*Updated: 03 May 2011 Tuesday.*

FINAL EXAM RESULTS: n 73 73 hi 184 200 lo 80 100 ave 150 160 Average Star= 18,000

- All quiz solutions (2-22) are posted now.
- The Late Final Exam is Friday 29 April 2011, 11:00am-1:00pm, in Bradley Commons next to Dr. Phil's office. Send Dr. Phil and e-mail if you plan on coming to the Late Final Exam, so I can plan to print up enough copies of XFL.

Monday 4/25: Office hours.

Tuesday 4/26: Office hours.

Wednesday 4/27: FINAL EXAM (2 HOURS) 2:45-4:45pm.Office hours.

Thursday 4/28: NOTE: No office hours.

Friday 4/29: LATE FINAL EXAM (2 HOURS) 11am-1pm, come to Dr. Phil's office. See: Office hours.

Monday 5/2: Office hours.

Tuesday 5/3: Grades will be done by Noon.

- Week 1 Checklist.

Monday 1/10: Class begins. The nature of studying Physics. Science education in the United States. Natural Philosophy. The Circle of Physics. Aristotle and the Greek Philosophers. Observation vs. Experiment - Dropping the book and the piece of paper (2 views).

Tuesday 1/11: Observation vs. Experiment - Zeno's Paradoxes. Theory and Measurement. "Speed Limit 70" First Equation: Speed = Distance / Time. In terms of variables, a classic three-variable equation: v = d / t . Development of Speed equation for Constant or Average Speed. An Equation is a contract -- the left and right sides must be the same thing and all terms must have the same units. Distribute syllabus.

- The Apollo 15 Hammer and Falcon Feather Drop webpage. QuickTime movie: (low res 8MB, higher res 80MB)
- Please note there will not be classes on Monday 17 January 2011 as Western observes the commemoration of Dr. Martin Luther King, Jr.-- MLK Day activities start on Friday 14 January 2011.

Wednesday 1/12: Our equations so far: *v = d /t* ; *x = x _{0}
+ v t* (for v = constant or average ONLY). Discussion of Formula Cards.
delta-x = x

Thursday 1/13: Speed. 60 m.p.h. = "A Mile A Minute". (1848: The Antelope) SI Metric System. What do we mean by Measurements? What is "1 m/s"? We need a few benchmark values to compare English and SI Metric quantities. 60 m.p.h. = 26.8 m/s. 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 (9.59 seconds) and World (9.58 seconds) record holder.) 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).

Friday 1/14: A simplified trip to the store --
The S-Shaped Curve.
Acceleration. a = dv/dt =
d^{2}x/dt^{2}. Integrating to find the set of Kinematic
Equations for constant acceleration. Kinematic
Equations for Constant Acceleration. The Equation Without Time -- Avoiding
the Quadradic Formula. The fundamental equations of motion are based on the
calculus: x, v and a are related by derivatives (slopes) and integrals (areas
under the curve). v = dx/dt, a = dv/dt = d²x/dt². There are higher
derivatives. For example, jerk is j = da/dt = d²v/dt² =
d³x/dt³. 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). What do we mean
by a = 1 meter/sec² ? You cannot accelerate at 1 m/s² for very long.
**How do we solve kinematic problems?** There are six kinematic variables
for constant acceleration in 1-D: *x _{0}*,

- Remember, no classes on Monday due to MLK Day Activities.
- Quiz 2 will be an in-class quiz on Tuesday 18 January 2011 on speed = distance/time. This will be our only non-metric quiz.
- Looking for something to do this weekend?
**Try this Algebra Check:**Use the 1st and 2nd kinematic equations for constant acceleration to find the Equation Without Time.

- Week 2 Checklist.
- Sample Book Problems (not to be handed in):
**Chapter 1**: 1, 9 11, 25, 31, 32.**Chapter 2**: 1, 5, 21, 47, 57.*NOTE: these are from the WMU 8th edition.* - Quiz 2 will be an in-class quiz on Tuesday 18 January 2011 on speed = distance/time. This will be our only non-metric quiz.
- NOTE: Dr. Phil has an appointment with the new PIO rep at 11:30am-Noon on Tuesday 18 January 2011.

Monday 1/17: MLK Day -- No Classes.

Tuesday 1/18: **Types of Motion: **No Motion (v=0, a=0), Uniform Motion
(v=constant, a=0), Constant Acceleration (a=constant). The fundamental
equations of motion are based on the calculus: x, v and a are related by
derivatives (slopes) and integrals (areas under the curve). v = dx/dt, a =
dv/dt = d²x/dt². There are higher derivatives. For example, jerk is j
= da/dt = d²v/dt² = d³x/dt³. Note that our simplified trip
to the store we had sudden changes in acceleration -- this would create
infinite slopes in da/dt. The real world is smoother -- accelerations tend to
be turned on and off over a brief time, not instantaneously. However, our
approximation that acceleration is strictly constant turns out to work pretty
well for many problems, so our simplification remains useful. On the other
hand, we could have a seventh derivative of position with respect to time.
Comments on Star Problems on our Exams. Back to our constant (or average)
acceleration problems. Example: acceleration and time for a bullet fired from a
rifle. Q2 in-class.

- The example in class today: (1) A bullet in a rifle starts from rest and
when fired is moving at a muzzle speed of 400. m/s at the end of a 1.00 meter
rifle barrel. Find
*a*. Here we used the Equation Without Time, the 4th Kinematic Equation, and get a very large answer -- 80,000 m/s²! And a very small answer for*t*-- we can find the time*t*using either the 1st or 2nd Kinematic Equation -- get the same answer to within 3 sig. figs. Using another equation to check your answers can be very helpful, especially early on. - The Physics Help Room opened for business on Tuesday 18 January 2011. The Physics Help Room is located in 0077 Rood Hall, sort of behind and underneath our lecture hall. If you go down the stairs near 1110 Rood, 0077 Rood will be right there when you get to the basement. Hours will be 9am to 4pm Monday through Friday, and Physics faculty and grad students will be on duty for most of those hours. Dr. Phil's hour will be Thursday at Noon, starting Thursday 20 January 2011.
- The Real World: Go to the Library, the magazine section of a book or
grocery store, or a personal collection. Look for automobile magazines like
*Road and Track*,*Car and Driver*, etc. Perhaps about 1/3 of the way in, look for a performance review of a new car with a graph of v vs. t under maximum acceleration conditions on a track. Note how the graph looks, as opposed to our Time Regions I and II in our S-Shaped Curve simplified trip. Do you understand why the real graph looks like it does? - Quiz 3 will be an in-class quiz on Friday 21 January 2011 on the Kinematic Equations for Constant Acceleration. Most or all of the remaining quizzes this semester will be take-home.
- NOTE: If you do NOT have a passing grade from the Prerequisite Courses, you WILL be dropped from PHYS-2050.

Wednesday 1/19: The P-O-R (Press-On-Regardless) road rally problem.
"You can't average averages." The only way to find the speed required
for the rest of the trip is *v = distance remaining / time remaining*.
Just like part (c) in Quiz 2. Demo: Our class webpages and what you can find on
them. Free fall, ignoring air resistance -- all objects near the surface of the
Earth will fall at an acceleration *g = 9.81 m/s²*. Re-writing the
Kinematic Equations for *x*, *y* and *y pre-loaded with
a _{y} = -g*. Note that the

Thursday 1/20: **Motion in Two-Dimensions**: *x* and *y*
directions are perpendicular to each other and are independent of each other.
You may be able to break a two-dimensional problem down into two
one-dimensional problems, connected by time, which you can already solve.
Example: The guy with the fedora and the cigar. There are 6 variables from the
first dimension (x_{0}, x, v_{0x}, v_{x},
a_{x}, t), but only 5 from the second (y_{0}, y,
v_{0y}, v_{y}, a_{y}), because time is the same. We
need to find v_{0x} , but we don't know the time. So we can find the
time it takes to fall from the top of the building in the *y*-problem,
then use that in the *x*-problem. Another problem with two motions linked
by time: Classic Simple Pursuit (Cop and the Speeder). Same Place at the Same
Time. *x _{1 }= x_{2} . Note that in our algebra for car 1 and
car 2, we cancelled a factor of t at one point -- this represents t = 0, which
by definition is also a solution*. But... because our problem is

- Explosion of NASA/USAF X-15-3 with XLR99 engine on test stand.
- Rusty on your math -- algebra, geometry, calculus? Check out the Appendices at the back of your book. There's a whole quick review of the math needed for this course in Appendix B.
- Quiz 3 will be an in-class quiz on Friday 21 January 2011 on the Kinematic Equations for Constant Acceleration.

Friday 1/21: Quiz 3 in class.

- Week 3 Checklist.

Monday 1/24: Motion in the *y*-direction. The consequences of Falling
Down... ...and Falling Up. The Turning Point ( v=0 but a = -g during whole
flight). The illusion of "hanging up there in the air" at the
turning point.

