Dr. Phil's Home

Lectures in PHYS-1070 (27)

Updated: 29 April 2014 Tuesday.



FINAL COURSE GRADES AND BREAKDOWN BY CATEGORY FOR PHYS-1070 Spring 2014

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

MID-TERM GRADES FOR PHYS-1070 CAN BE FOUND HERE. Updated 3-13-2014.

FIRST WORK MID-TERM GRADES FOR PHYS-1070 CAN BE FOUND HERE.

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  • Week of 21-25 April 2014.

    Monday 4/21: Office Hours.

    Tuesday 4/22: FINAL EXAM (10:15am-12:15pm) Office Hours.

    Wednesday 4/23: Office Hours.

    Thursday 4/24: Office Hours.

    Friday 4/25: LAST DAY TO MAKE UP EXAMS. Office Hours.

    Monday 4/28: Office Hours.

    Tuesday 4/29: Grades due at Noon.


    Week of 8-10 January 2014.

    Monday 1/6: First class canceled by winter storm.

    Tuesday 1/7: First class canceled by winter storm and dangerous cold and wind chills.

    Wednesday 1/8: Class FINALLY begins. The nature of studying Physics. Science education in the United States. The Circle of Physics.

    Thursday 1/9: 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. Distribute Syallabus.

    Friday 1/10: First Equation: Speed = Distance / Time. v = d/t . Development of Speed equation for Constant or Average Speed. delta-x = δx = xfinal - xinitial = xf - xi , x = x0 + v t . (Restrictions: This last equation is for constanr or average speed only.)

    Week of 13-17 January 2014.

    Monday 1/13: PTPBIP - Putting The Physics Back Into The Problem. English system of measurement. SI Metric System. Prefixes. What do we mean by Measurements? "Units will save your life."

    Tuesday 1/14: Xeno's Paradoxes. Discussion of formula cards. 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). Quiz 1 In-Class.

    Wednesday 1/15: 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. 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.)

  • 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."
  • Thursday 1/16: 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 = δv / δt is for constant or average acceleration. Finding the set of Kinematic Equations for Constant Acceleration.

    Friday 1/17: The 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. Topic 1 assigned. (Updated Searchable booklist available online here .) Quiz 2 is a Take-Home on the Kinematic Equations, due Tuesday 21 January 2014 in class.

    Week of 20-24 January 2014.

    Monday 1/20: MLK Day to Honor Dr. Martin Luther King, Jr. -- Classes Do Not Meet at WMU -- University-wide activities.

    Tuesday 1/21: Return Q1½. Collect Q2. 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. Revisit: 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 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). 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.

     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. 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.
  • The Real World: Go to the Library, the magazine section of a book or grocery store, or a personal collection. Look for automobile magazines like Road and Track, Car and Driver, etc. Perhaps about 1/3 of the way in, look for a performance review of a new car with a graph of v vs. t under maximum acceleration conditions on a track. Note how the graph looks, as opposed to our Time Regions I and II in our S-Shaped Curve simplified trip. Do you understand why the real graph looks like it does?
  • 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.
  • Wednesday 1/22: 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.

    Thursday 1/23: 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.

    Friday 1/24: Tallk about Sample Exam 1s. Discuss how to use the mph and sec/mile chart seen in the multiple-guess problems. 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. Example: It is 5.50 meters to the ceiling in 1110 Rood. Consider tossing a ball up to the ceiling. If we ignore air reistance, then the time to rise is the same as the time to fall -- the latter is easier to calculate because if you start a problem at the turning point, then v0y = 0. Quiz 3 is a Take-Home quiz on the Kinematic Equations and Free-Fall, due Tuesday 28 January 2014. Quiz 3 will be due the day AFTER we get back. This is in case we have to cancel Tuesday classes due to wind chills as well. I want to have a day where questions can be answered before turning in.

  • To fall from the ceiling is t = 1.059 sec. Final speed is vy = -10.39 m/s. Since for the whole trip y = y0, then t = 2(1.059 sec) = 2.118 sec.
  • 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.
  • Don't forget to update your Formula Card!
  • Week of 27-31 January 2014.

    Monday 1/27: Classes canceled by winter storm.

    Tuesday 1/28: 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. 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).

