Dr. Phil's Home
Updated: 05 December 2008 Friday.
Monday 12/1: The Great 19th Century Debate: Is Light a Particle or a Wave? (Wave-Particle Duality did not seem obvious at the time.) The Electromagnetic Wave travels at the speed of light. c = 300,000,000 m/s = 186,000 miles/sec. Electromagnetic Spectrum: Visible light (ROYGBIV=red orange yellow green blue indigo violet). Frequencies HIGHER and wavelengths SHORTER than visible light (UV ultraviolet, X-rays, Gamma rays). Visible light is 400nm to 750nm (4000 angstroms to 7500 angstroms). Cannot "see" atoms with visable light, because the atom is about 1 angstrom across (1.00E-10 meters). The visible light wave is too large to see something that small. So use X-rays. Why Superman's X-ray vision cannot work -- because everyday situations are "dark" in the X-ray band, thankfully! Frequences LOWER and wavelengths LONGER than visible light (IR infrared, Microwave, Radio waves, ELF extremely low frequency). First set of Sample Final Exams. (Click here and here for a copy.)
Tuesday 12/2: Optics: Optics: Geometric Optics (empirical) and Physical Optics (more wave and fieldlike). Ray Tracing: Rays from a spherical source become essentially parallel rays when you are far away. When a straight light ray hits a boundary between one material and another, three things can happen: Reflection, Absorption, Transmission. The Law of Reflection. The Optical Lever -- move a mirror by 10° and the reflected ray moves by 20°. (Dr. Phil's theory on the origin of "seven years of bad luck for breaking a mirror".) When light rays strike a rough surface, you get Scattering, which is reflections off many different angles. People tend to not like photographs of themselves, because they are used to seeing their mirror image -- their normal image, which the rest of us sees, looks "wrong". The Law of Refraction - Snell's Law. Light bent at the interface between two media, because the speed of light changes in the media. (Analogy: If you are driving along the road and your right tires go off onto the soft shoulder, they can't go as fast and the car turns towards the shoulder until all four wheels are driving off the road.) If going from an high index of refraction media to a lower index media ONLY, have a chance for Total Internal Reflection (T.I.R.). This is a "perfect" reflection, better than a mirror. Used in high-end optical systems instead of mirrors. Also useful in fiber optics cables. Quiz 19+20 Double-Quiz is a Take-Home handed out Tuesday 2 December 2008, due Thursday 4 December 2008. (Click here for a copy.)
Wednesday 12/3: Dispersion -- in vacuum all speeds of light are the same, but in a medium, there are slighltly different n's for each wavelength. As one goes from a high index of refraction to a low index, increasing the angle of incidence, white light will start breaking into the rainbox spectrum of colors. Thin Lenses. Simplest lens surfaces are spherical (convex = bows out, concave = bows in) and flat (plano). So some lenses might appear to be biconvex, plano-convex, biconcave, convex-concave. A biconvex lens is also called a positive or converging lens. Parallel light rays coming into such a lens will all pass through the focal point, a distance f from the center of the lens. By itself, could use as a magnifying lens. Concentrating sunlight: burning paper or popping ants? Ray tracing gets same results as doing Snell's Law on mulitple curved lens surfaces. Handy not to have to do all that refraction calculations! Real image formed by passing three rays through a positive thin lens. Three cases: object distance p > 2f (real, inverted, reduced image), 2f < p < f (real, inverted, magnified image), p < f (virtual, upright, magnified image = magnifying glass) -- latter two not shown here. Second set of Sample Final Exams -- the All-Titanic Exam. (Click here for a copy.) Quiz 21+22 Double-Quiz is a Take-Home handed out Wednesday 3 December 2008, due Friday 5 December 2008. (Click here for a copy.)
Thursday 12/4: Return X3. (Click here for a solution.) Analytic formula for object and image. Magnification: M = h' / h = -q / p. Use of Muliple Lenses -- Focal lengths in series add like series capacitors (by reciprocals) -- one can adjust the working distance to the object or image, or compact or expand the physical size of the lens. Dispersion -- in vacuum all speeds of light are the same, but in a medium, there are slighltly different n's for each wavelength. Diopters are the reciprocal of focal length in meters. Note that some eyepieces to optical devices have some diopter built in, so that if you add an eyepiece to the eyepiece, the second unit may be marked for the total diopter, not the diopter of that particular lens. In multiple lenses the effective diopter is just the sum of the diopters. A flat piece of glass is 0 diopters.
Friday 12/5: Last Regularly Scheduled Class. Discuss last quizzes and Final Exam. Review course topics in brief and look at a couple of Sample Final Exam Problems. Finish up the day with the course & teacher evaluations for the semester.
