Dr. Phil's Home

## Lectures in PHYS-1070 (26)

Updated: 30 April 2013 Tuesday.

## FINAL GRADES FOR PHYS-1070 CAN BE FOUND HERE.

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 15-19 April 2013.

Monday 4/15: 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. Last Day to turn in Topic 1 paper.

• 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!

Tuesday 4/16: The Simplest Circuit: Battery, wires, load (resistor). 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"). Power dissipated by Joule heating in a resistor. P = I V (3 forms of Power equation to with Ohm's "3 Laws").

• Technically the wires in a circuit also have a resistance and they too can get hot due to Joule heating. However, for our purposes, we'll treat the wires as perfect conductors, R = 0. There ARE superconductors, materials which below a critical temperature really do have perfect conductivity and zero resistance. None of them currently work at room temperature, however.
• NOTE ABOUT Pre-Final Grades: I had to CORRECT the data from what was first posted -- for most people, their letter grades either stayed the same or went up. If you looked at the posted grades on Monday 4/15 or early Tuesday 4/16, please check again. If you came to Dr. Phil's office or we exchanged grade info on emails between Fri 4/12 and Mon 4/15, get in touch with me again.
• Remember, if you're using the Testing Center for your Final Exam, reserve your time and send Dr. Phil an email. You may not be able to get the same day/time as the regular Final Exam.

Wednesday 4/17: The Simplest Circuit: Battery, wires, load (resistor). Series and Parallel Resistors. Two devices connected together in a circuit can only be connected two ways: series or parallel. In Series, same current, share voltage. Equivalent resistance is always larger. In Parallel, same voltage, share current. Equivalent resistance is always smaller. Resistor Network Reduction. The battery only "sees" an equivalent resistor, which controls its current. So we could (but won't) reduce a resistor network to a single equivalent resistance, go back and fill in the table for V = I R and then P = I V. In the example sketched in class, Resistor 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. Electricity and Magnetism Together Can Create Light. The Great 19th Century Debate: Is Light a Particle or a Wave? (Wave-Particle Duality did not seem obvious at the time. Later on, deBroglie showed that even matter has both a wave and a particle nature.) Q13 Take-Home on Simple Circuits and Resistors, due on Friday 19 April 2013. (Click here for a copy.)

• 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.

Thursday 4/18:

Friday 4/19:

### Week of 7-11 January 2013.

Monday 1/7: Class begins. The nature of studying Physics. Science education in the United States. Natural Philosophy. The Circle of Physics. "Speed Limit 70" First Equation: Speed = Distance / Time. In terms of variables, a classic three-variable equation: v = d / t .

• Quiz 1 will be in-class on Friday 11 January 2013. Part I will be some attendance paperwork. Part II will be on our equation v = d / t. (This will be our only non-Metric System quiz.)

Tuesday 1/8: To understand the underlying concepts we need to Simplify The Universe. Aristotle and the Greek Philosophers. Observation vs. Experiment - Dropping the book and the piece of paper (2 views). Theory and Measurement.

Wednesday 1/9: First Equation: Speed = Distance / Time. v = d/t . Development of Speed equation for Constant or Average Speed. delta-x = ´x = xfinal - xinitial = xf - xi , x = x0 + v t . Discussion of formula cards. Distribute Syllabus.

Thursday 1/10: 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. 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. 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).

• HW: (Not to be turned in.) Problems 1.7, 8, 9. (Odd numbered problems have solutions in the back of the book -- note that these are Problems with numbers, versus the more conceptual Questions.)
• About a hundred years after the Antelope, in 1947, Chuck Yeager piloted the Bell X-1 and "broke the sound barrier" by design for the first time.
• I've been telling the story of the Antelope for years, having learned about it in a kid's book on trains. Finally found a comment in Wikipedia, which says it wasn't five miles, but "First authenticated 60 mph, 26 miles in 26 minutes."
• Friday 1/11: Topic 1 assigned. (Updated Searchable booklist available online here .) Quiz 1 In-Class.