    Wednesday 1/29: Return Q2. 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). Note that (1) if you take a suqare root of t , you get two answers, +/- , (2) if you divide both sides of an equation by t then t = 0 is also a solution. In both cases, these other solutions may not be useful to our problem, because they occur at the beginning or before the problem starts -- the equations go on forever in the past or the future, but the problem is defined only over a narrow range.

    Thursday 1/30: 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.

    Friday 1/31: Exam 1 moved to Friday 7 February 2014. .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 Vectors and the Analytic Method, due Tuesday 4 February 2014.

  • 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.
  • Week of 3-7 February 2014.

    Monday: 2/3: The guy with the fedora and the cigar (Revisited). Finding final velocity of problem with the guy with the fedora and the cigar in Standard Form. Another Vector Problem: Ax = -3.17 m and Ay = -4.55 m. Formula cards.

    Tuesday 2/4: 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.

    Wednesday 2/5: Return Q3. 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°? Demo: A bullet fired horizontally has the same y-motion as a bullet dropped from the muzzle height. Use two pieces of chalk, one tossed, one dropped. They hit the table at the same time.Types of Motion: No Motion (v=0, a=0), Uniform Motion (v=constant, a=0), Constant Acceleration (a=constant).

    Thursday 2/6: 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.

    Friday 2/7: Exam 1. (Rescheduled from last week.)

    Week of 10-14 February 2014.

    Monday 2/10: U.C.M. 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.

    Tuesday 2/11: 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. 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.) 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.)

  • 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)
  • Wednesday 2/12: 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.). What if we hang the crate by a cable? There is no Normal Force, because the crate is not in contact with anything. "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.
  • Thursday 2/13: 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.

    Friday 2/14: Exam 1 returned. Q5 in-class. Q6 Take-Home on Forces and Free Body Diagrams, due Wednesday 19 February 2014.

    Week of 17-21 February 2014.

    Monday 2/17: "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.

    Tuesday 2/18: 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.

    Wednesday 2/19: Return Q4. Friction is a Contact Force Between Two Surfaces. The Normal Force is perpendicular to the plane of contact. Friction is parallel to the plane of contact, and depends on the Normal Force. 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. Kinetic friction opposes motion and is always Ff,k = µk Fn. Static friction opposes impending motion and can be zero to a maximum of Ff,s,max = µsFn. The actual static friction force is just big enough to keep the object from moving. If you apply a big enough force you (1) break the static friction barrier, (2) switch to kinetic friction, which is lower, and (3) the resulting net force means you are accelerating -- you've switched from Newton's 1st Law to 2nd Law. To move at a constane speed with kinetic friction, the applied force must equal Ff,k. You have to test to see if static friction holds.

    Thursday 2/20: 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. Kinetic friction opposes motion and is always Ff,k = µk Fn. Static friction opposes impending motion and can be zero to a maximum of Ff,s,max = µsFn. 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.

  • Dr. Phil is not driving in today due to potential weather problems coming and going -- lecture in 1110 Rood via Skype.
  • Another round of audio lectures:
  • Inclined Planes with and without Friction (MP3)
  • Anti-lock Braking and Traction Control (MP3)
  • Third Set of Sample Exam 2s is available on the class webpage.
  • If you are using the Testing Center for Exam 2, you must (a) make an appointment at the Testing Center AND (b) send me an e-mail saying that you are taking your Exam 2 at the Testing Center at such-and-such a time, so that I know to send an exam over there.
  • Temperature dropping hard on Friday after Thursday's warm up, rain and melting = ???? Dr. Phil is prepared to Skype in the lecture again. The Take-Home Q7 will be handed out in class, but is already available foe download.
  • Friday 2/21: Friction Problems: (1) A car moving at 70 mph (31.3 m/s) on dry concrete (coefficients of friction 1.00 and 0.800) -- find the shortest stopping distance. To find the distance, we need the acceleration. To find the acceleration we need to find the net force (F = ma). To find the forces, we need the sum of forces equations in x and y, which we get from the Free Body Diagram. Shortet stopping distance requires maximum static friction -- if tyhe car is moving to the right, friction must point to the left to stop. (2) Repeat for the car on sheer ice -- divide the coefficients of friction by 10 (0.100 and 0.0800) -- where in a panic the cars slides to a stop. (3) At 70 mph, what is the minimum radius r for a circular turn with a flat road -- in control on dry concrete? -- skidding on ice? For UCM we need the centripetal acceleration, which we get from the Centriptal Force: Fc = mac = mv²/r . Quiz 7 is a TWO-PAGE Take-Home on Friction, due on Wednesday 26 February 2014.