- Rusty on your math -- algebra, geometry, calculus? Check out the Appendices at the back of your book. There's a whole quick review of the math needed for this course in Appendix B.
- Quiz 4 will be a take-home quiz handed out on Tuesday 25 January 2001 on Falling Up and Falling Down, and due Friday 28 January 2011, in class or by 5pm.

Tuesday 1/25: More about Exams. Two kinds of numbers: Scalars (magnitude and
units) and Vectors (magnitude, units and direction). Adding and subtracting
vectors: Graphical method. To
generate an analytical method, we first need to look at some Trigonometry.
Right Triangles: Sum of the interior angles of
any triangle is 180°, Pythagorean Theorem (a² + b² = c²).
Standard Angle (start at positive *x*-axis and go counterclockwise).
Standard Form: 5.00m @ 30°. Practical Trigonometry.
S`OH`C`AH`T`OA`. First Sample Exam 1 (Click
here for a copy.) Quiz 4 take-home quiz on
Falling Up and Falling Down plus Simple Pursuit, due Friday 28 January 2011, in
class or by 5pm.

- REMINDER: It's really important that (a) you make a sketch of a vector
problem and (b) you don't inadvertently make 45°-45°-90° right
triangles unless you really DO have an isoceles right triangle, with the same
*x*- and*y*-components.

Wednesday 1/26: Adding and subtracting vectors:
Graphical method. To generate an
analytical method, we first need to look at some Trigonometry.
Right Triangles: Sum of the interior angles of
any triangle is 180°, Pythagorean Theorem (a² + b² = c²).
Standard Angle (start at positive *x*-axis and go counterclockwise).
Standard Form: 5.00m @ 30°. Practical Trigonometry.
S`OH`C`AH`T`OA`. Adding and subtracting vectors:
Analytical method and
Sketch of the problem. (Check to make
sure your calculator is set for Degrees mode. Try cos 45° = sin 45° =
0.7071) Why arctangent is a stupid function on your calculator. Finding the
final vector velocity of The guy with the fedora and the cigar problem.

- REMINDER: It's really important that (a) you make a sketch of a vector
problem and (b) you don't inadvertently make 45°-45°-90° right
triangles unless you really DO have an isoceles right triangle, with the same
*x*- and*y*-components. - Sample Book Problems (not to be handed in):
**Chapter 3**: 1, 3, 7, 11, 15, 21, 23, 47, 51.*NOTE: these are from the WMU 8th edition.*

Thursday 1/26: Return Q2, Q3. **Unit Vectors**: i-hat, j-hat, k-hat
(point in x, y, z directions, respectively), have unitary length (length of 1).
Allow you to describe a vector with x- and y-components times the i- and j-hat
unit vectors. Using Vector Addition for Velocities: Upstream, downstream
(rivers), Headwind, tailwind, crosswind (airplanes). **Ballistic (or
Projectile) Motion** -- applies equally to a thrown football and a
cannonball. Still working with *a _{x} = 0* and

- On Tuesday 18 January 2011, I gave an assignment to go look for a speed-vs-time graph from a car magazine. From the show of hands, so to speak, THREE of you did this. Please note you may be responsible for material that I assign, whether you do it or not.

Friday 1/27: **Ballistic (or Projectile) Motion**.
Two Dangerous Equations. You can only use
the Range Equation if the Launch Height = Landing Height. But the sin (2*theta)
term in the Range Equation means that (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). High and low trajectories for Range Equation. Topic 1 assigned. (Click
here for a copy of the handout.) Second
Sample Exam 1 (Click here,
here and here
for a copy.) Quiz 5 take-home quiz on Vectors, Standard Form and Vector
Addition, due Tuesday 1 February 2011, in class or by 5pm.

**Why do we sketch problems?**Because it helps us "see" the Physics. Particularly important for vectors.- To sketch a vector -- start at the origin and draw the x-component (it either points to the right or left), then from the tip of the arrow of the x-component, draw the y-component (it either points up or down). Finally, your resultant vector starts on the origin and points to the last tip of the arrow. Too many people either (a) "close" the triangle and have the resultant vector point back to the origin or (b) start BOTH the x- and y-components at the origin and connect the two tips together, either of which end up pointing the wrong way.
- You don't need a ruler or a protractor to make a sketch, but do make sure you set up your components so you can tell which one is longer. That will allow you to see which angle is the big angle (greater than 45°) or the little angle (less than 45°).
- See example: Adding and subtracting vectors: Analytical method and Sketch of the problem.
- Sample Book Problems (not to be handed in):
**Chapter 4**: 1, 3, 5, 9, 15, 17, 23, 27, 29, 35, 37, 47, 49, 55, 68, 71. - Sigh. There IS a reason the Syllabus talks about "my side of the table". Someone wandered off with part of my lecture notes, which weren't one of the three handouts. Thanks.

- Week 4 Checklist. (Includes Exam 1 Review)
- HEADS UP: Weather forecast for Tuesday night / Wednesday is for Serious Snow -- if the storm follows one particular track, we may have more than a foot of snow or more. Even if WMU is open on Wednesday, there is a chance I might not be able to dig out of my driveway in time.

Monday 1/31: Remember, the Range Equation can only be used if the landing
height is the same as the launching height, *y = y _{0}* . At the
maximum height,

Tuesday 2/1: **A final note on ballistic motion**: You have to have some
positive *v _{0y}* if you want to jump a gap, because otherwise you
start falling immediately once you are no longer supported.

- Dr. Phil has gone ahead and canceled class for Wednesday due to impending blizzard forecasts. Note official WMU Closing Policy. (And by 10pm Tuesday night, WMU had canceled all Wednesday classes...)
- Hollywood action movies rarely get the Physics right. Consider the bus
jumping the gap in the movie
*Speed*.*The Mythbusters*tested this in 2009, both with models and a full-size bus. See videos of the full-scale test -- note how the bus sails through the air in a nice parabolic arc, but only because it was launched from an angled ramp in the first place. - What are the other two "flaws" in Dr. Phil's sketch of the Space Shuttle in Low Earth Orbit?
**What Will Be On Exam 1?**With the Monkey Hunter problem we have effectively closed the book on the material for Exam 1. Though the Syllabus suggests Ch. 1-3 for Exam 1, realistically much of Ch. 4 is just Ch. 2 & 3 combined, so we will say Ch. 1-4 for Exam 1 material. However, U.C.M. will NOT be on our Exam 1.

Wednesday 2/2: WMU closed due to blizzard. No classes held.

Thursday 2/3: **Recap**: Our studies so far have described
"How" things move, and allow to say "When" and
"Where" things move, but not "Why" things move. For that we
have to start talking about Forces -- and that means Newton. Some stories about
Sir Isaac Newton. **Newton's Three Laws of Motion**: Zeroeth Law - There is
such a thing as mass. Mass is a measure of how much "stuff" an object
made of matter contains. SI unit of mass = kilogram (kg). 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__. The Normal Force is a contact
force perpendicular to a contact surface. *Example: A book laying on a table
experiences a Normal Force from the table pushing up.* 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.)
"If I were to punch the wall, then the wall punches back." The Normal
Force and the weight may be equal-and-opposite forces, but if they both apply
to the same object, this is First Law, not Third Law. Force is a vector.
Comments about Exam 1 tomorrow. Questions? *Uh, no one had any questions*.

- A "Zeroeth Law" is the underlying assumption which is required for the following laws to exist and be useful. In the case of Newton's Laws, it is that objects of matter have mass. Note that mass is a scalar quantity.

Friday 2/4: Exam 1.

- Week 5 Checklist.
- Sample Book Problems (not to be handed in):
**Chapter 5**: 1, 3, 5, 11, 13, 15, 21, 23, 31, 41, 42, 44, 46, 47, 61, 65.*NOTE: these are from the WMU 8th edition.* - IF YOU MISSED EXAM 1 -- Contact Dr. Phil As Soon As Possible To Schedule A Make-Up.

Monday 2/7: **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.) SI unit of mass = kilogram (kg). SI unit of force =
Newton (N) = (kg·m/s²). English unit of force = pound (lb.). English
unit of mass = slug (Divide pounds by 32. For English units, g = 32
ft/sec².). Force is a vector. **Free Body Diagrams**. Normal Force
(Normal = Perpendicular to plane of contact). Sum of forces in *x* or
*y* equations -- either will be equal to *0* (Newton's 1st Law) or
*ma* (Newton's 2nd Law). The sum of forces equations are the analytical
version of the graphical Free Body Diagram -- we generally need both to solve
Force problems. SI unit of mass = kilogram (kg). SI unit of force = Newton (N).
Examples: Pushing a 125 kg crate around. (Near the surface of the Earth, you
can use the relationship that 1 kg of mass corresponds [not "equals"]
to 2.2 lbs. of weight. So multiple 125 by 2 and add 10%... 250 + 25 = 275... so
a 125 kg crate has a weight of mg = 1226 N or 275 lbs.). "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."
Continue with the 125 kg crate. Variations as we allow for an applied force
that it at an angle.Quiz 7 take-home quiz on F.B.D. and Sum of Forces
equations, and due Thursday 10 February 2011, in class or by 5pm.