Due to time constraints, we obviously have not covered all the material in the text. If you want a rough guide to the topics we didn't cover at the end of the textbook, check out these topics from the PHYS-1150 course.
Monday 9/1: Labor Day <No Classes>
Tuesday 9/2: Class begins. The nature of studying Physics. Science education in the United States. Natural Philosophy. The Circle of Physics.
Wednesday 9/3: Aristotle and the Greek Philosophers. Observation vs. Experiment - Dropping the book and the piece of paper (2 views). Mechanics is the study of motion. So what is motion? Zeno of Elea -- Zeno's Paradoxes. Distribute syllabus.
Thursday 9/4: "Speed Limit 70" First Equation: Speed = Distance / Time. Development of Speed equation for Constant or Average Speed. delta-x = xf - xi . Q1 and your PID number. (If you missed class on this day, check with Dr. Phil sometime soon.)
Friday 9/5: Show Dr. Phil's WMU Homepage and the PHYS-1070 Class web page. Development of Speed equation for Constant or Average Speed (con't.). delta-x = xf - xi , x = x0 + v t . A simplified trip to the store -- The S-Shaped Curve. Acceleration.
Monday 9/8: Finding the set of Kinematic Equations for constant acceleration. Kinematic Equations for Constant Acceleration. The Equation Without Time -- Avoiding the Quadradic Formula. Finishing The S-Shaped Curve: plotting x-vs-t gives straight line in Region II, but parabolic curves for Regions I and III. 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 Wednesday 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).
Tuesday 9/9: 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. SI Metric System. 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 (World Record in 100m dash -- 9.69 seconds -- set at Beijing 2008 Summer Olympics). 345 m/s = Mach 1 (speed of sound). 8000 m/s = Low Earth Orbital Speed. 11,300 m/s = Earth escape velocity. 300,000,000 m/s = Speed of light. PTPBIP - Putting The Physics Back Into The Problem. Q2 in-class.
Wednesday 9/10: What do we mean by a = 1 meter/sec² ? You cannot accelerate at 1 m/s² for very long. Comments on Q2 -- solution already posted on class webpage. The P-O-R (Press-On-Regardless) road rally problem. "You can't average averages." Finishing The S-Shaped Curve: Look at real world v-vs-t graphs in a car magazine (Road & Track, Car & Driver, Motor Trend). The line is curved, not straight and has small hiccoughs (gear shifts). The variable for change in acceleration divided by change in time is called "jerk" (SI units m/s³), and you can feel it as a jerk.
Thursday 9/11: News: CERN's Large Hadron Collider -- not going to destroy the Earth. Problem: A car starts at rest, then accelerates at 3.00 m/s² for 8.00 sec. (a) Find final speed v. (b) Find distance traveled x. Assume x0 = 0. Use 1st kinematic equation to find (b) -- and check the solution with 4th kinematic equation, The Equation Without Time. Dr. Phil's Reasonable Significant Figures. 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.) Problem: A rifle bullet is fired from rest to nearly twice the speed of sound, 600 m/s, in a distance of 1.00 m. Find a. Answer, a = 180,000 m/s². This is huge, which is why we don't fire people out of rifle barrels. 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. Q3 Take-Home due Tuesday 16 September 2008, in class or by 5pm.
Friday 9/12: Rifle problem con't. Find t = 0.003333sec. Again, we can solve for t using two different equations, but will still get the same result because there is one Physics. Very large acceleration for very short time. How big is this acceleration? Comparison to 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 Wednesday. NASA defines a hammer blow as 100 to 500 times g. Explosion of NASA/USAF X-15-3 with XLR99 engine on test stand. Scott Crossfield survived a momentary 1000 g acceleration. Pumpkin Chunkin event -- the big compressed air cannons can't be too violent or the pumpkings turn into "pie".
Monday 9/15: Free-Fall: If we ignore air resistance, all objects near the surface of the Earth fall towards the Earth at the same rate. ay = -g ; g = 9.81 m/s². That's nearly ten times the acceleration a = 1 m/s² we talked about last week. Rewriting the Kinematic Equations for motion in the y-direction, pre-loading them for free-fall. 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.
Tuesday 9/16: 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. Q4 Take-Home, due Thursday 18 September 2008, in class or by 5pm. Read the quiz carefully. Part (d) is to look at how far the ball falls from the turning point in ¼T -- this is that region near the turning point we discussed for the Michael Jordan "defying gravity" illusion.
Wednesday 9/17: Two kinds of numbers: Scalars (magnitude and units) and Vectors (magnitude, units and direction). Adding and subtracting vectors: Graphical method. Standard Angle (start at positive x-axis and go counterclockwise). Standard Form: 5.00m @ 30°. First set of Sample Exam 1's handed out. (Click here and here for a copy.)