• If you missed class, 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.)

### Week of 14-19 January 2013.

Monday 1/14: The P-O-R (Press-On-Regardless) road rally problem. "You can't average averages." Comments on Q1½ -- solution already posted on class webpage. Note that part (c) is just like the P-O-R problem. 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). 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.

• Physics Help Room starting up today -- 2210 Rood I think is the new room number -- converted from one of the labs on the 2nd floor.

Tuesday 1/15: 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.) 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. 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.

• 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!
• 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.
• Wednesday 1/16: Return Q1½. Finish car acceleration problem from yesterday -- t = 19.03 sec. 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. 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 just talked about. With these two known accelerations, we can now have something to compare our accelerations a. How much acceleration can a human take? See story of Scott Crossfield below.

• Table of   a = 1.00 m/s² :
 t (seconds) v = a t (m/sec) x = ½ a t² (meters) 0 0 0 1.00 1.00 0.500 2.00 2.00 2.00 3.00 3.00 4.50 4.00 4.00 8.00 5.00 5.00 12.5 10.0 10.0 50.0 25.0 25.0 312.5

• If you were to accelerate at 1.00m/s² using your feet, you would not be able to do so for more than a few seconds. Because by 10.0 seconds you would be running at 10.0 m/s! And at 25.0 seconds you would be running at over 50 mph, which you can't do. This is different from a constant speed of 1.00 m/s, which you can do for a very long time.
• Example from class: Note that the procedures, the algebra and the equations we generated for the car problem are EXACTLY the same as the rifle problem from Thursday. There are only so many questions we can ask. Part of the Physics comes in seeing what the answers mean.
• Note that even though we generated some new equations, they should NOT be put on your formula card. We start from the definitions or the kinematic equations. We don't generate a bazillion equations, each one designed to solve just one problem, but develope a toolkit that will solve many problems.
• 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)
• The Physics Help Room opened for business on Monday 14 January 2013. The Physics Help Room is located in 2210 Rood Hall, on the second floor by the labs. Hours will be 9am to 3pm 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 17 January 2013.
• Rusty on your math skills? 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 2 In-Class on Friday 18 January 2013 on the Kinematic Equations for Constant Acceleration -- Significant Figures will be considered this time.
• Thursday 1/17: Prepping for 2-D Motion: We can look at motion in 1-dimension in different directions. We usually use x in the horizontal. y can either be another horizontal dimension or in the vertical. We can rewrite the Kinematic Equations for constant acceleration for x or y. It turns out that if x and y are perpendicular to each other, then they are independent, so we will be able to break down 2-D motion into two 1-D motion problems. 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. With these two known acceleratoins, we can now have something to compare our accelerations a. 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.

• When I updated yesterday, I failed to put the links up for the story of Scott Crossfield and the explosion of the X-15 -- you should scroll up to yesterday's bullet points and check it out.
• Back on the class web page, I started putting Sample Exam 1s -- some have solutions, some do not. The ones without solutions you need to figure out by PTPBIP or comparing answers with others to see if you're right. After all, you don't have the answers in front of you when you take the exams for real.
• FORMAT FOR EXAM 1: Problem 1 -- ten multiple guess questions very much like those you'll see in the Sample Exam 1s. The first group will use the handy little table for Number of Minutes per Mile at various speeds in mph. Problem 2 -- one problem with five parts, much like those in the Quizzes and like the problems in the Sample Exams 1s.

Friday 1/18: Quiz 2 in-class.

• Remember, no classes on Monday due to MLK Day Activities.

### Week of 21-25 January 2013.

Monday 1/21: MLK Day to Honor Dr. Martin Luther King, Jr. -- Classes Do Not Meet at WMU -- University-wide activities.

Tuesday 1/22: 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. 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.