- The problem with the First Law is that all too often, "an object in motion tends to come to a stop." But friction, as we shall see later, is an external force, which therefore makes that Second Law, not First. In the 1970s, NASA used some of the surplus Saturn V equipment to fashion a space station, Skylab. Videos: (drifting through Skylab), (Skylab launch, damage and repairs)

Tuesday 2/8: Continue with the 125 kg crate. Variations as we allow for an
applied force that it at an angle. "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." Push down and Normal
Force increases; pull up and Normal Force decreases -- though it cannot go
negative. "You can't push on a
rope." Since the force from a wire/string/rope/chain/thread/etc. can
only be in one direction, Dr. Phil prefers to call such forces T for Tensions
rather than F for Forces. Simple pulleys (Massless, frictionless,
dimensionless, only redirect the forces). "There is no free lunch."
The bracket for the pulley will have to support a force greater than the weight
of the hanging object. Mechanical advantage: multiple pulleys allow us to
distribute the net force across multiple cables or the same cable loop around
multiple times. Tension in the cable is reduced, but you have to pull more
cable to move the crate.

- Q7 Comment: In the two situations at the top of the page, on the Right Hand problem, the force F1 is in direct contact with Block 2. On the Left Hand problem, the force F1 is in direct contact with Block 1 -- to figure out what the forces on Block 2 are, you need to do your F.B.D.'s and consider Third Law force pairs. In any event, you need two F.B.D's for each part, since there are two blocks.

Wednesday 2/9: **Elevator Problems**. The Normal Force represents the
"apparent weight" of the person in the elevator. For the elevator at
rest or moving at constant speed, the Normal Force = weight, and the tension of
the cable = weight of loaded elevator. But if there is an acceleration vector
pointing up, the apparent weight and the tension of the cable increase; if the
vector points down, the apparent weight and the cable tension decrease. In true
Free Fall, without any air resistance, the Normal Force = 0 and you are
floating. **Atwood's Machine**: Two blocks whose motion is link via a common
cable and a pulley. Note that though they have a common magnitude of both speed
and acceleration, the velocity vector has no bearing on either the F.B.D. or
the solution to the Tension and acceleration. **Inclined Planes**: Change
the co-ordinate system, change the rules. In the tilted x'-y' coordinates, this is a
one-dimensional problem, not two-dimensional.

- Article on the 1945 crash of a B-25 bomber into the Empire State Building and subsequent elevator free fall.

Thursday 2/10: **Inclined Planes**: Change the co-ordinate system, change
the rules. In the tilted x'-y' coordinates,
this is a one-dimensional problem, not two-dimensional. **Friction Force:
**Two kinds of Friction: Static (stationary)
and Kinetic (sliding). Friction is a contact force, but whereas the Normal
Force is perpendicular to the contact plane, Friction is parallel to the
contact plane. For any given contact surface, there are two coefficients of
friction, µ, one for static and one for kinetic. Static is always greater
than kinetic. Static Friction is "magic", varying between zero and
its maximum value of µ times the Normal Force. Kinetic Friction is always
µ times the Normal Force. Kinetic Friction always opposes the motion,
Static Friction opposes the direction of *impending* motion (since the
object is not moving yet). If object is at rest, need to "test" to
see if an applied external force exceeds the maximum static friction force
("breaks the static friction barrier"). Static Friction can vary from
zero to its max value in either direction. Demonstration of block sliding down
inclined plane with friction. Finding the coefficient of static friction by
tilting. µ_{s} = tan(theta_{max}). Similar for kinetic
friction, except one has to tap the board to "break the static friction
barrier". 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. Friction while driving. Rubber on dry concrete, coefficients
are 1.00 and 0.800 . Tires rolling with friction on good roads -- this is
static friction not kinetic friction because the tires aren't sliding on the
pavement. Quiz 8 take-home quiz on Tensions & Simple Pulleys and Forces
& Friction, and due on Tuesday 15 February 2011, in class or by 5pm.

- Sample Book Problems (not to be handed in):
**Chapter 6**: 1, 3, 7, 8, 11, 16, 17, 19, 21, 23, 27, 33, 40, 44, 51, 53, 59, 63.*NOTE: these are from the WMU 8th edition. NOTE 2: we aren't in Chapter 6 yet. I just had a few minutes and wanted to get ahead and post these.*

Friday 2/11: Two kinds of Friction: Static
(stationary) and Kinetic (sliding). For any given contact surface, there are
two coefficients of friction, µ, one for static and one for kinetic.
Static is always greater than kinetic. Static Friction is "magic",
varying between zero and its maximum value of µ times the Normal Force.
Kinetic Friction is always µ times the Normal Force. **Examples** using
our 125 kg crate sliding on the floor. If object is at rest, need to
"test" to see if an applied external force exceeds the maximum static
friction force ("breaks the static friction barrier"). Static
Friction can vary from zero to its max value in either direction. **Friction
while driving.** Rubber on dry concrete, coefficients are 1.00 and 0.800 .
Tires rolling with friction on good roads -- this is static friction not
kinetic friction because the tires aren't sliding on the pavement. If you panic
and lock up the wheels (stop their rotation) and switch from static to kinetic
friction, you will take *longer* to stop because *µ _{k}
< µ_{s}* and so there is less available friction force.
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. First Sample Exam 2.
(Click here for a copy.)

- Week 6 Checklist.

Monday 2/14: Return X1. Discussion of "The Great Reality Check". Reminder that your X1 grade isn't the end of the world.

- Note that this time only, the A and B exams are the same (except one has a car and one has a ski boat in problem 1).
- By the way, if you have any trouble reading my terrible handwriting, you can always ask for a "Dr. Phil to English" translation.
- The Registrar has requested that Introductory courses post First Look grades -- essentially a first look at Mid-Term grades. These grades will be made available via GoWMU after Monday 14 February 2011. Note that these grades and the Mid-Term grades are NOT recorded, nor are they given to anyone. They are for your information only. Dr. Phil will be providing a break down of

Tuesday 2/15: **More with Forces and Tensions:** Hanging a sign with
angled wires -- still the same procedure: Sketch of the problem, Free Body
Diagram, Sum of Forces equations in the x- and y-directions, solve for
unknowns. Note that when the two wires have different angles, 30° and
45°, that T_{1x }and T_{2x} still have to cancel each
other. Also the two tensions, T_{1} and T_{2}, are each
supporting more than half the weight of the sign, but less than all the weight
of the sign, because they are pulling against each other. **Work: **A
Physics Definition (Work = Force times distance in
the same direction). Work = Energy. **Pay particular attention to
Units.** Dot products: one of two methods of
multiplying two vectors -- this method generates a scalar, which is a good
thing because Work happens to be a scalar, which is Work's virtue (i.e. why we
care). Dot products: run through two
3-dimensional vector case. *W = F d* can only be applied when (1) the
Force is constant and (2) the Force is parallel to the displacement vector,
i.e. the angle between the two vectors is 0°.

Wednesday 2/16: **We can talk about:** the Work done BY something, the
Work done ON something and the net Work (total work) done ON something.
Kinetic Energy -- an energy of motion, always
positive, scalar, no direction information. Work-Energy Theorem (net Work = Change in K.E.).
Re-derive using algebra: *W _{net} = F_{net}d = mad* and
the equation without time. Get K.E. and Work-Energy Theorem, but can only claim
that it is a general result -- calculus derivation earlier didn't have that
restriction. Lose angle and directional information because energy is a scalar,
not a vector. Example: Revisit The guy with the fedora and the cigar. Initial
speed is v = v

Thursday 2/17: Work through some examples of Work, the Work-Energy Theorem,
Conservation of Energy. For a conservative force, *U = -W* done by that
force. Gravitational P.E. *U _{g} = mgh = mgy* , Spring Force P.E.

- For Q9 part (a), I was imagining that you would draw a F.B.D. and solve the force problem. For the work and energy parts, remember to consider which way things point -- that's where your F.B.D. in part (a) may become handy again.

Friday 2/18: For a conservative force, *U = -W* done by that force.
Gravitational P.E. *U _{g} = mgh = mgy* , Spring Force P.E.

- ABC News video of a U.K. tanker truck with a car stuck on its front bumper. (Presumably NOT a head-on collision.)

- Week 7 Checklist. (Includes Exam 2 Review).
- This is going to be a short week. Do not put off starting to study for Exam 2. Have questions for Tuesday Office Hours.

Monday 2/21: Dr. Phil has canceled his classes due to treacherous roads.

Tuesday 2/22: Linear momentum is conserved in all types of collisions.
**Three example collisions:** head-on, rear-end, 2-D. (The Non-Collision --
if the car following is going slower, it isn't going to run into the car ahead.
PTPBIP.) Seat belts, shoulder belts, steel beams in doors and crumple zones.
What happens in a wreck. The myth of "better to be thrown from the
wreck." How airbags work. Momentum, *p*, is conserved in all
collisions, but K.E. is not conserved, except for T.E.C. We can see this in the
case of the head-on collision with identical momentums -- the final speed is
zero and so all K.E. is lost during the collision. Where does all the energy
go? Into the non-conservative work to break, bend and stop things. Fifth Sample
Exam 2. (Click here for a copy.)