Thursday 9/18: 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. For studying, find vector D = vector A - vector B, where in class you were given vector A = 5.00 m @ 30° and vector B = 7.00 m @ 120° . Q5 Take-Home, due Tuesday 23 September 2008, in class or by 5pm.
Friday 9/19: Finding the angle of vector B from tan-1 (By / Bx). Use your sketch to make up for the fact that arctangent is a stupid, lying function! (grin) Finding the final vector velocity of The guy with the fedora and the cigar problem. Ballistic or Projectile Motion covers any problem were ax = 0 and ay = -g. Covers a lot of problems, not just guns and cannons. Four pages of Topic 1 assignment handed out. (Full 27-page Handout as PDF File -- Searchable HTML Page )
Monday 9/22: Two Dangerous Equations. You can only use the Range Equation if the Launch Height = Landing Height. But the sin (2*theta) term in the Range Equation means that (1) 45° gives the maximum range for a given initial velocity and (2) that all other angles have a complementary angle (90° - theta) that gives the same range (but a different time and height). High and low trajectories for Range Equation. Types of Motion studied so far: No motion, Uniform motion (v=constant, a=0), Constant Acceleration. Up next: Uniform Circular Motion (UCM). Second Sample Exam 1. (Click here and here for a copy.)
Tuesday 9/23: Uniform Circular Motion (UCM): speed is constant, but vector velocity is not; magnitude of the acceleration is constant, but the vector acceleration is not. Velocity is tangent to circle, Centripetal Acceleration is perpendicular to velocity and points radial INWARD. ac = v²/r. Space Shuttle in Low-Earth Orbit. (There's still gravity up there!) Q6 Take-Home, due Thursday 25 September 2008, in class or by 5pm.
Wednesday 9/24: More on U.C.M. Possible to get quite high values for the centripetal acceleration, ac. F-16 and "9 g" turns. Texas Motor Speedway and drivers passing out in middle of turns. Hard drive failures. 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. 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.
Thursday 9/25: Using Vector Addition for Velocities: Upstream, downstream (rivers), Headwind, tailwind, crosswind (airplanes). Recap: Our studies so far have described "How" things move, and allow to say "When" and "Where" things move, but not "Why" things move. For that we have to start talking about Forces -- and that means Newton. Some stories about Sir Isaac Newton. Newton's Three Laws of Motion: Zeroeth Law - There is such a thing as mass. 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.) NOTE: No quiz today -- will hand out next week.
Friday 9/26: Demo: Rodney Reindeer and U.C.M. Newton's 3 Laws continued. 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.). 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. 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.
Monday 9/29: 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. 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. Variations as we allow for an applied force that it at an angle. "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. Discussion of "two pound test fishing line", stretching and breaking of cables, Safety Factors. Comments on Exam 1.
Tuesday 9/30: Exam 1. Q7 Take-Home, due Thursday 2 October 2008, in class or by 5pm. NOTE: For full credit you must include a Free Body Diagram, properly labeled.
Wednesday 10/1: "D.O. Wyble's 3 Things Physics Students Need to Know." Hanging a sign with angled wires -- still the same procedure: Sketch of the problem, Free Body Diagram, Sum of Forces equations in the x- and y-directions, solve for unknowns. For the problem in class, we had a sign with m = 15.0 kg and two tension forces, T1-vector = 107.7 N @ 150° and T2-vector = 131.9 N @ 45°. You can check to make sure these forces cancel in the x-direction and support the weight of the sign in the y-direction. Atwood's Machine -- two masses connected by a single cable via a simple pulley. They share a common acceleration, a, with one mass going up and the other going down. Elevator Problems. The Normal Force represents the "apparent weight" of the person in the elevator. For the elevator at rest or moving at constant speed, the Normal Force = weight, and the tension of the cable = weight of loaded elevator. But if there is an acceleration vector pointing up, the apparent weight and the tension of the cable increase; if the vector points down, the apparent weight and the cable tension decrease. In true Free Fall, without any air resistance, the Normal Force = 0 and you are floating.
Thursday 10/2: 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. 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. Q8 Take-Home, due Tuesday 7 October 2008, in class or by 5pm.
