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Lectures in PHYS-1070 (24)

Updated: 01 May 2012 Tuesday.

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FINAL COURSE GRADES AND BREAKDOWN BY CATEGORY FOR PHYS-1070 Spring 2012.

Estimated Pre-Finals Grades can be found here.
NOTE: I've posted the Revised Exam 2 curve here.
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Reminder that ICES Student Course Evaluations are available now online via GoWMU .

• Click the "Course/Instructor Evaluation System (ICES Online)" link in the "My Self Service" channel and follow the simple instructions.
• Week of 23-27 April 2012.

Monday 4/23: Office Hours.

Tuesday 4/24:

Wednesday 4/25: FINAL EXAM (12:30pm-2:30pm)

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.

Week of 9-13 January 2012.

Monday 1/9: Class begins. The nature of studying Physics. Science education in the United States. Natural Philosophy. The Circle of Physics.

Tuesday 1/10: Aristotle and the Greek Philosophers. Observation vs. Experiment - Dropping the book and the piece of paper (2 views). Mechanics is the study of motion. So what is motion? Zeno of Elea -- Zeno's Paradoxes. Distribute syllabus.

• The Apollo 15 Hammer and Falcon Feather Drop webpage. QuickTime movie: (low res 8MB, higher res 80MB)
• Reminder to those of you who need take the lab -- PHYS-1080 is a separate 1-credit course. Labs start next week.
• Wednesday 1/11: To understand the underlying concepts we need to Simplify The Universe. "Speed Limit 70" -- what does it really mean? First Equation: Speed = Distance / Time. v = d/t . Development of Speed equation for Constant or Average Speed. delta-x = xf - xi , x = x0 + v t .

• Quiz 1 will be in-class on Thursday 12 January 2012. It will be for attendance purposes. If you miss class on Thursday, you will be able to get some of the points by downloading Quiz 1A from the website and turning it in.

Thursday 1/12: English system of measurement. SI Metric System. Prefixes. What do we mean by Measurements? "Units will save your life." What is "1 m/s"? We need a few benchmark values to compare English and SI Metric quantities. NOTE: English-to-Metric conversions will NOT, with two exceptions, be tested on in this course. 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. He also has the World Record in the 200 meter dash (19.19 seconds).) Q1 and your PID number. Quiz 1 was given in-class on Thursday 12 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.)

Friday 1/13: What is "1 m/s"? We need a few benchmark values to compare English and SI Metric quantities. NOTE: English-to-Metric conversions will NOT, with two exceptions, be tested on in this course. 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 (9.683 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). Speed. 60 m.p.h. = "A Mile A Minute". It's a nice alliterative phrase and wasn't possible for Man to move at 60 mph until 1848: The Antelope, but it really isn't a special speed, just an accident of the English system of measurement. Significant Figures -- Although our calculators typical work with 12 digits and display 10 digits, a 10 digit measurement would have 10 significant figures. Such a measurement has to cost at least a million dollars to make. A meter stick measured to 10 significant figures requires us to know where the last few atoms are on the ends! We'll talk more about this on Tuesday. 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.

Week of 16-20 January 2012.

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

Tuesday 1/17: PTPBIP - Putting The Physics Back Into The Problem. Handout on (1) Prefixes for moving the decimal place for larger and smaller powers of ten in the SI metric system, (2) Scientific Notation, as in 1.23 × 1012 and using the"EE" key on your calculator, and (3) Dr. Phil's Simplified Significant Figures for multiplication, division and trig functions. (Click here if you need a copy.) A simplified trip to the store -- The S-Shaped Curve. Acceleration. 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).Q2 Take-Home quiz on speed = distance / time, due on Thursday 19 January 2012, in class or by 5pm.

Wednesday 1/18: A simplified trip to the store -- The S-Shaped Curve. Acceleration. Just as the equation v = d / t is for constant or average speed, the equation a = delta-v / delta-t is for constant or average acceleration. Finding the set of Kinematic Equations for Constant Acceleration. The Equation Without Time -- Avoiding the Quadradic Formula. To aid in setting up problems with the kinematic equations, you might try to list all six kinematic variables (x0, x, v0, v, a and t) and give the values for those you know, those you don't know and those you want to find out. This will help you choose which kinematic equation(s) you'll need. Finishing The S-Shaped Curve: plotting x-vs-t gives straight line in Region II, but parabolic curves for Regions I and III.

• Example from class: A car accelerates from rest to 60 mph (26.8 m/s) in a distance of 255 m. What is a? What is t?
• The kinematic variables become: x0 = 0, x = 255 m, v0 = 0, v = 26.8 m/s, a = ?and t = ?
• Answers: a = 1.408 m/s² , t = 19.03 sec. We checked t by using both Kinematic Equations (1) and (2).
• The Equation Without Time is generated by combining Kinematic Equations (1) and (2) to eliminate t as a variable. You should try this at home!
• The Physics Help Room is now open in 0077 Rood (basement level, underneath the lecture halls -- use Southwest staircase). This semester the Help Room will be staffed with two people most of the time and open from 10-3 MTWRF.

Thursday 1/19: Problem: A rifle bullet is fired from rest to faster than the speed of sound, 415 m/s, in a distance of 1.00 m. Find a. Answer, a = 86,110 m/s². This is huge, which is why we don't fire people out of rifle barrels. Find t = 0.004819sec. Again, we could solve for t using two different equations, but will still get the same result because there is one Physics. To aid in setting up problems with the kinematic equations, you might try to list all six kinematic variables (x0, x, v0, v, a and t) and give the values for those you know, those you don't know and those you want to find out. This will help you choose which kinematic equation(s) you'll need. 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 = g = 9.81 m/s². That's nearly ten times the acceleration a = 1 m/s² we just talked about. With these two known acceleratoins, we can now have something to compare our accelerations a. Q3 Take-Home quiz on the Kinematic Equations for Constant Acceleration, due on Tuesday 24 January 2012, in class or by 5pm.

• For a = 1.00 m/s², we created a table with 3 columns: t, v = at, x = ½at², with t0 = 0, v0 = 0, x0 = 0. We then found v and x for t = 1, 2, 3, 4, 5, 10, 25 and 100 seconds.
• NOTE: The 4 Kinematic Equations given in class are not in your textbook in this form. There are two problems with Chapter 1. (1) It seems to assume you've already had some Physics all ready, so it covers too much material, too fast. (2) It also falls short of the Kinematic Equations, treating our three simplest motions as separate phenomenon (no motion x = x0 ; constant speed x = vt from x0 = 0; constant acceleration x = ½at² from v0 = 0, x0 = 0), instead of allowing you to accelerate even if are already moving. (!!)
• What Dr. Phil is giving you is more complete and more useful -- and ultimately easier to understand.

