medium (air, water, glass, etc.)
c_{m} < c. The index of refraction of a medium is n_{m} = c
÷ c_{m} and is always greater than or equal to 1. n_{air}
is approximately 1. n_{water }= 1.33. For ordinary glass,
n_{glass} = 1.50. The Law of Refraction -
Snell's Law. For our purposes, Snell's Law tells us that if light goes from
a lower index of refraction to a higher index, then the angle must get smaller.
Light bent at the interface between two media, because the speed of light
changes in the media. (Analogy: If you are driving along the road and your
right tires go off onto the soft shoulder, they can't go as fast and the car
turns towards the shoulder until all four wheels are driving off the road.) If
going from an high index of refraction media to a lower index media ONLY, have
a chance for Total Internal Reflection
(T.I.R.). This is a "perfect" reflection, better than a mirror. Used
in high-end optical systems instead of mirrors. Also useful in fiber optics
cables.

- Those in attendance today had the choice of Last New Material: Optics or Nuclear Physics. By a squeaker -- and lots of non-voting -- Optics won. As far as the Final Exam goes, if we didn't cover it in lecture, we didn't cover it.
- A mirage is caused by slight changes in the index of refraction of air, due to heating or cooling, allowing you to either see reflections of the sky or "lensing" where you can see distant objects not normally seen.
- NOTE: In Monday's lecture I wrote down Planck's constant off the top of my
head -- and got it wrong. h = Planck's constant = 6.626
× 10
^{ -34}J·sec . - Finals Week Office Hours are now posted.

Friday 4/20: THE LAST CLASS.