- Note regarding the Sample Exam 2 handed out in class today -- that file is not on my computer here. (Click here for a copy.)
- And if you missed class today, you missed the excitement of having a tornado drill right at the end of class.
- Quiz 11 will be handed out Wednesday 23 February 2011 on Totally Inelastic Collisions, and not due until Tuesday 8 March 2011, in class or by 5pm.

Wednesday 2/23: Review for Exam 2. Quiz 11 on Totally Inelastic Collisions, not due until Tuesday 8 March 2011, in class or by 5pm.

Thursday 2/24: Exam 2.

Friday 2/25: Spirit Day. (No Classes)

WMU SPRING BREAK

- Hope you got some well-deserved break time in!

- Week 8 Checklist. (Back to work...)
- Don't forget! Quiz 11 was handed out Wednesday 23 February 2011 on Totally Inelastic Collisions, and not due until Tuesday 8 March 2011, in class or by 5pm.

Monday 3/7: **Momentum, p, is conserved in all collisions**, but
K.E. is not conserved, except for T.E.C. We can see this in the case of the
head-on collision with identical momentums -- the final speed is zero and so
all K.E. is lost during the collision.

Tuesday 3/8: 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 -- use conservation of momentum. NOTE:
Serway's derivation is similar, but he does not make two points totally clear:
(1) *dm = -dM* , the differential change of the mass M of the rocket is
negative; (2) since *M _{f} < M_{i}*, then

Wednesday 3/9: **The Ballistic Pendulum** -- Old School Physics, in the
days before all our modern electronics: We can find the speed of a projectile
through an Inelastic Collision followed by Conservation of TME. **Resistive
Forces: Air Resistance**. Low speed ( *F _{drag} = -bv* ) and
high speed air resistance (

- The low and high speed drag coefficients,
*b*and*c*, contain a lot of physics including things like the cross-sectional area. For example, Serway gives the high speed drag equation as*F*, where_{drag}= -(½D rho_{air}A) v²*c = (½D rho*, and_{air}A)*D*is a Drag Coefficient (which contains the information about shape and material surfaces),*rho*is the density of the air (mass per volume), and_{air}*A*is the cross-sectional area of the object.

Thursday 3/10: Final thoughts on Terminal Velocity:
World's
Record Free-Fall. And
27 May
2008 Failed Attempt. **UCM Revisited**: Centripetal Force,
*F _{c} = ma_{c} = mv²/r*. No such thing as
Centrifugal Force. Only the Centrepital Force, which points radial inward, just
like the centripetal acceleration. Note that the Centripetal Force is an ANSWER
to the sum of forces equation -- it does not show up in the F.B.D. directly --
something has to CAUSE the Centripetal Force, such as a Normal Force (or
component), tension, friction, or a combination of forces, etc. For a car on a
flat road making a turn, the maximum safe speed for a turn comes from the
maximum static friction. You aren't forced to the outside in a turn by some
outward pointing "centrifugal force), you merely move in a straight line
unless there is a force to keep you on the circle. Making "artificial
gravity" for long-duration space flight by living in a rotating object.
Test tube example. The story of the 50,000 rpm Ultra-Centrifuge and the Fresh
Rat's Liver.

- Webcomic xkcd on Centrifugal vs. Centripetal Force. (I thought I remembered it being Goldfinger, but I guess Randal used his usual troublemaker with the hat.) (grin)
- The problem of using UCM to create "artificial gravity" is not a trivial one for long-term space missions. Your internal organs "hang" suspended from your rib cage -- without gravity they not only float, but no longer require all the bone and muscle mass to support them and move around. Even dietary supplements and exercise do not stop the atrophy. See Spaceflight osteopenia.
- NASA and other operations can
simulate the
"weightless" or "zero G" environment by flying
parabolas -- the original plane they used was a VC-135, which got nicknamed
the "Vomit Comet". More recently NASA would like us to use the less
fun term Weightless Wonder.
Many
of the zero G scenes in the film
*Apollo 13*were shot using this technique.

Friday 3/11: **UCM Revisited**: Centripetal Force, *F _{c} =
ma_{c} = mv²/r*. No such thing as Centrifugal Force. Only the
Centrepital Force, which points radial inward, just like the centripetal
acceleration. Note that the Centripetal Force is an ANSWER to the sum of forces
equation -- it does not show up in the F.B.D. directly -- something has to
CAUSE the Centripetal Force, such as a Normal Force (or component), friction,
etc. For a car on a flat road making a turn, the maximum safe speed for a turn
comes from the maximum static friction. For a car on a banked (angled) curve,
there is a "natural" design speed where you can go around a curve
with that radius without friction. Demo: Rodney Reindeer on a string. Example
of a 14" and a 2" hard disk drive spinning at 3600 rpm (

- Time Change on Sunday! 2am Eastern Standard Time magically becomes 3am Eastern Daylight Time. Adjust your clocks accordingly.

Monday 3/14: Return X2. *Short discussion of events in Japan over the
weekend -- 9.0 magnitude quake, safety systems, tsunami damage, what's
happening in the ten damaged nuclear power plants*.

- Please note that in Exam 2A, Problem 1(e), the solution has an error such that no one could've gotten the full points. We will deal with this on Tuesday.
- Physics Help Room will temporarily move from 0077 Rood to Bradley Commons (2202 Everett -- next to Dr. Phil's office) from Monday 14 March 2011 to Friday 18 March 2011.

Tuesday 3/15: **General Rotational Motion**: Translating Linear physics
to Rotational physics (as "easy" as changing Roman/English variables
to Greek). The radian is a "quasi-unit" -- it's not really a unit,
but represents a fraction of a circle. (We can "wish" it away when we
need to.) Angular position, angular
velocity, angular acceleration, and the Kinematic Equations for constant
angular acceleration. **Continuing to fill in our Linear vs. Rotational
table**: Newton's 3 Laws of
Motion applied to rotations, Moment of Inertia = "rotational mass",
angular force = torque.

Wednesday 3/16: Angular
Kinematic Equations -- Example: A car traveling at 27.0 m/s in the +x
direction comes to a stop in 5.00 seconds. The tires have a diameter *D =
0.760 m* and a radius *r = 0.380 m*. Assuming the tires are in good
contact with the road (static friction), then we can use the linear information
to find the rotational problem. Note that the tire rotation is clockwise, which
is in the NEGATIVE direction. The angular acceleration *alpha* will
therefore be positive.Find *omega _{0}*,

Thursday 3/17: **Extended Objects:** We have been treating our objects
really as dimensionless dots, that have been allowed to have mass. Now we want
to start considering how that mass is distributed. An airplane with mass
unevenly concentrated in front, back or to one side, may not be flyable. Center
of mass is a "weighted average", meaning it combines a position with
how much mass is involved. Center of mass in the x-direction:
discrete case and
1-D uniformly distributed mass (Example: A
meter stick balances at the 50 cm mark.) We have been calculating the motion of
the center of mass all this time -- it's the dot in the Free Body Diagram. Mass
per unit length (lamda = M/L), mass per unit area (sigma = M/A), mass per unit
volume (rho = M/V). **2-D uniformly distributed mass** -- Center of mass in
x-direction and in y-direction. Rectangular plate. Note that the center of mass
value depends on the coordinate system, but the center of mass point remains in
the same place. Triangular plate -- parameterizing y = y(x) (y as a function of
x) and x = x(y) (x as a function of y).

Friday 3/18: **Center of Mass** (con't.): Demo: Suspending real objects
from different points to find the center of mass -- hung from the center of
mass, the object is perfectly balanced. Include: irregular plate, rectangular
plate, triangular plate, Michigan (Lower Pennisula), Florida. The center of
mass does NOT have to be located ON the object -- the obvious example is a ring
or hoop, where the center is empty. Demo: The toy that "rolls uphill"
-- actually, whether with the cylinder or the double-cone, the center of mass
is going downhill. Start discussion of **Moment of Inertia**. We will be
reproducing the results from Table 10-2 in your textbook, but you can use these
results on your Formula Card and on this next quiz.
Moment of Inertia, discrete case.
Parallel Axis Theorem. Moment of
Inertia by Integration, 1-D uniformly distributed mass. Axis through center
of mass: I = 1/12 ML² . Axis from end: I = 1/3 ML² -- note that this
is four times larger than through the center of mass, we had predicted that the
moment of inertia would be higher when rotated from the end. Checked results
with parallel axis theorem! First Sample Exam 3. (Click
here for a copy.) Quiz 15 on Discrete Cases of
Center-of-Mass and Moment of Inertia, due Tuesday 22 March 2011, in class or by
5pm. *And yes, that means there are TWO quizzes out right now.*

- Would really appreciate it if you don't watch the NCAA March Madness games during class... (evil grin) Because I can't while I teach. (bursts into sobs) (Not really, but I figure the "guilt thing" might work.)
- Last day for Physics Help Room in 2202 Everett (Bradley Commons) -- next week the Physics Help Room returns to 0077 Rood Hall.
- Remember that in starting to study for Exam 3, there were some items which may have showed up on Sample Exam 2s which we hadn't covered yet.
- There are two known grading issues with Exam 2: On the A-exam (WHITE), the Solution had the wrong numbers for 1(e), which means you could've been marked off for having all or some of the right work. On the B-exam (PINK), the little star symbol and the (a) didn't appear in 2(a), which means that the grader might not have circled the star and counted any star points earned on 2(a). For either cases, please fill out an Exam 2 Grade Fix sheet and show me the test and the form when you can. You are entitled to all the points you earned.