Friday 1/20: Free-Fall: If we ignore air resistance, all objects near the surface of the Earth fall towards the Earth at the same rate. ay = -g ; g = 9.81 m/s². That's nearly ten times the acceleration a = 1 m/s² we talked about last week. Rewriting the Kinematic Equations for motion in the y-direction, pre-loading them for free-fall. Example: Falling off a ten-foot roof (3.00 meters). The consequences of Falling Down... ...and Falling Up. The Turning Point ( vy = 0, but ay = -g during whole flight). The illusion of "hanging up there in the air" at the turning point.

• Many students at this point seem to "hate" all these Physics variables, so they make the mistake of replacing the letters with numbers as soon as possible, and then try to do algebra on numbers. This is a lot harder. Note that Dr. Phil on the blackboard does all the algebra first, then puts the numbers (and units!) in, checks the units and only then does the math on the calculator.
• At this point in the course we are battling a Lack of Experience doing these sorts of problems and Lack on Confidence that you can do these sorts of problems -- these two things feed off each other and can make you miserable. The solution? Do more problems. Then talk with someone else in the class or come to Office Hours.
• Physics Misconceptions: Falling Down is easy. But if you are Falling Up, the tendency is to have a positive acceleration because you're going up -- except you're slowing down so a = -g. At the turning point the speed is zero ONLY for an instance of time. Just because the speed is zero, doesn't mean a = 0. If acceleration WAS zero at the turning point, you could toss an object up in the air, it would slow to a stop -- and stay there!
• Rusty on your math? 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.
• Week of 23-27 January 2012.

Monday 1/23: The P-O-R (Press-On-Regardless) road rally problem. "You can't average averages." Comments on Q2 -- solution already posted on class webpage. Note that part (c) is just like the P-O-R problem. Motion in Two-Dimensions: You may be able to break it 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 (x0, x, v0x, vx, ax, t), but only 5 from the second (y0, y, v0y, vy, ay), because time is the same. Remarkably, with a couple of reasonable assumptions, there are only 3 unknown variables (v0x, t, vy). Time links the two one-dimensional problems together. We need to find v0x , 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.

• Quiz Solutions are posted on the class web page.
• Friday's class notes now updated below.

Tuesday 1/24: Demo: These class webpages online. How much acceleration can a human take? See story of Scott Crossfield below. Two kinds of numbers: Scalars (magnitude and units) and Vectors (magnitude, units and direction). Adding and subtracting vectors: Graphical method. Q4 Take-Home quiz on Falling Up and Falling Down, due on Thursday 26 January 2012, in class or by 5pm.

• Quiz 3 due date extended to Wednesday 25 January 2012, in class or by 5pm. (Click here for a copy.)
• You really want to do the algebra first and substitute in your numbers and units only after you have an equation in the form where it will give you the answer you need. Much easier to check your work and check your units to see if you equation is valid, then just doing this stuff in your head.
• (I thought the following was in your syllabus, but it wasn't.) "... since one of the grading requirements is that you "show your work" on the paper, unless you intend to staple your calculator to each problem, you simply can’t get any credit for simply using your Solver function. It is the same thing as "doing the work in my head" – unless you intend to staple your head to the paper, you won’t get credit for the work."
• a = 1000 g for a millisecond: Discovery Channel and YouTube come through! I've been telling the story of North American Aviation company test pilot Scott Crossfield and the static test stand explosion of the X-15 for years, and just now discovered that there's video online of this! You can see more successful flights of the three X-15 aircraft in this video and the first segment of this newsreel video. For more detailed shots of training, flights, landing, and the damage from a white covered X-15 flight that reached Mach 6.7, one last video. The X-15 lands as a glider, like the Space Shuttle, but it's a lousy glider. The only way the F-104 chase planes can follow it easily to the dry lakebed runway is to drop flaps and landing gear, and the X-15 still falls out of the sky like a brick. (grin)

Wednesday 1/25: 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. SOHCAHTOA. Adding and subtracting vectors: Analytical method. (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.

• NOTE: QUIZ 4 Parts (d) & (e) are poorly written (!!). Using the time from (c) plus the principle that the "time to fall" is the same as the "time to rise" and calculate (d) the position of the ball and (e) the speed v of the ball for at the end of the entire trip from when Jacque tosses the ball up to its return to his hand. Note: The answer to (e) is not zero.
• Note that today's lecture on vectors may be the single hardest concept all semester -- so if you have questions, you are probably not alone!
• Key things to keep in mind about vectors: (1) Draw a sketch of your problem. (2) DON'T draw a 45°-45°-90° isoceles right triangle, unless that is what you REALLY have. (3) Usually your vector's triangle should have a long side and a short side, plus the hypotenuse which is the longest side, as well as a small angle and a large angle, plus the 90° right angle. (4) Always check to see if your calculator is in Degrees mode before you start. (5) With the four equations for x-component, y-component, Pythagorean Theorem and the Arctangent equation for the angle theta, you can always check your work and make sure your numbers are correct.

Thursday 1/26: Standard Form: Vector-A = 5.00m @ 30°, Vector-B = 7.00m @ 120°. Adding and subtracting vectors: Analytical method. (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. Examples: vector C = vector A + vector B, vector D = vector A - vector B. Use you sketche to check your work.

• Facebook never sent me any notices of people trying to join Dr. Phil's New Physics Class on Facebook -- so when someone emailed that they hadn't heard anything, I checked and there were 24 names awaiting approval. (!!) All but two have been added. If your Facebook name is NOT the same as your WMU name, send me an email and we'll add you.
• Paul Pancella will be giving a public lecture, "Hondatron: An Amateur Electric Vehicle Conversion", this Friday at 4 p.m. in 1118 Rood Hall. Further info may be found here: http://www.wmich.edu/wmu/news/2012/01/053.html .
• Due to the problem with unclear wording in Q4, we'll collect them on Friday 27 January 2012.
• Rusty on your math? 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.
• Note that today's lecture on vectors may be the single hardest concept all semester -- so if you have questions, you are probably not alone!
• Key things to keep in mind about vectors: (1) Draw a sketch of your problem. (2) DON'T draw a 45°-45°-90° isoceles right triangle, unless that is what you REALLY have. (3) Usually your vector's triangle should have a long side and a short side, plus the hypotenuse which is the longest side, as well as a small angle and a large angle, plus the 90° right angle. (4) Always check to see if your calculator is in Degrees mode before you start. (5) With the four equations for x-component, y-component, Pythagorean Theorem and the Arctangent equation for the angle theta, you can always check your work and make sure your numbers are correct.

Friday 1/27: Ballistic or Projectile Motion 2-D problem where ax = 0 and ay = -g. Covers anything shot, thrown or kicked into the air which is unpowered and where we can ignore air resistance. Ancient cannons. 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. Sample Exam 1: First Set here (includes pp. 5-6, handed out in class). Quiz 5 is a Take-Home quiz on Vectors, handed out on Friday 27 January 2012 , and due on Tuesday 24 January 2012, in class or by 5pm.