Wednesday 1/23: Another problem solved by using two linked 1-D problems: 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. Two kinds of numbers: Scalars (magnitude and units) and Vectors (magnitude, units and direction). Compass directions (N, S, E, W, NE, SE, SW, NW).

• 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.
• Thursday 1/24: (Apologies for being late to class due to excessive number of accidents on the icy roads.) Return Q2. Demo these class web pages. Look at Sample Exam 1s. Discuss how to use the mph and sec/mile chart seen in the multiple-guess problems.

• NOTE: If on any one part (a-e) of Q2 you lost 4000-6000 points, please return your Q2 to Dr. Phil -- I want to check the grading.

2nd and 4th wrecks of the day -- drive careful out there! (Click on photos for larger.)

Friday 1/25: Quiz 3 in-class.

• 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.
• Originally I was going to hand out a take-home Quiz 4 on Friday, but with Thursday's shortened class, we'll hand it out next week.

### Week of 28 January-1 February 2013.

Monday 1/28: 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. Examples: vector C = vector A + vector B, vector D = vector A - vector B. Dr. Phil's Method uses a table you fill out with the x- and y-components, to allow you to easily add or subtract the columns. Then use your sketch to check your work. Q4 Take-Home on Vector Addition, due on Wednesday 30 January 2013.

• Note that the 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.
• Tuesday 1/29: Finishing vector problems: (1) Examples: vector C = vector A + vector B. (For studying, you might try to find vector D = vector A - vector B). (2) Finding final velocity of problem with the guy with the fedora and the cigar in Standard Form. 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. We can always use the Kinematic Equations, but we can also derive specialized equations: Max Height, h = v0² sin² ¸ / 2 g .

• With vectors, we have officially closed the book on material for Exam 1. If you run across a problem in the Sample Exam 1s that you don't know what it means, it might be something we haven't covered yet! (grin) The material we started today on Ballistic/Projectile motion is based on the kinematic equations for constant acceleration and vectors, things that we have covered. However, the specialty equations we are developing are NOT part of Exam 1.
• Q4 is "due Wednesday". You can turn it in at class, turn it in during Office Hours to me, or turn it in at the beginning of class on Thursday if you need to -- please don't do Q4 during our class or skip class because it isn't done.

Wednesday 1/30: Return Q3. 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. We can always use the Kinematic Equations, but we can also derive specialized equations: Max Height, Time to Max Height, Range Equation. Two Dangerous Equations. You can only use the Range Equation if the Launch Height = Landing Height. But the sin (2 θ) 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° - θ) that gives the same range (but a different time and height). High and low trajectories for Range Equation.

Thursday 1/31: WMU Closed Today -- Classes Canceled.

• Western Michigan University is closed and all classes and public events are canceled today, Jan. 31, due to severe winter weather. The closure includes the University's main campus in Kalamazoo as well as regional locations in Grand Rapids and Battle Creek.

Friday 2/1: Exam 1 MOVED to TUESDAY 5 February 2013. Cannonball example: if v0 is 100. m/s @ 30° and lands at launch height, y = y0. Find range R, height h, time of flight t -- note that the latter is for the full flight. What changes if you use the complementary launch angle of 60°? 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.

• If WMU is open Friday, we will have a normal class.
• With WMU Closed on Thursday, we'll take late Q4 papers on Friday, assuming normal classes.

### Week of 4-8 February 2013.

Monday 2/4: (Apologies for being late to class due to slow speeds on the icy roads. 2½ hours isn't a record, but it's up there.) 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. Space Shuttle in Low-Earth Orbit. (There's still gravity up there!) Comments on Free Fall vs. "zero gravity" in space.