- Week 10 Checklist.
- The Physics Help Room should be moved back to 0077 Rood now.

Monday 3/21: Review of 2-D and 3-D
Integration (as PDF handout). Rectangular
(area, volume), Polar (circumference, area), Cylindrical (volume, surface
area). Spherical Coordinates (volume, surface area, hollow volume). **Moment
of Inertia** of Ring, I = MR² by inspection, by integration.

- Q14 now due on Tuesday 22 March 2011,
~~due on Monday 21 March 2011~~, along with Q15. - Note that there seem to be two different forms of Spherical Coordinates.
(1) Theta is the same angle in the x-y plane as in polar coordinates and phi is
the azimuthal angle OR (2) reverse theta and phi "for no good
reason". Also note that
*r*in spherical coords is NOT the same*r*as in polar coords -- some math texts use*rho*for the radius in spherical coords, but in PHYS-2050 and -2070, we need to integrate a physics variable called*rho*in spherical coords, so using*r*makes sense. - For "HW", try to come up with and solve the integral for calculating the moment of inertia for a thin-walled hollow sphere. Compare your answer to the result in Table 10.2 .

Tuesday 3/22: Moment of Inertia by Integration,
Double- and Triple-Integrals in
Spherical Co-ords. Moment of Inertia of Ring, Solid Disk. Moment of Inertia
of Solid Cylinder, Hollow Sphere, Solid Sphere. Note that I_{thin ring}
> I_{solid-disk} and I_{hollow-sphere} >
I_{solid-sphere}, which makes sense because in the solid, more mass is
near the axis of rotation, while in the hollow, more mass is far away from the
axis of rotation**. Rotational K.E.**: Rolling objects down an incline
(rolling without slipping). mgh = ½ mv² + ½ I*w*², the
energy available from the P.E. is split between linear K.E. and rotational K.E.
Because I is a multiple of MR² and *omega = v / r*, the rotational
K.E. term ends up as some multiple of mv². So we get cases, based on what
type of round object we have rolling, and what its moment of inertia I is.
Start with thin ring / hoop / thin-walled cylinder, with I = MR². Final
speed v = sqrt(gh), which is less that v = sqrt(2gh), the speed of a block
sliding down the same incline with no friction. With friction, however, the
block may not even move!

- NOTE: I will not be posting the solutions to Q14 or Q15 on Tuesday night, so if you "need" another night of work, you can turn them in before class on Wednesday.
- Some perspective on radiation, from the brilliant author of the webcomic xkcd -- article and chart.

Wednesday 3/23: **Rotational K.E.**: Rolling objects down an incline
(rolling without slipping). mgh = ½ mv² + ½ I*w*², the
energy available from the P.E. is split between linear K.E. and rotational K.E.
Because I is a multiple of MR² and *omega = v / r*, the rotational
K.E. term ends up as some multiple of mv². Depending on the moment of
inertia of the rolling object, the final speed at the bottom of the incline
varies, but does not depend on the mass *m* or the radius *R*. All
are slower than a block sliding down an incline without friction. (With
friction, we don't know what the block may do without more information -- it
may not move at all.) **Demo**: A "race" down an incline between
two steel balls of different sizes is pretty much a dead heat (mass M and
radius R is not a factor), and finally between a metal ring, a solid disk, a
hollow ball and a solid ball (here the finish order depends on the I used).
Rolling objects need both linear K.E., because it takes work to move the
center-of-mass, and rotational K.E., because it takes work to rotate the moment
of inertia.

Thursday 3/24: **The Cross Product and Right-Hand Rule (R.H.R.)**. Using
Right Hand Rule to assign directions to x,y,z coordinates and the sense of
rotations for theta, omega (angular velocity), alpha (angular acceleration) and
tau (torque) -- the vectors for these variables ends up pointing up or down the
axis of rotation. Torque = r F, when applying a linear force perpendicular to a
radius line to the axis of rotation. (Most torques we apply are done this way.)
A "breaker bar" is a pipe used to extend the handle of a wrench --
this increases the torque for a given applied force, but the use of a breaker
bar may damage the thing you are trying to torque. Angular momentum L = r p,
when the linear momentum vector is perpendicular to the radius vector. The
Cross Product (or Vector Product) is the exact opposite of the Dot Product (or
Scalar Product). Multiplying two vectors together by a cross product gives us
another vector (instead of a scalar). And the cross product is not commutative,
vector-A × vector-B = - (vector-B × vector-A), so the order is
paramount. **How we solve force problems:** (1) Free Body Diagram, (2) Sum
of Forces equations, (3) Newton's Laws. **How we solve torque problems:**
(1) Free Rotation Diagram, (1A) Choose an axis of
rotation. (2) Sum of Torques equations, (3) Newton's Laws. **Real
pulleys vs. Perfect Massless Pulleys.** Atwood's Machine with a real pulley.
Get 3 equations with 3 unknowns -- the two tensions and the common
acceleration. Note that two tensions, T_{1} and T_{2}, are no
longer equal, because they have to supply the net torque to rotate the pulley.
Each of the tensions, T_{1} and T_{2}, attach tangent to the
pulley and therefore, by definition, are already perpendicular to the radius
line. The equations depend on the moment of inertia, I, of the pulley, which
depends on its mass and how that mass is distributed. Note that in connecting
the rotational problem with the linear problems, the radius R of the pulley
cancels. The acceleration of the two masses is less than the acceleration with
a simple pulley, because it takes work and energy to rotate the real pulley.
Still, the tensions and the common acceleration only change a little. When we
simplified the Physics to do Atwood's Machine with a perfect pulley, the answer
isn't too far off from using a real pulley. The more we add to the Physics,
sometimes we don't change the answer much. So sometimes taking a simplified
Physics approach is a useful approximation. Second Sample Exam 3. (Click
here for a copy.)

- Our Atwood's Machine problem has masses
*m*and_{1}= 5.00 kg*m*. Adding in a real pulley,_{2}= 7.00 kg*M = 2.00 kg*and*R = 0.100 m*, reduced the acceleration to*a = 1.509 m/s²*. What was the acceleration when we assumed a perfect pulley? - Reminder that Exam 3 is Friday 1 April 2011.
- Reminder that the Topic 1 Book Report is due on Thursday 14 April 2011, Friday 15 April 2011 or Monday 18 April 2011. If you are planning on doing a draft paper, the last day to turn in such a draft is Monday 11 April 2011.

Friday 3/25: The "Free Rotation Diagram". **Statics**: objects
not translating in any direction and objects not rotating in any direction. The
teeter-totter or seesaw -- (1) if the pivot is located at
the center of mass (c.m.), then two children of equal mass will balance the
teeter-totter when located equal radius arms from the pivot; (2) if the pivot
is located at the c.m., then an adult of mass M can balance against a child of
mass m when the adult radius R = (m/M) r, or we can say that the adult has
"cheated" or "scooted" forward on the board; (3) if the
adult of mass M and the child of mass m are both located at the ends of the
board, then they can balance if we move the pivot point closer to the mass M,
but then the weight of the board at the c.m. of the board now provides a torque
which must be accounted for in the F.R.D. Free Body Diagrams, Free
Rotation Diagrams (sum of forces, sum of torques). *Helpful hint: You can
choose to put your pivot point (axis of rotation) anywhere you like, because if
an object is not rotating, it is not rotating around any axis. So put the pivot
point where one of your unknown forces is attached, and the algebra is
easier.* Unloaded bridge supported at ends by two support pier forces
F_{1} and F_{2}. Easy to show that F_{1} =
F_{2}. Loaded bridge, with truck located closer to pier 2, then
F_{1} < F_{2}. Diving board is a bridge where pier 2 is
located to the left of the board's c.m. When we treat F_{1} and
F_{2} as both pointing up, as in the bridge problems, it isn't apparent
at first that F_{1} will be negative and therefore points down. This is
not a problem -- a minus sign merely tells us that the vector force points the
other way. Third Sample Exam 3. (Click here
and here for a copy.) Quiz 16 on Torque
Problems, due Tuesday 29 March 2011, in class or by 5pm.

- Week 11 Checklist. (Includes Exam 3 Review).
- Seriously: (1) Have you kept your Formula Card up to date? (2) Have you worked on Sample Exam 3 Star Problems and looked at Sample Exam 3 Star Problem solutions? If the answer to either of these questions is "No", then ask yourself, "Why?" Seriously.