• More Sample Exam 1s can be found on the class web page. NOTE: There are Exam 1's from previous semesters with solutions -- most Sample Exams do NOT come with solutions, so you can learn how to assess your own answers. PTPBIP!

Week of 30 January-3 February 2012.

Monday 1/30: Ballistic / Projectile Motion: You can only use the Range Equation if the landing height is the same at the launch height. If it is not, you can still break the problem into two pieces and find the t and height h at the turning point, then solve for the time from rest in the y-direction down to the landing point, no matter whether it is above or below the launch height. Classic Simple Pursuit (Cop and the Speeder). Starting from rest, the contant accelerating cop ends up with a final speed twice that of the uniform motion speeder -- because they both have to have the same average speed (same place, same time). There are two times when they are in the same place and the same time -- the other solution is at t=0.

• 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.
• If you have to take a square root to get an answer, remember that there are two possible answers, plus or minus, to a square root.
• If you divide both sides of an equation by t , then algebra says that t=0 is one of your solutions.
• Something to think about for Tuesday -- when we did the problem with guy with the cigar and fedora, we found the x- and y-components of the final velocity. What is v-vector in Standard Form?
• Look at real world v-vs-t graphs in a car magazine. The line is curved, not straight and has small hiccoughs. The variable for change in acceleration is called "jerk" (SI units m/s³), j = delta-a/delta-t, and you can feel it as a jerk. We may talk about jerk in this class, but we won't be creating the Kinematic Equations for Constant Jerk in PHYS-1070.

Tuesday 1/31: Types of Motion: No Motion (v=0, a=0), Uniform Motion (v=constant, a=0), Constant Acceleration (a=constant). Uniform Circular Motion (UCM): speed is constant, but vector velocity is not; magnitude of the acceleration is constant, but the vector acceleration is not. Velocity is tangent to circle, Centripetal Acceleration is perpendicular to velocity and points radial INWARD. ac = v²/r. You can generate very large centripetal acclerations very quickly. Example: A hard disk drive spinning at 3600 rpm (60 times a second, time for one revolution = 1/60th of a second). Q6 Take-Home quiz on Projectile Motion, due on Thursday 2 February 2012, in class or by 5pm.

• REPEAT REQUEST: Something to think about for Tuesday Wednesday -- when we did the problem with guy with the cigar and fedora, we found the x- and y-components of the final velocity. What is v-vector in Standard Form?

Wednesday 2/1: Using Vector Addition for Velocities: Upstream, downstream (rivers), Headwind, tailwind, crosswind (airplanes). Uniform Circular Motion (UCM): speed is constant, but vector velocity is not; magnitude of the acceleration is constant, but the vector acceleration is not. Velocity is tangent to circle, Centripetal Acceleration is perpendicular to velocity and points radial INWARD. ac = v²/r. Space Shuttle in Low-Earth Orbit. (There's still gravity up there!)

Thursday 2/2: Demo: Rodney Reindeer and U.C.M. The moment the centripetal acceleration is zero, Rodney travels ballistically with an initial velocity that is the last tangential velocity. The guard around a circular saw blade takes the sawdust and broken bits which shoot out tangentially from the blade and redirects them to a bucket -- improves safety and makes less of a mess. 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. (Falling apple and Mars.) Review for X1. Return Q3.

Friday 2/3: Exam 1.

Week of 6-10 February 2012.

Monday 2/6: 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. (Reeding on the edge of the silver shilling or a U.S. dime/quarter, "mad as a hatter" from mercury poisoning.) 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.)

• IF YOU MISSED EXAM 1: Dr. Phil would like to be able to arrange for Make-Up Exam 1s to be given on Monday 6 February 2012 (50 minutes 10:30-11:45 or 2:30-4:30) or Tuesday 7 February 2012 (50 minutes 11:45-12:45 or 2:30-4:30). Send Dr. Phil an email either confirming one of these times OR arrange for some other time. Thanks!

Tuesday 2/7: Newton's Three Laws of Motion. SI unit of mass = kilogram (kg). SI unit of force = Newton (N). 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). The normal force does NOT automatically point up and it is not automatically equal to the weight -- we have to solve for the normal force. "The Normal Force is NOT automatically present -- you have to be in contact with a surface. The Normal Force does NOT automatically point up -- FN is perpendicular to the surface. The Normal Force is NOT automatically equal to the weight. FN = mg only if there are no other forces in the y-direction." Sum of forces in x or y equations -- either will be equal to 0 (Newton's 1st Law) or ma (Newton's 2nd Law). Example of 125 kg crate being dragged/pushed 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.). Variations as we allow for an applied force that it at an angle. Push down and Normal Force increases. Q7 Take-Home, due on Thursday 9 February 2012, in class or by 5pm.

Wednesday 2/8: Example of 125 kg crate being dragged/pushed 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.). Variations as we allow for an applied force that it at an angle. 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. 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.

• For the problem in class, assume we had a sign with m = 15.0 kg, then find the two tension forces, T1 and T2.

Thursday 2/9: 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. For the problem in class, we had a sign with m = 15.0 kg and two tension forces, T1-vector = 107.7 N @ 150° and T2-vector = 131.9 N @ 45°. You can check to make sure these forces cancel in the x-direction and support the weight of the sign in the y-direction. Discussion of "two pound test fishing line", stretching and breaking of cables, Safety Factors. Inclined plane problems: Change the co-ordinate system, change the rules. In the tilted x'-y' coordinates, this is a one-dimensional problem, not two-dimensional. Q8 Take-Home quiz on Force and Acceleration, due on Tuesday 14 February 2012, in class or by 5pm.

• Note how when we put the numbers into the Sign with angled wires problem that we were able to check our answer by finding the x- and y-components of the two tensions and verify that the x-components cancel and that the y-components support the weight, at expected. PTPBIP.

Friday 2/10: X1 returned. Atwood's Machine -- two masses connected by a single cable via a simple pulley. They share a common acceleration, a, with one mass going up and the other going down. 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.

Week of 13-17 February 2012.

Monday 2/13: Two kinds of Friction: Static (stationary) and Kinetic (sliding). For any given contact surface, there are two coefficients of friction, µ, one for static (µs) and one for kinetic (µk). Static is always greater than kinetic. 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. If velocity vector and acceleration vector point in the same direction, then the speed is increasing. If they are in the opposite direction, then the speed is decreasing. In either case, for a car the force involved must be in the same direction as the acceleration vector -- this seems to be confusing whereby the static friction force on the tires from the road points forward when you are speeding up. The conflict arises because you might be thinking "friction opposes motion" and not thinking about the motion of the tires versus the motion of the car. 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"). 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.

• 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.

Tuesday 2/14: Friction 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") and we switch to kinetic friction, or if static friction "wins" then we remain at rest. Static Friction can vary from zero to its max value in either direction. Kinetic Friction has only the one value. If you push with a force equally the kinetic friction, you will move at a constant speed. Otherwise you will either a positive or negative acceleration. Finding the coefficient of static friction by tilting: µs = tan(thetamax). Similar for kinetic friction, except one has to tap the board to "break the static friction barrier". Rubber on concrete. Can µ be greater than 1? Means thetamax greater than 45° -- rare, but yes. Q9 Take-Home quiz on Tensions and Friction, due on Thursday 16 February 2012 (?), in class or by 5pm.