• My sketch of the Space Shuttle in orbit has 3 flaws. The first being no human has ever orbited the Earth in polar orbit (going strictly north and south), though the US Air Force planned to launch Space Shuttles into polar orbits from Vandenberg AFB before the Challenger disasater.
• Sidebar discussion of the sketch of the Space Shuttle in Low Earth Orbit (LEO) -- and the book Shuttle Down by Lee Correy
• Class time was provided for going over some Sample Exam 1 problems, but not enough questions.
• Tuesday 2/5: Exam 1. (Rescheduled from 2/1.)

• If you missed Exam 1, you need to email Dr. Phil so we can schedule a make-up exam.

Wednesday 2/6: 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. Examples: A hard disk drive spinning at 3600 rpm (60 times a second, time for one revolution = 1/60th of a second). 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. (Reeding on the edge of the silver shilling or a U.S. dime/quarter.) (Mad as a hatter -- from mercury poisioning.)

Thursday 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). 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.

• For a pair of equal and opposite forces -- it's First Law if they both act on the SAME object and Third Law if they both act on DIFFERENT objects.
• 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)

Friday 2/8: Quiz 5 in-class.

• Heavy wet snow Friday morning convinced me not to try to drive to Kalamazoo on a morning where I could get someone else to come in and administer the quiz. Sorry for any inconvenience, but I did give y 'all a heads up!
• For future reference: Why yes, we really CAN see where you are looking from the front of the lecture hall.

### Week of 11-15 February 2013.

Monday 2/11: 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; 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.

• FIRST LOOK GRADES are input to the Registrar. This should show up on GoWMU as "Mid-Term Grades"? Please note that these grades are heavily influenced by Exam 1. I only gave an "E" grade to people who did not take Exam 1, otherwise the lowest estimated course grade recorded right now is a "D".
• First Sample Exam 2s on class web page.

Tuesday 2/12: "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. 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. Article on the 1945 crash of a B-25 bomber into the Empire State Building and subsequent elevator free fall.

Wednesday 2/13: 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. 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. Discussion of guy wires to help support a very tall antenna. 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. More Elevator Comments. The Normal Force represents the "apparent weight" of the person in the elevator. Like Atwood's Machine, we can hang a counterweight on a cable and a pulley and support all or some of hte weight of the elevator. The elevator will go one way and the counterweight will go the other way.

• For the sign problem, the equations are
• T2 = T1 (cos30°/cos45°)
• T1 = mg / [sin30° + (cos30°)(sin45°)/(cos45°)

Thursday 2/14: Return X1. 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.

• The "curve" for Exam 1 -- just add 3000 points to your score. But if your curved score was still less than 40,000 points, round it up to 40,000.

Friday 2/15: Quiz 6.

### Week of 18-22 February 2013.

Monday 2/18: 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. Inclined plane with and without friction. Finding the coefficient of static friction by tilting: μs = tan(θmax). 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 θmax greater than 45° -- rare, but yes. 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.

• It is static friction in play when we are driving and have our vehicle under control, because the tread of our tire is lowered onto the pavement, does not slide, and then is lifted off. We often don't notice that the coefficients of friction have dropped greatly when it is slippery outside, until we need to steer or brake, and then we start skidding. Slow down! (grin)
• Link to Phil Plait's Bad Astronomy Blog about the Russian meteorite, the near miss asteroid and statistics and coincidences.

Tuesday 2/19: Dr. Phil canceled drive in and office hours due to slippery conditions + crosswinds. Prof. Michael Famiano came in to pinch hit and do some friction problems.

Wednesday 2/20: 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 = δp / δt = change in momentum / change in time instead of F=ma, but really the same thing. Impulse Equation: δp = F δt .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.

Thursday 2/21: Linear momentum is conserved in all types of collisions .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.

• For the wrecks today, Car 1 had m1 = 1750 kg, v1 = 22.1 m/s, so p1 = m1v1 = 38,680 kg·m/s ; Car 2 had m2 = 2340 kg, v2 = 16.5 m/s, so p2 = m2v2 = 38,610 kg·m/s. Total mass of both cars, M = m1 + m2 = 4090 kg. The head-on collision left the wreck with speed V = 0.171 m/s ; the rear-end collision had V = 18.90 m/s and the side-impact collision had V = 13.36 m/s and ¸ = 44.9°.