    Week of 24-28 February 2014.

    Monday 2/24: Return Q5. 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 = ´p / ´t = change in momentum / change in time instead of F=ma, but really the same thing. Impulse Equation: ´p = F ´t .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.

  • ABC News video of a U.K. tanker truck with a car stuck on its front bumper. (Presumably NOT a head-on collision.)
  • For Yugo and Cement Truck: m1 = 1000 kg, v1 = 25.0m/s (to right), m2 = 20,000 kg, v2 = 25.0 m/s (to left). V = -22.62 m/s.
  • NOTE: Exam 2 will NOT include Newton's Universal Law of Gravity or Conservation of Energy, as we are running a bit late with our snow days.
  • Tuesday 2/25: Return Q6. 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. 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 -- KE = ½mv² -- an energy of motion, always positive, scalar, no direction information. Momentum is conserved in all collisions, KE is conserved only in Totally Elastic Collisions. For all other colisions, KE is lost. The energy goes into damage, heat and noise.

    Wednesday 2/26: More on automobile safety systems and how they work to save your life. What's the opposite of a Totally Inelastic 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). Review for Exam 2.

    Thursday 2/27: Exam 2.

    Friday 2/28: WMU SPIRIT DAY -- No Classes.

    Week of 3-7 March 2014.

    SPRING BREAK -- NO CLASSES.

    Week of 10-14 March 2014.

    Monday 3/10: 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. 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).

    Tuesday 3/11: 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. 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.).

    Wednesday 3/12: 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.

    Thursday 3/13: 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 ) 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. 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 in the same time.

    Friday 3/14: (It's Pi Day!) Return 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? 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). Q8 is a Two-Page Take-Home on Universal Gravity, Work and Conservation if Energy, due on Wednesday 19 March 2014.

    Week of 17-21 March 2014.

    Monday 3/17: Return Q7. 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). 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. 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.

    Tuesday 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. 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. 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.

    Wednesday 3/19: 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. 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. How to get liquid out of a cup using a straw -- or why Physics does not "suck", but pushes using a pressure difference.

    Thursday 3/20: 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. 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.

    Friday 3/21: Bernoulli's Equation. The Water Tower and the Faucet Problem. Why the water tower needs a vent. The Continuity Equation. Want Smooth Continuous Flow, not Turbulent Flow or Viscous Flow. Flow rate = Volume / time = Cross-sectional Area × Speed. Topic 2 Worksheets (Click here for 1st Worksheet and Directions) Q9 Take-Home Quiz on Mass-to-Volume Ratio and Bernoulli's Equation, due Wednesday 26 March 2014.

    Week of 24-28 March 2014.

    Monday 3/24: 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 (Fdrag = -bv ) and high speed (Fdrag = -cv²) air resistance. The minus sign is there to remind us that air resistance, like friction, opposes motion. 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.

    Tuesday 3/25: 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.

    Wednesday 3/26: 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).

    Thursday 3/27: 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. 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.

  • 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.
  • 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.
  • Friday 3/28: Review Exam 3 topics. (See below.) Problems: A gas tank is filled when the temperature is around 0°F (-20.0°C). The temperature then rises to 68°F (+20.0°C). For the tank, V0 = 20.0 gal. and αsteel = 12.0 × 10-6 °C-1. For the gasoline, V0 = 19.0 gal. and βgasoline = 950. × 10-6 °C-1. Find the new volume of the tank. Find the new volume of the gasoline. What about the air in the tank? It's original volume was 20.0 gal - 19.0 gal = 1.00 gal and it's initial pressue is 1.00 atm (101,300 Pa). But air is a gas -- it's compressible. We need... 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. Q10 Take-Home on Length & Volume Expansion and the Ideal Gas Law, due on Wednesday 2 April 2014. To be clear, parts (c) and (d) are different ways of calculating the same thing.