• New York Central M-497 Jet Powered Train (not using static friction for acceleration): Article - Video 183.68 mph.

Wednesday 2/15: We are not done with Forces, but some problems cannot easily be solved by using forces. Collisions, for example, are very complex if we have to put in all the forces of bending and breaking and mashing things. Need a simpler way of looking at the problem. "Inertia" is a word which isn't used much today, but it is the same as "momentum" -- represents some kind of relentless quality of movement. It takes a force to change the momentum, otherwise it just continues on, i.e., Newton's 1st Law. Linear Momentum ( p = mv ) is a vector quantity. Newton's form of the 2nd Law: F = delta-p / delta-t = change in momentum / change in time instead of F=ma, but really the same thing. Two extremes in collisions: Totally Elastic Collision (perfect rebound, no damage) and Totally Inelastic Collision (stick together, take damage). Linear momentum is conserved in all types of collisions . Totally Inelastic Collisions. Example: The Yugo and the Cement Truck with numbers. Real Head-On collisions. Three example collisions: (1) Head-on Collisions. (2) Rear-end Collisions. (Also... The Non-Collision -- if the car following is going slower, it isn't going to run into the car ahead. PTPBIP.) (3) ...

Thursday 2/16: Three example collisions: Head-on Collisions. Rear-end Collisions. (The Non-Collision -- if the car following is going slower, it isn't going to run into the car ahead. PTPBIP.) 2-D Side Impact (vector) collision. Real crashes. Interactions of safety systems: Seat belts, shoulder belts, steel beams in doors and crumple zones. The myth of it being better to be "thrown clear from the wreck". What happens in a wreck. How airbags work. Note: We do NOT want our cars to have Totally Elastic Collisions -- the whiplash on our fragile bodies would be awful. Instead, our cars are designed to crumple and "die" for us.

• Exam 2 has been moved to TUESDAY 28 February 2012.

Friday 2/17: What's the opposite of a collision? An explosion. Or recoil. Example: A clown on roller skates at rest -- when he hurls a pie to the left, he goes to the right. Total momentum of the system remains constant (in this case, zero). We've talked about How things move (Kinematic Equations) 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. Kinetic Energy -- an energy of motion, always positive, scalar, no direction information. Work-Energy Theorem (net Work = Change in K.E.). Using the Work-Energy Theorem to find a final speed. Q10 Take-Home quiz on Total Inelastic Collisions, due on Tuesday 21 February 2012, in class or by 5pm.

• Reminder that Exam 2 has been moved to TUESDAY 28 February 2012.

Week of 20-24 February 2012.

Monday 2/20: Work: A Physics Definition (Work = Force times distance in the same direction). Work = Energy. Power = Work / time. Kinetic Energy -- an energy of motion, always positive, scalar, no direction information. Work-Energy Theorem (net Work = Change in K.E.). Using the Work-Energy Theorem to find a final 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, Fc = mac = mv²/r , comes only from the weight, w = mg. Remember, that the centripetal force is a NET force, i.e., F = ma is Newton's 2nd Law, so the net external force goes on the right side of the sum of forces equations.

• Trading height (PE) for speed (KE) and vice versa is standard practice in aircraft. Also utilitized on NASA's zero gravity simulators, affectionately known as the Vomit Comet. Most of the zero-gee scenes in the movie Apollo 13 were filmed on a NASA KC-135A.

Tuesday 2/21: Example: Rollercoaster with h1 = 45.0 m, v1 = 0, h2 = 0, h3 = 12.0 m, h4 = 0 (bottom of loop-the-loop), h5 = 12.0 m (top of loop-the-loop, making D = 12.0 m and r = D/2 = 6.00 m). Results: v2 = 29.xx m/s, v3 = 25.44 m/s. v5 = v3 is well above the minimum speed to safely do the loop-the-loop. Exchanging height for speed with conservation of T.M.E. -- because energy is a scalar, we lose all directional information, so the path taken between points 1 and 2, and the initial/final directions do not matter. Work = Energy. Power = Work / time. Power is rate that work can be done. 1 horsepower = 1 h.p. = the amount of work that one man, one horse and one plow can do in a day. An engine with "more power" can either do the same work in less time, or do more work. Q11 Take-Home quiz on Conservation of Energy, due on Thursday 23 February 2012, in class or by 5pm.

• A horsepower is based on the amount of work that one man and one horse and one plow can do in one day. Of course, in the real world, there is a lot of variation in horses, fields, plows, etc., so some horses can have power more or less than 1 h.p. If you've seen the beginning to the movie War Horse, you can have some idea of the suitability of having a thoroughbred race horse plowing a field.

Wednesday 2/22: Return Q2/4/5/6/7. 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 into a block of wood, followed by Conservation of TME, as the block+projectile swings up and comes to a stop. Newton's Universal Law of Gravity (or Newton's Law of Universal Gravity). 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 calculus to integrate over layers to get the observed value of 9.81m/s². UCM Revisited. 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.

• Finding the universal constant G was complicated by (1) the gravitational force between two ordinary objects is very small and (2) how do you figure out the mass of the Earth when you're standing on it?

Thursday 2/23: Four Fundamental Forces in Nature: Gravity, E & M, Weak Nuclear Force, Strong Nuclear Force. Surprisingly, gravity is the weakest of these, but it holds the universe together because things like planets, stars and galaxies have so much mass. 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. Geosynchronous orbits occur when 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. Newton's Law of Universal Gravity and Tides (high/low, spring/neap). Q12 is a Take-Home quiz on Newton's Law of Universal Gravity, and due on Monday 27 February 2012, in class or by 5pm.

• Quiz 12 says you need to draw separate F.B.D.s for both people. Seriously. You need to. Do this. You're welcome.

Friday 2/24: Dr. Phil has canceled today's classes due to weather / illness. Updates later today. NOTE: Exam 2 has been moved to TUESDAY 28 February 2012.

• Q12: You are not trying to find the force between the Earth and the Moon. And I have already given you the weight of the men from Earth's gravity.
• The mass of the Moon should be in your textbook. But it is: 7.36 × 10²² kg.

Week of 27 February-2 March 2012.

Monday 2/27: Review for X2. We've asked: How do things move? (kinematics) Why do things move? (forces) What effort does it take to move? (work and energy) Now we ask -- What moves? 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).

• NOTE: Winter Ice Storm Warning from Tuesday 10pm to Wednesday 7pm. Plan accordingly, keep track of the weather.

Tuesday 2/28: Exam 2.

Wednesday 2/29: 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. 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. Why Boats Float. Example: Front lab table as a 250 kg boat with 4.00 m³ volume. 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.