Friday 2/22: Quiz 7. Course Reset... Discussion and Q&A session of problems and communications issues in PHYS-1070 this semester.

• Quiz 7 In-Class Take-Home on Friction and Forces, handed out Friday 22 February 2013 and due on Tuesday 26 February 2013.
• Quiz 8 Take-Home on Totally Inelastic Collisions, will be handed out on Monday 25 February 2013 and due on Wednesday 27 February 2013 in class or by Noon. NOTE: The date on this says Tuesday, but we'll collect them on Tuesday and Wednesday...

### Week of 25 February-1 March 2013

Monday 2/25: 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 and Energy). Work: A Physics Definition (Work = Force times distance in the same direction). Work = Energy. SI units: (N)(m) = (kg·m²/s²) = (Joule) = (J). 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.

• Quiz 7 In-Class Take-Home on Friction and Forces, handed out Friday 22 February 2013 and due on Tuesday 26 February 2013.
• Quiz 8 Take-Home on Totally Inelastic Collisions, due on Wednesday 27 February 2013 in class or by Noon. NOTE: The date on this says Tuesday, but we'll collect them on Tuesday and Wednesday...
• For the clown on roller skates, take the clown to have a mass of 85.0 kg, the pie a mass of 1.00 kg, the speed of the pie when thrown is 5.00 m/s, then we found the speed of the clown after the throw, V = -0.05882 m/s. On your own... if a second clown on skates, also with mass 85.0 kg, gets hit in the face by the moving pie (totally inelastic collision), then find the speed of the clown+pie.
• Tuesday 2/26: Return Q6. 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.

• Here's a quiz for my other class that you can use as a study problem on conservation of momentum. And its solution.
• Another Sample Exam 2 on the class web page.
• If Winter Storm Rocky keeps you from getting to WMU on Wednesday and turning in your Q8 in class or by noon, email Dr. Phil the final answers to "stop the clock" and get the hardcopy in at your next class. Example: (a) 3.45 m, (b) 4.56 m/s, (c) 5.67 m/s^2. Don't scan your paper or take a photo and attach a large file to your email.

Wednesday 2/27: Demo: a suspended bowling ball shows conservation of T.M.E. All P.E. when swings up to a stop on either side, all K.E. at bottom of swing. (There must be non-conservative forces, such as air resistance and friction in the pivot point on the ceiling -- because the bowling ball never quite gets up as high as it starts.) Totally Elastic Collisions:-- perfect rebound, no damage, conserve both momentum and K.E. The equations get messy because each object has both an vi and a vf. Worse, momentum is a vector and can have components, while K.E. is a scalar and a square (½mv²). Two special cases: (1) m1 = m2 , v2i = 0, so v2f = v1i and v1f = 0. All the momentum and K.E. transfer from object 1 to object 2. (2) m1 = m2 , v1i = - v2i , so they just bounce off each other and go the other way. Close approximations, Demo: The Executive Time Waster. Why you want inelastics collisions in a wreck. 5 mph versus 3 mph impact bumpers.

• We will NOT be doing Totally Elastic Collision problems.
• What if... you made a car with soft, deformable body parts? So after a wreck you could just mold it back into shape? From Saturday Night Live: "Adobe: The Little Car Made of Clay". Hulu video.
• NOTE: Normally my Thursday at Noon office hours are in the Help Room. However on Thursday 28 February 2013, I'll be in my office at noon, so that I'll be able to get to my Exam at 1pm on time.

Thursday 2/28: Exam 2.

Friday 3/1: WMU SPIRIT DAY -- No Classes.

• WMU Spring break next week. Our next class will be Monday 11 March 2013.

### Week of 4-8 March 2013.

SPRING BREAK -- NO CLASSES.