  • Remember Exam 3 is next Friday!
  • Note: For linear and volume expansion, the length or volume variables don't have to be converted to metric. All that's required is that that L0 and δL or V0 and δV have the same units.
  • Answers: New volumes are 20.0288 gal for the tank, 19.722 gal for the gasoline, and 0.3068 gal for the air. New pressure for the air is 3.7748 atm. Not only did the gasoline expand more, it's pressurized to nearly four atmospheres!
  • What would have happened if the initial volume of the gasoline had been 19.5 gallons?
  • 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.
  • Exam 3 Topics:
    
    Leftover from Sample Exam 2:
    == Work, KE, PE, Conservation of Energy
    == Newton's Law of Universal Gravity
    
    Current topics:
    == Mass-to-volume ratio (density)
    == Floating and displacement
    == Pressure = Force / Area
    == Pressure due to a column of liquid
    == Bernoulli's Law
    == Continuity Equation
    == Length and Volume Expansion
    == Simplified Ideal Gas Law
    
    Next topics:
    >> Heat capacity and energy to change phases 
       (This material will NOT be covered in Spring 2014 and will NOT be on Exam 3.)
    == Heat engines and efficiencies 
       (This material WILL be covered on Monday and Tuesday and WILL be on Exam 3. 
        It will also be used on Worksheet 4 for Topic 2.)
    >> Sound, wavelengths, resonance and interference 
       (This material WILL be covered and WILL appear on the Final Exam. 
        It will NOT be on Exam 3.)

    Week of 31 March-4 April 2014.

    Monday 3/31: 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).

    Tuesday 4/1: The Heat Engine and Three Efficiencies (Actual, Carnot and 2nd Law). Power is Work per time. We talk of Useful Work, Total Energy, Waste Energy -- we can substitute the rate work is done, power, for Useful Power, Total Power, Waste Power. Example: It takes 15 to 50 h.p. from your car's engine to maintain highway speed due to air resistance and friction. 15 h.p. × 746 W/h.p. = 11,190 W = 11,190 J/s . This is the useful power. Each second, the useful work is W = 11,190 J. Assume the hot reservoir is TH = 850.°C and the cold reservoir is TC = 95.0°C. This allows us to find the Carnot effiiciency. If, for the purposes of simplicity, we take the 2nd Law efficiency as 100%, then the Carnot efficiency = Actual efficiency. This allows us to find the Total energy, QH , and the waste heat, QC .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 -- there is not much room between the actual efficiency and the Carnot efficiency to make an 8- to 10-fold increase in m.p.g. To use less fuel, do less work.

    Wednesday 4/2: What happens if we reverse the arrows in the Heat Engine diagram? We get a refrigerator. 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 .

    Thursday 4/3: Review.

    Friday 4/4: Exam 3.

    Exam 3 Topics:
    
    Leftover from Sample Exam 2:
    == Work, KE, PE, Conservation of Energy
    == Newton's Law of Universal Gravity
    
    Current topics:
    == Mass-to-volume ratio (density)
    == Floating and displacement
    == Pressure = Force / Area
    == Pressure due to a column of liquid
    == Bernoulli's Law
    == Continuity Equation
    == Length and Volume Expansion
    == Simplified Ideal Gas Law
    
    Next topics:
    >> Heat capacity and energy to change phases 
       (This material will NOT be covered in Spring 2014 and will NOT be on Exam 3.)
    == Heat engines and efficiencies 
       (This material WILL be covered on Monday and Tuesday and WILL be on Exam 3. 
        It will also be used on Worksheet 4 for Topic 2.)
    >> Sound, wavelengths, resonance and interference 
       (This material WILL be covered and WILL appear on the Final Exam. 
        It will NOT be on Exam 3.)

    Week of 7-11 April 2014.

    Monday 4/7: 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 . Demonstration: the Slinky shows both longintudinal (string type) and transverse waves (sound type). Waves and Resonance. Standing Waves on a string. Fundamental, First Overtone, Second Overtone, etc. Demonstration: First and higher overtones on a string driven by a saber saw. We are varying the speed of the wave by changing the tension. With a fixed frequency from the saber saw, this changes the wavelength. (Can't see the Fundamental on the saber saw demo, because the tension required usually breaks the string.) Standing Waves in a tube. Topic 2 Worksheets 2-4 (Click here for all 4 Worksheets and Directions)

    Tuesday 4/8: 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. 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 | .