• Table 4-4 on p. 145 of O&B shows mass-to-volume ratios of various materials: Lead (Pb) = 11,340 kg/m³; Gold (Au) = 19,300 kg/m³; Liquid mercury (Hg) = 13,600 kg/m³.

Thursday 3/1: Q13 In-Class. Example: Front lab table as a 250 kg boat with 4.00 m³ volume. 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. 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. Sinking of the RMS Titanic; Edmund Fitzgerald. Archimedes and Eureka! (I found it!) 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. Pressure at a depth due to supporting the column of liquid above. Absolute (total) Pressure vs. Gauge Pressure (difference between two readings). Pressure due to a column of water = 1 atm. at h = 10.33m = 33.86 feet. The perils of SCUBA diving.

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

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

Week of 5-9 March 2012.

SPRING BREAK -- NO CLASSES.

Week of 12-16 March 2012.

• 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.
• Mid-Term course grades are available via the Mid-Term Grades on GoWMU. Please note that these are still rough estimated grades only. (1) If you haven't yet taken Exam 2, then your Exam 1 grade was used for an estimated grade. (2) We have sufficient quiz grades recorded that your current 3 lowest quiz grades have been dropped.

Monday 3/12: Reset. One Atmosphere standard air pressure = 1 atm. = 14.7 psi = 101,300 Pa. Pressure at a depth due to supporting the column of liquid above. Absolute (total) Pressure vs. Gauge Pressure (difference between two readings). Pressure due to a column of water = 1 atm. at h = 10.33m = 33.86 feet. Absolute (total) Pressure vs. Gauge Pressure (difference between two readings). Using a column of liquid to make a barometer to measure air pressure. Switch from water to mercury changes h at 1 atm. from 10.33 m to 0.759m. The aneroid barometer. How to get liquid out of a cup using a straw -- or why Physics does not "suck", but pushes using a pressure difference.

• Table 4-4 on p. 145 of O&B shows mass-to-volume ratios of various materials: Lead (Pb) = 11,340 kg/m³; Gold (Au) = 19,300 kg/m³; Liquid mercury (Hg) = 13,600 kg/m³. (From various examples given before Spring Break and today.)

Tuesday 3/13: Water is unusual in two ways: (1) Water is relatively incompressible. If the depth h isn't too deep, then the Mass-to-Volume ratio for water is constant. For great depths, such as the bottom of the oceans, we can't use our simple equation because rho is not constant. Air and gasses are compressible, so we can't use our pressure from a column of fluid equation either, though the air pressure here on the surface of the Earth is based on supporting the weight of the column of air above us. (2) 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. 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. Water Tower and the Faucet Problem. Why the water tower needs a vent. Q13 Take-Home quiz on Pressure and Bernoulli's Equation, due on Thursday 15 March 2012, in class or by 5pm.

• Bernoulli's Equation, with six terms, is the longest equation of the semester. But like the Conservation of TME, upon which it is based, often we don't need all six terms and Bernoulli often simplifies to quite managable equations.
• Note that the solution to the water tower problem is the same equation as if I had just dropped the water from rest at the top of the water tower. (grin)

Wednesday 3/14: (Happy Pi Day! 3.14...) 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. Air Resistance. Low speed and high speed air resistance. If allowed to drop from rest, then a real object may not free fall continuously, but may reach a Terminal Velocity (Force of gravity down canceled by Drag force up) and doesn't accelerate any more. Ping-pong balls versus turkeys (or pennies).

• The Discovery Channel's show Mythbusters has, of course, done some episodes on things like the terminal velocities of pennies -- or falling bullets from guns fired straight up. The real world, as usual, is much more complicated than the simplified Physics we introduce here, but the concepts remain the same.

Thursday 3/15: Air Resistance: Low speed and high speed air resistance. If allowed to drop from rest, then a real object may not free fall continuously, but may reach a Terminal Velocity (Force of gravity down canceled by Drag force up) and doesn't accelerate any more. Ping-pong balls in free-fall, vs. being hit with a paddle in a world-class table tennis match. What is the terminal velocity of a falling person? It depnds on clothing and orientation -- aerodynamics, streamlining, cross-sectional area, composition of the air are all part of the drag coefficients b and c. World's Record Free-Fall. Why the steel bands wrapped around an old fashioned water tower or a farm silo are closer together at the bottom than at the top. A farm silo holds grain, which like sand, etc., is made up of solids but in small particles. Such flowable solids or fluidized solids can act like fluids and be piped around.

• Q13 is now due Friday 16 March 2012, in class or by 5pm.
• Q13 HINT: When we did the roller coaster example in class, we had the cars moving very slowly at the top of h1, so that v1 was approximately zero. That meant it was all PE and no KE. If we invoke conservation of TME and have no friction or air resistance, the roller coaster cars can never go higher than h1. Now consider the cartoon version of a small boat with a hole in it -- you get a huge fountain of water shooting up from the bottom and ending up much higher than the boat. But can it do that? If the water coming in at the bottom is all kinetic pressure and no potential pressure, and P1 = P2, then the water not only can't go higher than the sides of the boat -- it can't go any higher than the waterline, where it is all potential pressure and no kinetic pressure, by conservation of pressure (Bernoulli). Now, just show this...

Friday 3/16: Return X2. 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). Q14 Take-Home on Air Resistance and Drag, due on Tuesday 20 March 2012, in class or by 5pm.

• Absolute Zero: Most people believe that at Absolute Zero (0 K, -273°C, -460°F), that everything is frozen solid. Actually, this is not true. Absolute Zero represents the LEAST amount of motion and vibration that atoms and molecules can have. For helium, which really doesn't like to enter into chemical reactions with other atoms -- it doesn't even want to stick to itself much. So helium doesn't even become a liquid until like 4.2K, and then is still a liquid at 0 K and 1 atm pressure. You have to press on helium at 0 K with 4.4 atm of pressure for it to finally become a solid. (grin)

Week of 19-23 March 2012.

Monday 3/19: Linear Expansion: Most objects expand when heated, shrink when cooled. Length Expansion. Example: One 39 ft. (12.0m) steel rail expands 5.88 mm from winter to summer, but that's 0.75 meters for every mile of railroad track. Expansion joints. Bridge expansion joints. Pavement expansion joints. I-57 in Chicago and the expanding asphault in 1983.

• In June 2011, I-69 southbound north of Marshall MI -- heated up beyond 95°F too quickly and the concrete buckled and folded up, forming a launching ramp. Tire marks showed where some speeding cars touched down over fifty feet from the buckled concrete.
• Table 5.2 on p. 179 of O&B shows coefficients of linear expansion (alpha) for some common materials.