### Week of 11-15 March 2013.

Monday 3/11: 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. 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. Example: Rollercoaster with h1 = 30.0 m, v1 = 0, h2 = 0 (bottom of loop-the-loop), h3 = 12.0 m (top of loop-the-loop, making D = 12.0 m and r = D/2 = 6.00 m). Results: v2 = 24.26 m/s, v3 = 18.79 m/s. v3 is well above the minimum speed to safely do the loop-the-loop (7.672 m/s from FN = 0 and mv²/r = mg )

• If you need to take Exam 2 -- send an email to Dr. Phil immediately.
• Take the numbers for the rollercoaster and check them, using conservation of energy and U.C.M.
• 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.

Tuesday 3/12: 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. 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. Newton's Law of Universal Gravity + U.C.M: 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.

• 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?

Wednesday 3/13: Newton's Law of Universal Gravity and Tides (high/low, spring/neap). Water is more flexible than land, so it can be influenced by the weak gravitational forces from the Moon (a quarter million miles away) and the Sun (93 million miles away). 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). Note than in the absense of chemical reactions, that the progression from Solid to Liquid to Gas for a material goes from lower temperatures to higher temperatures. Two Extreme States of Matter: Plasma (electrons stripped off, high temperature), Cryogenics (extreme cold, odd behavior).

• That our oceans are all connected together and that the Moon's influence creates tides is very important to life on Earth. In particular, the boundaries between fresh and salt waters include marshes and estuaries, which are some of the most productive breeding grounds for creatures on the planet, in part due to the twice daily flushing effect of the tides to wash away wastes and flood in nutrients.

Thursday 3/14: Return Q7, Q8. 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). Sea water is 1030 kg/m³ ; sugar water is 1060 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. Q9 Take-Home on Newton's Law of Universal Gravity, due on Monday 18 March 2013.

Friday 3/15: Return X2. 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.

### Week of 18-22 March 2013.

Monday 3/18: Archimedes and Eureka! (I found it!) Using mass-to-volume ratio and water displacement to determine if gold crown was solid gold or not. 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. Calculating 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. 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.

• Q9 is a Take-Home on Newton's Law of Universal Gravity, handed out on Thursday 14 March 2013, and due on Monday 18 March 2013 Tuesday 19 March 2013.
• Table 4-4 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.
• 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.)

Tuesday 3/19: 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. 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). The perils of SCUBA diving. 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.

• SCUBA = Self-Contained Underwater Breathing Apparatus -- invented by the famous Jacques Cousteau in WW II.

Wednesday 3/20: How to get liquid out of a cup using a straw -- or why Physics does not "suck", but pushes using a pressure difference. 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. The Water Tower and the Faucet Problem. Why the water tower needs a vent.

• 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)
• During our "class reset" before break, we had a list of things we wanted to add. The Word of the Day (WOTD) mentioned in the beginning of every class is in case you need me to stop, get out of the way, repeat something, translate my handwriting or write bigger. (grin) However, no one has used it, so in case you forgot, here's your reminder. Also, here are some more problems to work on:
• Problems Chapter 4: 1, 5, 7, 13, 17, 27, 28.

Thursday 3/21: Bernoulli's Equation and the Continuity Equation. Want Smooth Continuous Flow, not Turbulent Flow or Viscous Flow. Flow rate = Volume / time = Cross-sectional Area × Speed. The faster the fluid flow, the lower the Pressure. Example: The aspirator -- a vacuum pump with no moving parts. Example: Air flow around a wing. (Faster air over top means lower pressure on top, so net force is up -- Lift.) Spoilers -- doors open in wing to allow air to pass between upper and lower surfaces, thus "spoiling the lift" by eliminating the pressure difference. Why the Mackinac Bridge has grates on the inside north- and soundbound lanes. 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.