Monday 3/28: **Statics problems** (no translation, no rotation about any
axis) con't. The ladder leaning on the wall. Choose pivot point at floor to
eliminate two of the three unknown forces from the sum of torques equation.
Figure out whether the perpendicular components of the weight and the wall
(normal) force use sin or cos of theta, the angle the ladder makes with the
floor. Is there enough static friction to hold it? (theta = 70°, m = 15.0
kg, L = 3.00 m, mu's of 0.600 and 0.700 for floor only, no friction with wall.)
*If you're keeping score at home, Statics is in Chapter 12 of your book, and
teeter-totters and the leaning ladder are both examples in the book*.
Stability of objects -- demo with heavy lead brick. Falls over when
center-of-mass is unsupported. Tall & skinny objects much easier to tip
over, than low & wide.

- Q16 (a): Note that the FBD isn't all that useful in this case. For the FRD and Sum of Torques equation, consider the loaded board, and not just the board itself.
- If you're keeping score at home, Statics is in Chapter 12 of your book, and
teeter-totters and the leaning ladder (tomorrow) are both examples in the book.
*Figure 12.6 -- Serway made these wine bottle holders and used to give them away when he was introducing a new edition of the book.*

Tuesday 3/29: **Stability of objects**. Objects fall over when
center-of-mass is unsupported. Tall & skinny objects much easier to tip
over, than low & wide. Stability around a curve also connected with
previous discussion of stability and center-of-mass. Rollovers,
"J-Turns" (a U-turn with a rollover), Jeep CJ (narrow width, high
c.m.) vs. Jeep YJ (wider width gave more stability). Ground clearance and the
HUMVEE. (Very wide width, relatively low c.m., and rim wheel drive means no
drive shaft or differential housing hanging underneath vehicle.) **Extended
Objects** -- Allowing for Deformation. Tension, Compression, Shear, Bulk.
Stress = Force / Cross-sectional Area. Pressure also is Force = F/A. (SI units
= N/m² = Pascal = Pa) Strain = Delta-L / L_{0} , the amount of
deformation divided by the original length.
Stress versus Strain graph. Linear
region (no damage), elastic limit, plastic deformation, brittle and ductile
failures -- failure occurs before the curve turns down in brittle failure,
after the curve turns down in ductile failure. Tensile Strength, necking,
voids, failure. Young's Modulus.
Tension, Compression. Bulk Modulus. Table 12.1, p. 359. Steel has Young's
Modulus Y = 20×10¹° N/m², Shear Modulus =
8.4×10¹° N/m², Bulk Modulus 14×10¹°
N/m². Compare to Bulk Modulus of "nearly incompressible" water,
0.21×10¹° N/m². Example: Find the change in length,
delta-L, of the steel cable that we used to hang the bowling ball for the
conservation of energy demonstration. (L_{0} = 2.00 m, 16 lbs. bowling
ball m = 7.27 kg, diameter of steel cable D = 4.00 mm.) Quiz 17 on Elastic
Deformation by Tension, due Thursday 31 March 2011, in class or by 5pm.

- Helpful Reminder Of The Day: Are the moment of inertia formulas from Table 10.2 on your formula card?
- The second part of Q17 always seems to stump people. But if we are in the linear elastic region, then applying a tension force will stretch the cable and if we let it go it will return to its original length. This is very much like a spring obeying the linear Hooke's Law force.

Wednesday 3/30: Example: Find the change in length, delta-L, of the steel
cable that we used to hang the bowling ball for the conservation of energy
demonstration. (L_{0} = 2.00 m, 16 lbs. bowling ball m = 7.27 kg,
diameter of steel cable D = 4.00 mm.) We found delta-L to be
5.68×10^{-5} m = 0.0568 mm -- essentially no detectable stretching
of the cable. (A slightly smaller delta-L was found by those who calculated
using a square cross-sectional area of sides d = 4.00 mm, which makes sense
because the square has a larger area than the inscribed circle.) For many
materials, the Young's Modulus for tension and the compression modulus are the
same. But some are different. Wood, for example, has different values depending
on which way the grain of the wood points. Knotholes, where branches meet a
larger part of the tree, have weak spots (voids). One way around these problems
is to make plywood -- alternating thin sheets of wood with the grain in
different directions held together by layers of glue. Some boards in
construction are now made out of plywood, rather than single pieces of wood. On
the other hand, particle board -- small pieces of wood bound together in a glue
matrix -- is very weak because there are no long pieces of wood together, so it
fractures easily. **Pre-Stressed Concrete**: Concrete is strong in
compression, weak in tension. But you can cast large concrete beams with wires
inside and tighten the wires to put the concrete into net compression, even if
you put it in a tension situation. **The four fundamental forces in
nature**, from weakest to strongest: Gravity, Electromagnetism, Weak Nuclear
Force, Strong Nuclear Force. Gravity may be the weakest, but it holds us onto
this planet and "binds the galaxies together". Fourth Sample Exam 3.
(Click here for a copy.)

- Dr. Phil recommends that you take 50 minutes and with just your formula card, calculator and pen / pencil, work on the Fourth Sample Exam 3. After 50 minutes is up, continue to try to finish the Sample Exam.
- With Tension Deformation and Young's Modulus, we have closed the book on Exam 3 material.
- Sample Exam 3 problems on Newton's Universal Gravity and Simple Harmonic Motion/Simple Harmonic Oscillators are NOT going to be on our Exam 3.
- Sample Book Problems (not to be handed in):
**Chapter 12 (Set 2)**: 27, 29, 31, 33, 35, 37, 41, 43.*NOTE: these are from the WMU 8th edition.* - The first part of Q17 is straightforward. For some reason the second part
misses some people. If we are in the elastic region, then the equation for
Young's Modulus can be rewritten as Hooke's Law (F
_{s}= - kx). NOTE: There are TWO ways to find the spring constant "k" -- one is to rewrite the Young's Modulus equation and one is to just solve Hooke's Law. You should do BOTH and prove to yourself that the assertion that elastic tension is like a linear spring. HOWEVER:*NOTE: For the second part of Q17, do NOT just write down Hooke's Law F = -kx and solve for x. Instead, I want you to rewrite the equation for Young's Modulus so it LOOKS like Hooke's Law, and then identify and calculate what k is. NOTE 2: Where does the minus sign in Hooke's Law come from? The spring constant k is NOT negative.*

Thursday 3/31: Review for Exam 3.

April 4/1: Exam 3. (NOT an April's Fool Joke!)

**If you missed Exam 3:**Contact Dr. Phil immediately. I have at least two people taking a make-up Exam 3 on Monday 4 April 2011, at 11am and 2pm. Come by my office.- Week 12 Checklist.

Monday 4/4: Newton's Universal Law of Gravity (or
Newton's Law of Universal Gravity). Gravity is
attractive between any two masses. Same magnitude, opposite direction by
Newton's Third Law. Use Universal Gravity to check "g". The value we
calculate is close, 9.83m/s², which turns out to be only off by 0.2%. Why
is it off? Because using Univeral Gravity in this manner makes the assumption
that the entire Earth is uniform and homogenous from the surface to the core --
which it is not. We would need to integrate over layers to get the observed
value of 9.81m/s². On the other hand, an error of only 0.2% suggests that
treating a roughly spherical Earth as sphere of radius *r* with its mass
at the center of mass, works pretty well. The Shuttle in Low Earth Orbit
(Revisited). Calculating g(r) for *r = 6,770,000 m* (the radius of the
Earth plus the height of 400 km for Low Earth Orbit), we get a value somewhat
different than we found for the centripetal acceleration. Working backwards, we
discover for this radius that the period *T = 5542 sec* and NOT the
estimated 5400 sec (90 minutes) we had started with before. Each radius of
circular orbit has a different value of g(r). As *r* increases, *v*
decreases and *T* increases. Orbital mechanics: Speed up and radius
decreases, slow down and radius increases. For the Moon, the period is around
28 days at a quarter of a million miles away.

Tuesday 4/5: **Orbital mechanics**: Speed up and radius decreases, slow
down and radius increases. 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.
**Tides** (high/low, spring/neap). **Planetary Orbits**. Ptolemy to
Copernicus to Johannes Kepler. Models of the Universe eventually became Models
of the Solar System as we began to understand just how big the Universe is.
Early Man would certainly have felt as if the Earth was the Center of the
Universe (geocentric). But the Sun is very bright and powerful, and it is also
possible to construct models where the Sun is the Center of the Universe
(heliocentric). One could also suggest which objects in the sky were nearer and
which were farther. The BIG stumbling block was that some of the planets, most
especially Mars, exhibited this bizarre retrograde motion, whereby the seem
over the course of some nights to slow down, stop, turn around, go backwards
against the fixed stars, then resume the normal progress through the stars. The
problem of Mars in retrograde. Epicycles, elliptical orbits and Occam's Razor.
Tycho Brahe's observatory and his data. Quiz 18 Take-Home on Universal Gravity
and Kepler, due Friday 8 April 2011, in class or by 5pm.