Tuesday 3/20: Linear Expansion: Why "Bridge Freezes Before Roadway" signs. Question: Does the material expand into a hole when heated, or does the hole expand? (Think about what happens to the disk removed from the hole -- does it expand or contract when heated?) Volume Expansion of Solids and Liquids. Coefficient of Volume Expansion usually given for liquids; for solids, beta = 3 × alpha. Ideal Gas Law (PV/T = constant or our form: P1V1/T1 = P2V2/T2) -- must use Kelvins for temp and absolute Pressures, because neither P or T can be zero or negative. Q15 Take-Home on Linear and Volume Expansion, due on Thursday 22 March 2012, in class or by 5pm.

• Remember: L = L0 + delta-L and V = V0 + delta-V.
• During Spring, cold gasoline from underground storage can expand to larger than your gas tank if you overfill the tank. During Fall, warm gasoline from underground storage can shrink and if the vent is blocked, your gas tank can collapse if you overfill the tank.

Wednesday 3/21: Heat Energy (Q) and Temperature Change & Phase Change. 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, or the Heat Capacity (J/mole·K) for objects with n moles of atoms or molecules. Add/remove Heat Energy Q will change its phase between solid-liquid-gas using the Latent Heat of Fusion, Lf, between solids and liquids, or the Latent Heat of Vaporization Lv, between liquids and gasses. Example: Take a 1.00 kg block of ice from the freezer (T = -20°C, about 0°F) and heat it in a pan until it is all boiled away. (1) Heat ice from -20°C to ice at 0°C; (2) melt ice to water at 0°C; (3) heat water from 0°C to 100°C, (4) boil water into steam at 100°C. Using Power = Work/time, we can apply heat at the rate of 1000 W = 1000 J/sec, and estimate how long each of these steps take. Ice has a low specific heat, 2000 J/kg·°C-1, so ice very quickly warms up to the melting point. The latent heat of fusion for melting ice / freezing water is 336,000 J/kg. Wet ice is at T = 32°F = 0°C = 273K. The specific heat of water is 4186 J/kg·°C-1 = 1 Calorie (1 "Big C" Calorie = 1 Food Calorie). This is the energy it takes to raise the temperature of 1 kg of water by 1°C. (In the English system, we have the British Thermal Unit, where 1 BTU is the energy it takes to raise the temperature of 1 pound of water by 1°F. You see BTU ratings on air conditioners and furnaces, for example.) "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. Water doesn't drown the fire, it removes heat from the fire, lowering its temperature eventually below the ignition point. Can't use water on all fires. Class D (magnesium) fires, electrical fires. Halon gas fire supression systems protect computer hardware in a big data center, but displace the breathable air -- get out when alarm sounds!

Thursday 3/22: Heat content versus Thermal conductivity. Leidenfrost Effect. 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. Heat Energy (Q). The Heat Engine and Three Efficiencies (Actual, Carnot and 2nd Law).

• Space Shuttle Tiles: "Much of the shuttle is covered with LI-900 silica tiles, made from essentially very pure quartz sand.[1] The insulation prevents heat transfer to the underlying orbiter aluminum skin and structure. These tiles are such poor heat conductors that one can hold one while it is still red hot."
• Fire Walking -- tested on MythBusters.
• "Keep the hot side hot, and the cool side cool." -- The McDonalds McDLT.

Friday 3/23: 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. Q16 Take-Home quiz on the Heat Engine, due on Tuesday 27 March 2012, in class or by 5pm.

• 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 TH or lowering TC.
• We will be swapping lecture halls between 1118 Rood and 1110 Rood on Tuesday 27 March 2012. Don't miss the exciting demonstrations on Tuesday! One Day Only! Be There!
• Remember that Exam 3 is next Friday, 30 March 2012. The Sample Exam 3s are on the class web page.

Week of 26-30 March 2012.

Monday 3/26: Reverse the arrows in the Heat Engine and you get a Refrigerator. NOTE: 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. 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. 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.

• We will be swapping lecture halls between 1118 Rood and 1110 Rood on Tuesday 27 March 2012. Don't miss the exciting demonstrations on Tuesday! There will be Dangerous Power Tools! Fun for the whole class!
• Remember that Exam 3 is Friday, 30 March 2012. The Sample Exam 3s are on the class web page.

Tuesday 3/27: [TODAY ONLY -- Meet in 1110 Rood at 1pm.] 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 = | f1 - f2 | .

Wednesday 3/28: Waves and Resonance continued. Standing Waves on a string. Fundamental, First Overtone, Second Overtone, etc. Standing Waves in a tube. Beat frequencies occur when two sounds have almost the same frequency -- get a distinctive wah-wah-wah sound, whose beat frequency = | f1 - f2 | . Takes time for sound to travel over a distance. Constructive and Destructive Interference. Acoustics of concert halls. The range of "normal" human hearing: 20Hz-20,000Hz (10 octaves). Artilleryman's ear -- mid-range hearing loss. Topic 2 Worksheets (Click here for 1st Worksheet and Directions). Q17 is a Take-Home quiz on Standing Waves, due on Thursday 29 March 2012, in class or by 5pm. Note the short due date so I can post the solution after 5pm for your studying purposes.

• Remember that the Topic 2 Worksheets count as much as an exam or the Topic 1 paper.
• And Safety First! Do not try to write data down on Worksheet 1 while you are driving!
• Video: The Tacoma-Narrows Bridge Disaster. Page down to see the video -- it has NOT been speeded up.
• Find out which ultrasonic ringtones you can hear! Dr. Phil's result today: "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." Considering I'm age 53, I'll take it. (grin)
• 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.

Thursday 3/29: Review for X3. The speed of sound in air. Sonic Booms and other shockwaves. Bullwhip stories. Waves take time to travel. Sound takes time to travel. An echo takes times to get to the reflecting surface and travel back -- to and fro. The reflected wave can arrive in phase and constructively interfere, or out of phase and destructively interfere, based on the distance traveled divided by the wavelength. Also, there are some Sample Exam 3 problems which involve ratios -- finding V2/V1 from the Ideal Gas Law, so that you find how many times larger (or smaller) V2 is than V1, rather than giving you a specific value for V1. Or finding the ratio of the speeds v2/v1 from the Continuity Equation or even Bernoulli's.

• As April dawns, we will begin talking about Electricity and Magnetism -- and you'll begin to see what Dr. Phil means by saying that Physics really is cummulative and One Big Physics. (grin)
• The first silencers were for rifles, so you could hunt in town without disturbing people. With a silencer, you could hear the tiny sonic booms reflected by telephone poles from supersonic bullets passing by... early 1900s.
• The solution to Q17 is being posted at 5pm today.

Friday 3/30: Exam 3.

Week of 2-6 April 2012.

Monday 4/2: 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. Four Fundamental Forces in Nature: Gravity, E & M, Weak Nuclear Force, Strong Nuclear Force. The Hydrogen Atom. Real Electric Charges. Two charges: like charges repel, unlike (opposite) charges attract. Coulomb's Law looks like Newton's Law of Universal Gravity.

Tuesday 4/3: 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. A Nickel coin has a mass of 5 grams, so about 1/10th of a mole. Find number of Coulombs of positive and negative charges. It's over 200,000 C! But... at the atomic level, each nickel atom has the same number of electrons and protons, so overall each atom and the whole nickel coin is charge neutral -- so not dangerous. 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. 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.