Friday 3/22: 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 (old). (NEW Sunday 10/14/2012) Problem: Spray can. (Inside: P1 = 200,000 Pa, v1 = 0, h1 = h2. Outside: P2 = 100,000 Pa. Find v2.) Problem: RMS Titanic is on the bottom of the Atlantic, about 2½ miles down. When James Cameron made his movie, he rode the Mir submersibles to the wreck. Find the speed of the water shooting into the sub if there is a leak. Find the water pressure at that depth. (P1 = P2, v1 (on surface) = 0, h1 = 3821 m, h2 = 0, ρseawater = 1030 kg/m³.) Actually the water pressure is higher, due to the fact that with hundreds of atmospheres of pressure, the seawater is slightly compressed and so the mass-to-volume ratio isn't constant, but increasing. Q10 Take-Home on Mass-to-Volume Ratio and Bernoulli's Equation, due Tuesday 26 March 2013. (Click here for a copy.)

### Week of 25-29 March 2013.

Monday 3/25: 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).

• Note that (1) Hot and Cold are relative terms and (2) Heat in Physics means Heat Energy -- there is no Cold, just less Heat.
• A typo on the last page of the Syllabus listed this week as "25-28 March" instead of "25-29 March", which led some people to thinking there was no class on Friday, despite no other place in the Syllabus or on the website saying that Friday was a No Class day.
• Quiz 11 will be a Take-Home, handed out Thursday 28 March 2013, and due Monday 1 April 2013. (No fooling!)
• Reminder that Exam 3 is Friday 5 April 2013.
• Reminder that the Topic 1 Book Report is due on Thursday 11 April 2013, Friday 12 April 2013 or Monday 15 April 2013. If you are planning on doing a draft paper, the last day to turn in such a draft is Monday 8 April 2013.
• HEY GUYS! Looking up into the class today I saw a whole of people reading their phones, reading a book, working on homework and other inappopriate activities that were annoying or embarassing other students -- and threatening to derail my train of thought. Let's clean it up...
• Tuesday 3/26: 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. Linear Expansion: Why "Bridge Freezes Before Roadway" signs. Bridge expansion joints. Pavement expansion joints.

• Table 5.2 on p. 179 of O&B shows coefficients of linear expansion (alpha) for some common materials.
• Problems Chapter 5: 3, 5, 6, 9, 13, 25, 27.
• UPDATE: Q11 will be a Take-Home quiz. it will be handed out on Thursday 28 March 2013. There will be class on Friday 29 March 2013 -- it will be a problem solving session.

Wednesday 3/27: Linear Expansion: Pavement expansion joints. I-57 in Chicago and the expanding asphault in 1983. 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, β = 3α. 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.

• Remember: L = L0 + δL and V = V0 + δV.
• 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.
• 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.
• Thursday 3/28: 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. Q11 Take-Home on Expansion, due Monday 1 April 2013 Tuesday 2 April 2013. (Click here for a copy.)

Friday 3/29: Problem: A steel tea kettle has a volume of 2.00 L. At 20.0°C, is is half filled with water or 1.00 L. The kettle is sealed and heated to 80.0°C. Using the equatinon volume expansion, ²steel = 3±steel and ²water = 207 × 106 °C-1, find the new volume of the kettle and the volume of the water. Finally, consider the air sealed above the water. Initially, it's volume is 1.00 L, but at 80.0°C, the volume is less, because the water expands more than the kettle. Use P1V1/T1 = P2V2/T2 to find the final pressure, assuming the initial pressure was 101,300 Pa. Problem: 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. Find the heat energy Q to: (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!

• Because the air in the tea kettle above inceases pressure, then if you have a whistling tea kettle, rather than a sealed container, the higher pressure will cause air to rush through the hole -- this will get fast enough when the water is boiling to create the whistle.
• If you look closely at a whistling tea kettle while it is whistling, there is a clear gap between the whistle and the billowy white clouds. The cloud is condensing water vapor, NOT steam. The steam is that jet of clear air in the gap. Do NOT put a dry finger in that gap, you will severely burn your finger, while the billowy white cloud many inches from the kettle will feel cool and damp.
• 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. Note: Slightly different numbers than example given in class.
• Remember Exam 3 is next Friday!