- Article on Sattelites and Orbits. Diagram.
- Two modern observations: (1) Kepler had to fudge Tycho's data to get his ellipses to work. An analysis of the data indicates that one of the beams in Tycho's physical observatory was apparently cut wrong -- correcting the data makes Kepler's ellipses work just fine. (2) Computer modeling and computational physics sometimes make calculations with simpler models. The set of circular epicycles forms a complete set -- if use you enough epicycles you can reproduce any orbital shape, including non-physical things like a square orbit (!) or proper ellipses. This does NOT mean that orbits really are epicycle-based, only that mathematically you can use them. Remember, there is no good Physics reason for Mars to orbit a point which orbits a point which orbits the Sun -- what would make it do it?
- Sample Book Problems (not to be handed in):
**Chapter 13**: 1, 3, 7, 11, 13, 15, 17, 21, 23, 27,43, 45.*NOTE: these are from the WMU 8th edition.* - Due to copier issues, there weren't enough copies of Q18 in class for everyone (although I ended up with quite a number left.) Either get a hard copy on Wendesday in class, or print from the website.

Wednesday 4/6: **Kepler's First Law** -- All orbits are ellipses, with
the larger mass at one focus. Circular orbits are a special case where the
semi-major axis is the same as the semi-minor asix: *a = b = R*.
**Kepler's Second Law** -- The Equal Area Law is equivalent to a statement
of Conservation of Angular Momentum. **Kepler's Third Law** -- *T² =
C R³*, where *R* is the radius of a circular orbit, or the
semi-major axis *a* in an elliptical orbit. There is one value for the
constant C for every orbital system, i.e. one C for objects orbiting the Earth,
another C for objects orbiting the Sun. More on Kepler's Laws: **1st Law
--** Elliptical orbits, where
*a* is the semi-major axis, *b* is the semi-minor axis and *c*
is the offset between a focus and the center. For an ellipse, *a² =
b² + c²* and the eccentricity is *e = c / a* . The circle is
a special case of an ellipse with *a = b = r* and *c = 0*, making
*e = 0*. **3rd Law --** Again, starting with the universal the
graviational force F_{G} , and using a circular orbit, we can set *F
= ma = ma _{c} = mv² / r* . Using

- Note that in Q18, for Elliptical
orbits we are often not given
*a, b*and*c*, but rather the minimum and maximum distances. Further, we may be given those distances not to the center of the mass*M*, but above its surface. A careful sketch and some straight-line geometry will allow us to calculate*a, b*and*c*.

Thursday 4/7: **Three Classical States of Matter**: Solid, Liquid, Gas.
If chemical reactions do not occur, then there is a progression from Solid to
Liquid to Gas as temperature increases, and vice versa. **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).
Mass-to-Volume Ratio (Density). NOTE: Do not
confuse the Density of the Materials with the Mass-to-Volume Ratio of the
OBJECT.

- For orbits such as Low Earth Orbit, there is a limit to how eccentric an
elliptical orbit is allowed, because as the ellipse elongates in one direction,
it narrows in another, and an object would either hit the atmosphere, either
burning up or skipping off, or hit the Earth -- a disaster in any case. The
eccentricity is
*e = 0*for a circle, and then increases to not quite*e = 1*. - Sample Eccentricities for the Solar System: Earth (e = 0.016711263), Pluto (e = 0.24880766), Halley's Comet (e = 0.967).
- Note that the period for Halley's Comet is not constant, as passing by Jupiter can advance or retard its return by ±6 months or so. Currently T = 75.3 years and Halley's next closed approach to the Sun will be on Thursday 28 July 2061.
- Sample Book Problems (not to be handed in):
**Chapter 14**: 1, 3, 5, 9, 11, 12, 15, 17, 27, 33, 37, 39, 41, 43, 51, 59, 63.*NOTE: these are from the WMU 8th edition.*

Friday 4/8: Mass-to-Volume Ratio Density).
NOTE: Do not confuse the Density of the Materials with the Mass-to-Volume Ratio
of the OBJECT. Density of Water built into the SI metric system (1
gram/cm³ = 1000 kg/m³). Note that a 1 m³ fish tank would have
1000 L of water, or over 250 gallons, and weigh over one ton.
Pressure = Force / Area. SI unit: Pascal (Pa).
Example: Squeezing a thumbtack between thumb and forefinger. One Atmosphere
standard air pressure = 1 atm. = 14.7 psi = 101,300 Pa. Note that 1 Pa is a
very small unit. Pressure at a depth due to supporting the column of liquid
above, *P = (rho) g h *. The difference between Gauge Pressure (pressure
difference inside and out, can be positive, negative or zero) and Absolute
Pressure (total pressure, always positive or zero only for vacuum).

- Beginning Monday, April 11, the Course/Instructor Evaluation System (ICES Online) will open to students for the spring 2011 administration. (via GoWMU)
- The kilogram is the last of the SI units to be defined by an object -- The Standard Kilogram. They are in the process of putting in a new atomic based standard. There is some controversy that the official Standard Kilogram in Paris has lost some mass over the years, probably due to overzealous cleaning.
- rho
_{water}= 1000 kg/m³ ; rho_{seawater}= 1030 kg/m³ ; rho_{sugarwater}= 1060 kg/m³. - Monday 11 April 2011 is the last day to turn in a Draft paper for your science literacy book report.

- Don't forget about your 2010 taxes, if you have to file.
- Monday is last day to turn in a Draft paper, if you want to.
- Week 13 Checklist.

Monday 4/11: Return X3. Pressure at a depth due to supporting the column of liquid above. Water pressure = 101,300 Pa at depth h = 10.33 m. Why you need a qualified SCUBA instructor.

Tuesday 4/12: Water pressure = 101,300 Pa at depth h = 10.33 m. How a straw works in a cup of liquid -- Physics Does Not Suck. Using a column of liquid to make a barometer to measure air pressure. Switch from water to mercury (rho = 13,600 kg/m³) changes h at 1 atm. from 10.33 m to 0.759m. The aneroid barometer. Pressure from a column of liquid looks like P.E. Create a Kinetic Pressure term which looks like K.E. to create Bernoulli's Equation. Water Tower and the Faucet Problem.

Wednesday 4/13: Fluid flow = volume/time = Av. Bernoulli's Equation and the Continuity Equation. When speed goes up, pressure goes down. 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 -- generating Lift.) Classic F.B.D. for straight level flight: Lift vs. Weight and Thrust vs. Drag. The spoiler is a vent door in a wing designed to allow air to flow from bottom to top and thus "spoiling" the pressure difference and "spoiling" the lift. Why the Mackinac Bridge has grates on the inside north- and soundbound lanes -- inside lanes are open metal grates and cannot support a pressure difference. Quiz 19 Take-Home, on Fluids, due Friday 15 April 2011, in class or by 5pm.

Thursday 4/14: **Why Boats Float.** Example: Front lab table as a 250 kg
boat with 4.00 m³ volume. Not only floats, but floats very high.
Calculating how much load can be (safely) added to our "boat".
Buoyant Force = Weight of the Boat = Weight of the Water Displaced by the
Submerged Part of the Boat. Calulating the amount of the boat submerged, by
using the fact that the mass of the boat and the displaced water are the same.
Why many ships leave seacoast harbors during high tide. First Day to turn in
your Topic 1 Paper. First Sample Final Exam.
(Click here and
here for a copy.)

- Sample Book Problems (not to be handed in):
**Chapter 15**: 1, 3, 5, 7, 13, 15, 17, 25, 27, 29, 65, 74 (use as thought question).*NOTE: these are from the WMU 8th edition.* - 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.
- Reminder that ICES Student Course Evaluations are available online via GoWMU 4/11 Mon through 4/24 Sun.

Friday 4/15: Steel canyons and plywood towers -- pressure difference popping
out the windows in a Boston skyscraper (see above). Note that the building
passed its wind tunnel tests by itself, the problem came from not being the
only tall building in Boston. (grin) **More on Water Displacement:**
Archimedes and the Crown -- essentially a non-destructive test to find the
volume displaced by the crown and comparing to the volume displace by an
equivalent mass of gold. **Floating in Air: **The mass-to-volume ratio for
air is 1.29 kg/m³. Balloons, blimps, zeppelins, etc. are all Lighter Than
Air aircraft and can float or rise in air by either using a gas like hydrogen
or helium with a density less than air, or by heating the air (hot air balloon)
and expanding it to lower the total mass of the balloon. (As opposed to Heavier
Than Air aircraft, like airplanes, which depend on Lift to stay in the air.)
**Periodic Motion, Waves and Resonance**. Recall that for any periodic
motion, such as U.C.M., there is a Repeat Time *T *(Period). Frequency*
f = 1/T* . SI units (1/sec) = (Hertz) = (Hz). Revisit Mass on a spring, but
this time in motion. F = -kx = ma. For an open coil spring, at x=0 there is no
force. Stretch the spring to x = +d and let the mass go from rest and will
oscillate back and forth. At x = ±d, v = 0 and |a| = a_{max}. At x
= 0, |v| = v_{max} and a = 0. (Think of conservation of energy, without
friction energy goes back and forth between K = ½ mv² and
U_{s} = ½kx² .) Next, we need a set of equations that do
this, as F_{s} is not a constant and we cannot use kinematic equations.
**Revisit Mass on a spring**. F = -kx = ma.
Generates a 2nd Order Differential
Equation - sine & cosine solutions. Any time you have a conservative
linear restoring force that can act as periodic motion you have a Simple
Harmonic Oscillator that undergoes Simple Harmonic Motion. S.H.O. & S.H.M.
Mass on a spring has an angular frequency *omega = 2pi f= sqrt(k/m)*.
Second Day to turn in your Topic 1 Paper.
Second Sample Final Exam. (Click here and
here for a copy.) Quiz 20 Take-Home on
Floating and Sinking, due Tuesday 19 April 2011, in class or by 5pm.