• NOTE: Click on the link "Gravity loses to Electric Force..." above to get corrected numbers from the class example.
• Quiz 18 will be an In-Class quiz on Real Electric Charges q and the Coulomb's Law Electric Force equation, on Thursday 5 April 2012. Quiz 19 will be a Take-Home quiz, handed out Thursday 5 April 2012 and due on Tuesday 10 April 2012, in class or by 5pm.
• The remaining Worksheets (2-4) for Topic 2 are now available for downloading on the Topic 2 Directions page. (Note: I also noticed that the Worksheet 1 file had myseriously disappeared from the website, so I restored it. You can now print out all 4 worksheets.)

Wednesday 4/4: Discussion of Topic 1 Book Report. How does q1 know that q2 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 FE = q E (Electric Force = charge times E-field the charge is emersed in). Maximum E-field in air, E-max. Electric Potential (Voltage). Spark gaps. Voltage can be measured, then used to find strength of E-field. SI units: E-field is (N/C) or (V/m) - both work. Charges tend to accumulate on long pointy things, which explains why church steeples get hit by lightning. Or why it's your fingertips which can get shocked when reaching for the light switch after walking on carpet in the wintertme.

• Quiz 18 will be an In-Class quiz on Real Electric Charges q and the Coulomb's Law Electric Force equation, on Thursday 5 April 2012. Quiz 19 will be a Take-Home quiz, handed out Thursday 5 April 2012 and due on Tuesday 10 April 2012, in class or by 5pm.
• NOTE: Monday 9 April 2012 is the last day to turn in a Draft Paper for evaluation, if you want -- it is not required. Final papers will be accepted starting on Thursday 12 April 2012 and continue on without penalty under Monday 19 April 2012 at 5pm.

Thursday 4/5: Charges tend to accumulate on long pointy things, which explains why church steeples get hit by lightning. Or golfers and trees on golf courses. Conductors (metals) versus non-conductors (insulators). Semi-Conductors sit in the middle. Sometimes they conduct and sometimes they don't. This means they act like a switch or valve, and this is the basis for the entire electronics semi-conductor industry. D.C. Electrical circuits. Ohm's Law. V=IR form. (Ohm's "3 Laws"). The Simplest Circuit: Battery, wires, load (resistor). Q18 In-Class quiz on Real Electric Charges and Coulomb's Law. (Solution already posted.) Q19 Take-Home quiz on Series and Parallel Resistors, due on Tuesday 10 April 2012, in class or by 5pm. NOTE: We handed it out on Thursday, but haven't covered all the material on this yet in class.

• Benjamin Franklin invented the lightning rod -- a series of metal spikes on the roof of a building, connected by metal conducting paths to channel the moving charges (current) from a lightning strike away from the roof. Please note that the spacing and maintenance of lightning rods needs to be done by qualified professionals. Space them too close together or too far apart and the lightning will hit between the lightning rods, guaranteeing that the roof will burn down!
• YES -- We have class on both Friday 6 April 2012 and Monday 9 April 2012.

Friday 4/6: D.C. and A.C. circuits. Ohm's Law. V=IR form. (Ohm's "3 Laws"). The Simplest Circuit: Battery, wires, load (resistor). Power dissipated by Joule heating in a resistor. P = I V (3 forms of Power equation to with Ohm's "3 Laws"). The Simplest Circuit: Battery, wires, load (resistor). Series and Parallel Resistors. Reminder of Significant Figures again. 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 R1 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.

• NOTE: Monday 9 April 2012 is the last day to turn in a Draft Paper for evaluation, if you want -- it is not required. Final papers will be accepted starting on Thursday 12 April 2012 and continue on without penalty under Monday 19 April 2012 at 5pm.
• REMINDER: The remaining Worksheets (2-4) for Topic 2 are available for downloading on the Topic 2 Directions page.

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

• Click the "Course/Instructor Evaluation System (ICES Online)" link in the "My Self Service" channel and follow the simple instructions.

Week of 9-13 April 2012.

Monday 4/9: "Magnetism is just like Electricity, only different." Real Magnets are dipoles (North and South ends, linked). Break a magnet in half, and you either get two new magnets -- or nothing. So far, there is no evidence that there are Magnetic Monopoles (magnetic charges: isolated North or South poles). Rules similar to Electric Charges: Unlike poles attract, like poles repel. Dropping a permanent magnet can result in a reduction of its magnetic field (B-field) as the shock allows some iron atoms to flip 180° and therefore cancel instead of add to an adjacent iron atom's magnetic field. The horizontal compass needle rotates until its North end points North (or rather to the North Magnetic Pole, which is of course a South pole of the Earth's magnetic core); the vertical compass rotates so that it lines up with the B-field along the surface of the Earth at the point. At the Equator, the vertical magnetic should be parallel to the ground, at the magnetic poles, it should be perpendicular to the ground. Is the Earth's magnetic field going to flip some day? And what about Mars? SI Units for B-field: (1 Tesla = 1 T). "Other" unit for B-field: ( 1 Gauss = 1 G ; 1 T = 10,000 G ). Earth's B-field is about 1 Gauss at the Earth's surface. Example of the 4T NMR magnet at Michigan Tech and the 10-foot radius line on the floor and erasing ATM cards within that circle. The Great 19th Century Debate: Is Light a Particle or a Wave? (Wave-Particle Duality did not seem obvious at the time.)

• On Thursday 5 April 2012 I brought one of my cameras to 1118 Rood, to document the growth of the "rock collection" on the front desk. As everyone was coming in, I explained what I was doing. While people were taking the in-class quiz, I had nothing else to do, so I got out my camera and took a couple of pictures of the lecture hall with students working. Someone apparently contacted the Dept. Chair wondering what I was doing taking pictures with "a zoom lens" -- rather than just asking me. Frankly, amongst digital SLR cameras, just about every lens today is a zoom lens, as are most of the compact consumer digital cameras as well. This particular setup was an obsolete 10-year-old Nikon D1H (cheap on eBay!) professional camera set up in black&white picture mode, using a Nikon 24-120mm f3.5-5.6G ED IF Aspherical SWM VR AF-Nikkorlens -- the pros used to call this lens "the streetsweeper" because it has a huge range so you can do all your work with pretty much one lens. I use it because it has VR -- vibration reduction technology -- which allows me to use it under poor lighting conditions, like an indoor lecture hall. -- Sorry if I upset anyone.

Tuesday 4/10: 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). Q20 Take-Home quiz on Light as Waves, due Thursday 12 April 2012, in class or by 5pm.

• 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 4/11: Return X3. Update on remaining class time, discussion of format of the Final Exam. Visible light (ROYGBIV=red orange yellow green blue indigo violet). 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!