### Week of 1-5 April 2013.

Monday 4/1: 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. 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.
• As we'll see on Monday, miles per gallon (m.p.g.) is NOT an efficiency.
• Tuesday 4/2: The Heat Engine and Three Efficiencies (Actual, Carnot and 2nd Law). Fuel Economy (miles per gallon) is not an Efficiency. There is no conspiracy to keep big 100 m.p.g. cars out of our hands. To use less fuel, do less work. Reverse the arrows in the Heat Engine and you get a Refrigerator. 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.

• 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.
• A typo on the last page of the Syllabus lists the last week as "15-18 April" instead of "15-19 April", which might lead some people to thinking there was no class on the last regular class day, despite no other place in the Syllabus or on the website saying that Friday was a No Class day. -- This is essentially the same typo as the last time.

Wednesday 4/3: Air conditioners and Heat Pumps. 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 λ (wavelength) and a Repeat Time T (Period). Frequency = 1/Period  or f = 1 / T . Wave speed = frequency × wavelength ; v = f λ . 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. Demonstration: the Slinky shows both longintudinal (string type) and transverse waves (sound type).

• General Reminder: All semester long I have been talking about units, significant figures and showing all work. Just about everything put on the blackboard has complete equations, then solved for the problem. All numbers have their units at all times. Correct sig.figs. is applied, even to intermediate results. And grading is done accordingly.

Thursday 4/4: Review. Topic 2 Worksheets (Click here for 1st Worksheet and Directions)

• And Safety First! Do not try to write data down on Worksheet 1 while you are driving!
• Beginning Monday, April 8, the Course/Instructor Evaluation System (ICES Online) will open to students for the spring 2013 administration. (via GoWMU)

Friday 4/5: Exam 3.

### Week of 8-12 April 2013.

Monday 4/8: 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. (Pink tube missing - tried to use a shop vac hose, too heavy, too slow.) 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. Musical instruments: Accoustic string instruments can change tuning by changing the tension of the string and the string itself can be shortened on the neck of violins, guitars, etc. Brass instruments start from the "natural trumpet", which can only play the fundamental and overtones for the pipe. Woodwind instruments get more complicated.

• If you missed Exam 3 on Friday 5 April 2013, please contact Dr. Phil as soon as possible to take a make-up exam.
• Sample Final Exams are starting to appear on the class web page. Note that there is still two weeks of new material coming.
• Topic 1 Book Reports can be turned in on any of these three days: (1) Thursday 11 April 2013, (2) Friday 12 April 2013 or (3) Monday 15 April 2013. Papers turned in after that will be assessed a 10,000 point/day penalty.
• Today is the last day to turn in a Draft paper, if you wish to.
• Remember the Topic 2 worksheets!
• The Student Evaluation system (ICES) is now open for you. See the link at the top of this page.
• Tuesday 4/9: The range of "normal" human hearing: 20Hz-20,000Hz (10 octaves). Resonance boxes, accoustic guitars. 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.

• 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.
• Wednesday 4/10: 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 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.

• The Student Evaluation system (ICES) is now open for you. See the link at the top of this page.

Thursday 4/11: The Two-Fluid Model of Static Electricity (A & B), to account for the two types of behavior noted. Franklin's One-Fluid Model of Electricity. Occam's Razor: If you can't decide between two competing ideas for how Nature works, take the simpler model. Real Electric Charges. Two charges: like charges repel, unlike (opposite) charges attract. Coulomb's Law looks like Newton's Law of Universal Gravity. 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 (!!!). Q12 Take-Home on Standing Waves, due on Monday 15 April 2013. (Click here for a copy.) First Day to turn in Topic 1 paper.