- Last thoughts on Bernoulli, Lift and spoilers. "Canyons" in skyscraper cities -- windows popping out of the Hancock Tower in Boston. Rotating baseballs.
- Helpful Hint: Remember this is a Science Literacy paper, NOT just a Physics paper. Some of the books don't touch much on Physics at all -- they're on the list to help cover all the sciences, engineering, math, computers, technology, medicine -- and the morality and ethics of using them.

- Monday is the last day to turn in your Topic 1 papers, in class or by 5pm.
- Get your taxes done?
- Week 14 Checklist.
- Reminder that ICES Student Course Evaluations are available online via GoWMU 4/11 Mon through 4/24 Sun.

Monday 4/18: **Mass-on-a-Spring** -- S.H.M. of a S.H.O. Angular frequency
*omega = sqrt (k/m)*. *f = (1/2pi)(sqrt (k/m))*. *T = 1/f =
(2pi)(sqrt(m/k))*. **Simple Pendulum** -- All the mass *m* is in the
bob, a distance *L* from the pivot point. The string or rod is considered
massless. The Small Angle Approximation is that if *theta _{max}*
is kept "small", then

Tuesday 4/19: **Rewriting our solution:** Since the sine curve and the
cosine curve are the same shape, just offset by 90°, we can write *x(t)
= A cos ((omega) t + phi)*, where *phi* is called a phase angle to
shift between cos and sin functions and linear combinations of the two.
**Quick mentions**: Damping with *Drag Force = - bv.* Adds an
exponential term to our S.H.O. solution, because our differential equation now
has both a first and a second derivative in it -- see Serway. Three cases:
Underdamped, overdamped, critically damped. Need a tuned suspension with shock
absorbers to drive a car safely on the road. **Waves**: Single Pulse vs.
Repeating Waves. The motion of the material vs. the apparent motion of the
wave. Demonstration: the Slinky shows both longintudinal (string type) and
transverse waves (sound type). Hand out Q21.

- Topic 1 Papers, unless you had a Draft evaluated by Dr. Phil, are now officially LATE -- and will incur a 10,000 point a day penalty.
- Remember: If you had a Draft paper evaluated by Dr. Phil, then you should also turn in that marked-up Draft, along with your Final Paper. (If you forgot to do this, just hand the Draft in to Dr. Phil.)

Wednesday 4/20: For Repeating Waves, we
have a Repeat Length (wavelength) and a Repeat Time (Period). Frequency =
1/Period. Angular frequence *omega = 2 pi f*. Wave Number *k = 2 pi /
wavelength* .Wave speed = frequency × wavelength. Using our knowledge
of the differential equation of the S.H.O. and its solution, we can generate
the Wave Equation for a traveling wave
moving through space (x) and time (t). **Superposition Addition of Waves:
**Constructive and Destructive Interference. **Resonance** allows us
to see the wave confined to the geometry of the problem.
Standing Waves on a string.
Fundamental, First Overtone, Second Overtone, etc. Demonstration: First and
higher overtones on a string driven by a saber saw. Vary the wave speed by
changing the tension -- *v = sqrt(T / µ)*, where *µ =
mass/length = m / L* . Standing
Waves in a tube. Demo: Variable length organ pipe (closed at one end),
plastic tube (open at both ends). Musical instruments: Accoustic string
instruments have a resonance box and can have many strings (piano) or few
(guitar, violin). Brass instruments start from the "natural trumpet",
which can only play the fundamental and overtones for the pipe. It is a mixture
of overtones in various proportions to the fundamental which allows us to tell
instruments apart. Quiz 22 Take-Home on Resonance and Standing Waves, due
Friday 22 April 2011. *NOTE: This is the Last Quiz which requires Physics.
Remember, of Q1-23, the lowest three scores (including zeroes) are
automatically dropped.*

- Video: Standing waves and resonance can occur when you don't want them to,
sometimes with disasterous results. See
The
Tacoma-Narrows Bridge Disaster.
*NOTE: The video in this article is shown in real time -- it is NOT speeded up.* - Q21 erroneously says due "Wednesday 21 April 2011", which can't be. (grin) So we will collect Q21 on Thursday.
- If you still need to take an Exam 1, 2 or 3, contact Dr. Phil by email immediately.
- Quiz 23 will be a Check-Out form to fill out after you've taken the Final Exam. If you don't remember your 5-digit PID number, you will be able create a 2nd PID number.

Thursday 4/21: **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. Demo: Tuning forks require both tines to work
-- the "sound of a tuning fork with one tine" is that of silence. 256
Hz tuning fork attached to a resonance box optimized for the wavelength of
sound from *f = 256 Hz* at room temperature. A second indentical box will
sympathetically resonate in response. "Normal" human hearing is
frequencies from 20 Hz to 20,000 Hz. Artilleryman's ear -- mid-range hearing
loss. 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} |* .Constructive and Destructive
Interference. Acoustics of concert
halls. If you exceed the wave speed in a material, you get a Shock Wave --
distinctive V-shaped pattern from front and back of moving object. Sonic booms
in air (actually get a double-boom, because of the two V's.), wake from a boat
in water.

- NOTE: If you looked at the Q20 Solution earlier, parts (d) and (e) were not for this quiz. Apologies for the confusion. Fixed now.
- NOTE: Find out which ultrasonic ringtones you can
hear! Dr. Phil's result today: "
." Considering I'm age 52, I'll take it. (grin)**You are a thirtysomething**. You're a little frustrated that you can't hear all the tones that the young 'uns can but will be more than happy if it means you don't have to listen to their damn ringtones on the bus anymore. The highest pitched ultrasonic mosquito ringtone that I can hear is 14.9kHz - NOTE 2: Technically, any of the sounds you can hear from 14kHz to 20kHz are within the range of human hearing, and by definition are NOT ultrasonic.

Friday 4/22: Last Day of Class. Review.

- Finals Week Office Hours posted.
- Note that Dr. Phil will NOT be in to campus on Thursday 28 April 2011.
- The Late Final Exam is Friday 29 April 2011, 11:00am-1:00pm, in Bradley Commons next to Dr. Phil's office. Send Dr. Phil and e-mail if you plan on coming to the Late Final Exam, so I can plan to print up enough copies of XFL.
- Quiz Solutions 2-21 are posted. Q22 will be posted later, since people are still turning those in.
- What with snow days, etc., we ended up one lecture shy of what Dr. Phil
covered in his Fall 2010 class. These topics, which are on the Sample Final
Exams, will NOT be on our Final Exam:
- The Laws of
Thermodynamics. (Zeroeth Law -- There is such a thing as temperature.)
Entropy examples -- It takes work to clean or restore things. Left to
themselves, everything falls apart. The Heat
Engine and Three Efficiencies (Actual, Carnot
and 2nd Law). To get temperatures in Kelvins, add 273 to the temp in
°C -- we need Kelvins so that the temperatures cannot be zero or negative.
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.
Smaller, lighter cars with smaller, lighter engines. To improve efficiency, can
reduce T
_{C}or raise T_{H} - Note: Reverse the arrows in the Heat Engine and you
get a Refrigerator. Cannot place an open refrigerator or a window air
conditioner in the middle of a room and cool the room, because the exhaust heat
to the hot side includes the heat pulled from the cold side plus the work done
on the compressor. A Heat Pump is a reversible system which cools inside of the
house in summer and heats the inside of the house in winter -- just because it
is cold outside, doesn't mean there is not heat energy Q in the outside air.
(There
*has*to be, otherwise the air would be at 0 K.)

- The Laws of
Thermodynamics. (Zeroeth Law -- There is such a thing as temperature.)
Entropy examples -- It takes work to clean or restore things. Left to
themselves, everything falls apart. The Heat
Engine and Three Efficiencies (Actual, Carnot
and 2nd Law). To get temperatures in Kelvins, add 273 to the temp in
°C -- we need Kelvins so that the temperatures cannot be zero or negative.
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.
Smaller, lighter cars with smaller, lighter engines. To improve efficiency, can
reduce T