• Fixing the error in Exam 3A (white) question 1(e).
• Reminder: Apr. 25 Wed - Final Exam 12:30-2:30pm (2 hours)

Thursday 4/12: Return X3 (again). Electromagnetic Spectrum: Visible light (ROYGBIV=red orange yellow green blue indigo violet). Frequencies HIGHER and wavelengths SHORTER than visible light (UV ultraviolet, X-rays, Gamma rays). Optics: Geometric Optics (empirical) and Physical Optics (more wave and fieldlike). Ray Tracing: Rays from a spherical source become essentially parallel rays when you are far away. 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".) First day to accept finished Topic 1 Book Reports. (Last day to accept without penalty is Monday 16 April 2012 by 5pm.) Q21 Take-Home quiz on Reflection and Refraction, and due Tuesday 17 April 2012, in class or by 5pm.

• For Thursday, you can start Q21 with just the Reflection part, as we haven't covered Refraction yet -- which includes the bits about water and glass.
• Dr. Phil's Blog entry which includes some neat reflections off a window.

Friday 4/13: The Law of Refraction - Snell's Law. 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. Second day to accept finished Topic 1 Book Reports. (Last day to accept without penalty is Monday 16 April 2012 by 5pm.)

• Reminder about The Last Quiz: Quiz 23 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.

Week of 16-20 April 2012.

Monday 4/16: Thin Lenses. Simplest lens surfaces are spherical (convex = bows out, concave = bows in) and flat (plano). So some lenses might appear to be biconvex, plano-convex, biconcave, convex-concave. A biconvex lens is also called a positive or converging lens. Parallel light rays coming into such a lens will all pass through the focal point, a distance f from the center of the lens. By itself, could use as a magnifying lens. Concentrating sunlight: burning paper or popping ants? Ray tracing gets same results as doing Snell's Law on mulitple curved lens surfaces. Handy not to have to do all that refraction calculations! Real image formed by passing three rays through a positive thin lens. Three cases: object distance p > 2f (real, inverted, reduced image). Last day to accept finished Topic 1 Book Reports without penalties -- unless you had Dr. Phil look at a Draft Paper.

Tuesday 4/17: Thin Lenses. Real image formed by passing three rays through a positive thin lens. Three cases: object distance p > 2f (real, inverted, reduced image), 2f < p < f (real, inverted, magnified image), p < f (virtual, upright, magnified image = magnifying glass). Quantum Mechanics. ... the Bohr Atom (derivation on the reverse side Dr. Phil's Periodic Table) to see how Coulomb's Law combines with Uniform Circular Motion and the Modern Physics concepts of the deBroglie wavelength (matter also has wave-particle duality) and quantum physics (like the stepped terraces of our lecture hall, 1118 Rood, the electron cannot exist at just any energy level or radius from the nucleus). (Click here for the Atomic & Nuclear Physics handout (not given in class) and here for the Periodic Table handout.) Q22 Take-Home quiz on Objects & Images From a Thin Lens, due Thursday 19 April 2012, in class or by 5pm.

• My other class is having their Final Exam on Tuesday 24 April 2012 from 2:45-4:45pm in 1104 Rood Hall. Send me an email if you feel you have too many Finals on Wednesday and want to take an Early Final Exam on Tuesday.

Wednesday 4/18: "A Taste of Modern Physics" -- goes to size/time/length scales far outside our normal experience. The point of today's lecture is to give you a taste for how strange things get in the real world. Quantum Mechanics. ... the Bohr Atom (derivation on the reverse side Dr. Phil's Periodic Table) to see how Coulomb's Law combines with Uniform Circular Motion and the Modern Physics concepts of the deBroglie wavelength (matter also has wave-particle duality) and quantum physics (like the stepped terraces of our lecture hall, 1118 Rood, the electron cannot exist at just any energy level or radius from the nucleus). In effect, the allowed electron orbitals in the Bohr Atom are standing waves set on a circular string. (ooh!) The deBroglie wavelength -- Wave/Particle Duality for Matter. Planck's constant -- a very small number, but it is NOT zero ( h = 0 in Classical Physics). So the deBroglie wavelength only matters for very small objects, not Buicks. For an electron to move from one orbit to another, it must gain or lose energy. Going from a higher n to a lower n, the difference in the energy is release as a photon with E = hf. To go from a lower n to a higher n, the electron has to absorb a photon of E=hf. And now we have an explanation of the spectral lines which we had once described as "fingerprints for elements". Burn hydrogen and the light emitted, when run through a prism will split not into a rainbow, but individual lines of individual colors -- these are emission lines. Take white sunlight, shine it through a prism and look at the rainbow of colors under a microscope and you will see that individual lines of color are missing -- these are absoption lines caused by the hydrogen gas in the Sun's atmosphere removing those colors and moving their electrons to higher orbits or ionizing completely. If we try to solve the helium atom (Z=2) in a similar way, we find that with one nucleus and two electrons, we have a three-body problem and we can't solve that in closed form. However, we can use our Bohr equations for hydrogenic ions (hydrogen-like) which have only one electron, so we can solve for He+, Li+2, Be+3, B+4, C+5, ... , U+91, etc.

• NOTE: In today'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 .

Thursday 4/19: Nuclear Physics. A brief look at Nuclear Physics. There are some118 Elements in the Periodic Table. For each element, there may be many Isotopes -- same Z (# of protons) but different N (# of neutrons). The atomic mass starts out as A = Z + N. The actual atomic mass numbers listed in the periodic table are averages of all the isotopes found in nature. From Hydrogen to Calcium (1-20), typically we have as many neutrons as protons. Starting with Scandium (Z=21), we need more and more neutrons to stabilize against the Coulomb repulsion of so many protons, so N > Z. By Uranium (Z=92), there are so many neutrons that nuclei are generally unstable. Radioactive particles: alpha = nucleus of a Helium atom, beta = electron or positron, gamma = high energy gamma rays from the protons and neutrons shifting in their orbitals, much like the electrons and their photons. The Einstein relation, E=mc2 -- energy can be turned in matter and matter can be turned into energy. Fission = nucleus breaking into small pieces creating smaller elements, fusion = nuclei combining to form larger elements. (Click here for the Atomic & Nuclear Physics handout (not given in class) and here for the Periodic Table handout -- with today's derivation on the back.) For all intents and purposes, we have closed the book on the Final Exam material on Thursday.

• Finals Week Office Hours are now posted.
• Due to time constraints, we obviously have not covered all the material in the text. If you want a rough guide to the topics we didn't cover at the end of the textbook, check out these topics from the PHYS-1150 course.
• If there is anything you need to turn in -- T1 book report, T2 worksheets, etc. -- you MUST get it turned into the office by Friday 27 April 2012 for Dr. Phil to see it before finishing grades. Similarly, if there are any Exams you have to make up, the last day to do this is Friday 27 April 2012, so arrange something with Dr. Phil.
• REMEMBER: Topic 2 Worksheets due on Friday 20 April 2012.

Friday 4/20: THE LAST CLASS.