    Wednesday 4/9: 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 | . The speed of sound in air. 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. Constructive and Destructive Interference. Acoustics of concert halls. The range of "normal" human hearing: 20Hz-20,000Hz (10 octaves). Sound levels -- the amplitude of sound waves is due to the pressure change up and down from the base air pressure, P0. dB = decibel, a logarhythmic scale. A change in ±3 dB is twice or half the sound intensity, while a change in ±10dB is a factor to ten. Sound Meter results from a previous semester: ambient noise in 1110 Rood = 56 dB; Dr. Phil talking at ½ meter = 63 dB; Class shouting = 83 dB; Dr. Phil shouting at ¼ meter = 108 dB. Q11 Take-Home Quiz on Standing Waves, due Tuesday 15 April 2014.

  • 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 55, 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 4/10: dB = decibel, a logarhythmic scale. A change in ±3 dB is twice or half the sound intensity, while a change in ±10dB is a factor to ten. (log(2) = 0.3, move the decimal place get 3, log(10) = 1, move the decimal place get 10.) Signal-to-noise ratio: How much louder the sound (signal) you want is over the background hiss (noise). Example: A good CD player is advertised as having a signal-to-noise ratio of 96dB. What does this mean? 109 = 1,000,000,000, move the decimal place get 90. Breaking up our dB into pieces, 96dB = 90dB + 3dB + 3dB, represents 1,000,000,000 × 2 × 2 = 4,000,000,000. So a 96dB range represents a 4 billion times difference between the signal and the background noise! O&B p. 250 -- Table of sound levels. The speed of sound in air. Sonic Booms and other shockwaves. First Day to turn in Topic 1 paper.

    Friday 4/11: Problems: (1) A lightning bolt strikes 1 mile = 1609 m away. The flash travels at the speed of light, c = 300,000,000 m/s, the sound at 68°F = 20°C, travels at 344 m/s. v = d / t, so t = d / v. 5.363 millionths of a second for light and 4.677 seconds for sound. (2) An empty Coke resonantes with its fundamental (pipe open at one end and closed at the other). L = 25.0 cm = 0.250 m. λ / 4 = L, λ = 4 L = 1.000 m . v = f λ , f = v / λ = 344 Hz. The sound wave comes from a vibrating string, fixed at both ends, vibrating at the same frequency f. λ / 2 = L , λ = 2 L, so if L = 80.0 cm = 0.800 m, then λ = 1.600 m. The wave speed in the string, which has nothing to do with the wave speed in air, is v = f λ = 550.4 m/s. (3) Sound A is 65dB. Sound B is 80 times louder. 80 = 10 × 2 ×2 × 2, which translates to 10dB + 3dB + 3dB + 3dB = 19dB. So Sound B is 65dB + 19dB = 84dB. Second Day to turn in Topic 1 paper.

    Week of 14-18 April 2014.

    Monday 4/14: Return X3. 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 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. Third Day to turn in Topic 1 paper.

    Tuesday 4/15: 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.

    Wednesday 4/16:

    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"). 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. Q12 Take-Home on Series and Parallel Resistors, due Friday 18 April 2014.

    In case you suddenly realize you need data for Topic 2:
    
    1996 T-10 Chevy 4WD Blazer
    4300 lbs., 185 hp
    0 to 45 mph in 12 seconds
    Trip and Gas Run Together:
    313,895.3 to 314179.6
    7:33am to 9:15am (stops of 10 min + 20 min)
    2:50pm to 4:30pm (stop of 7 min)
    7:34am to 9:30pm (stops of 7 min + 20 min)
    4:55pm to 6:30pm (stop of 7 min)
    gas at 2nd fill: 15.83 gallons
    
    Dr. Phil

    Thursday 4/17: "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, 1110 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 = Planck's constant = 6.626 × 10 -34 J·sec , 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. Topic 2 Worksheets due TODAY.

    Friday 4/18: THE LAST CLASS.