Friday 10/3: Static & Kinetic Friction continued: Examples using our 125 kg crate sliding on the floor. If object is at rest, need to "test" to see if an applied external force exceeds the maximum static friction force ("breaks the static friction barrier"). Static Friction can vary from zero to its max value in either direction. Rubber on concrete. Tires rolling with friction on good roads -- this is static friction not kinetic friction because the tires aren't sliding on the pavement. If velocity vector and acceleration vector point in the same direction, then the speed is increasing. If they are in the opposite direction, then the speed is decreasing. In either case, for a car the force involved must be in the same direction as the acceleration vector -- this seems to be confusing whereby the static friction force on the tires from the road points forward when you are speeding up. The conflict arises because you might be thinking "friction opposes motion" and not thinking about the motion of the tires versus the motion of the car. If object is at rest, need to "test" to see if an applied external force exceeds the maximum static friction force ("breaks the static friction barrier"). Anti-Lock Brakes and Traction Control. ABS works by monitoring the rotation of all four wheels. If one wheel begins to "lose it" and slip on the road while braking, it will slow its rotation faster than the other tires, so the computer releases the brake on that wheel only until it is rolling without slipping again.
Monday 10/6: More comments on friction and ABS systems in cars. 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 = change in momentum / change in time instead of F=ma, but really the same thing. Two extremes in collisions: Totally Elastic Collision (perfect rebound, no damage) and Totally Inelastic Collision (stick together, take damage). Linear momentum is conserved in all types of collisions . Totally Inelastic Collisions. Example: The Yugo and the Cement Truck with numbers. Real Head-On collisions.
Tuesday 10/7: Linear momentum is conserved in all types of collisions . Totally Inelastic Collisions. Examples: 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. What happens in a wreck. How airbags and seatbelts work. Q9 Take-Home, due Thursday 9 October 2008 (or possibly later).
Wednesday 10/8: Real crashes. More on airbags. Interactions of safety systems. The myth of it being better to be "thrown clear from the wreck", Part II. Totally Elastic Collisions -- some brief comments. Why you want inelastics collisions in a wreck. 5 mph versus 3 mph impact bumpers. "Adobe: The Little Car Made of Clay".
Thursday 10/9: What's the opposite of a collision? An explosion. Or recoil. Example: A pitcher on ice skates at rest -- when he hurls a fastball to the right, he goes to the left. Total momentum of the system remains constant (in this case, zero). We've talked about How things move (Kinematic Equations) and Why things move (Forces, momentum). Now we want to talk about the Effort to make things move. Work: A Physics Definition (Work = Force times distance in the same direction). Q10 Take-Home, due Tuesday 14 October 2008.
Friday 10/10: Work = Energy. Kinetic Energy -- an energy of motion, always positive, scalar, no direction information. Work-Energy Theorem (net Work = Change in K.E.). Using the Work-Energy Theorem to find a final speed. 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. 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.) Simulate a Totally Elastic Collision (p and KE conserved) with the Executive Time Waster. It can't be totally elastic because it makes a noise, and that took some of the energy. First Sample Exam 2. (Click here and here for a copy)
Monday 10/13: (Columbus Day -- no U.S. mail delivery, but classes meet) Continue with 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. 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.
Tuesday 10/14: World's Record Free-Fall. UCM Revisited. Centripetal Force, Fc = m ac. Note that the Centripetal Force is an ANSWER to the sum of forces equation -- it does not show up in the F.B.D. directly -- something has to CAUSE the Centripetal Force, such as a tension, normal force or a combination of forces. No such thing as Centrifugal Force. Only the Centrepital Force, which points radial inward, just like the centripetal acceleration. You aren't forced to the outside, you merely move in a straight line unless there is a force to keep you on the circle. Test tube example. How you could "get thrown clear of the wreck" in the old days. Although a loop-the-loop is not a proper UCM problem, we can apply UCM at the top of the loop and determine the minimum safe speed for going around the loop without falling off. At the minimum speed, the Normal Force between the wheels and rail goes to zero (the wheels just "kiss" the track), so the centripetal force is just equal to the weight, w = mg. The story of the 50,000 rpm Ultra-Centrifuge and the Fresh Rat's Liver. Q11 Take-Home, due Thursday 16 October 2008. NOTE: In the version handed out in class, the word "brick" should be "cherry pie". NOTE: The speed 8.00 m/s should be, of course, 7.00 m/s.
Wednesday 10/15: The Ballistic Pendulum -- We can find the speed of a projectile through an Inelastic Collision followed by Conservation of TME. Making "artificial gravity" for long-duration space flight by living in a rotating object. 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.
Thursday 10/16: The formula w = mg gives us the gravitational force near the surface of the Earth. Newton had to work out gravity for anywhere, hence "Universal Gravity." Specifically Newton was working on trying to solve the problem of the motion of Mars in the night sky. Newton's Universal Law of Gravity (or Newton's Law of Universal Gravity). Takes two masses -- there are two forces, according to Newton's Third Law. Use Universal Gravity to check "g". The value we calculate is close, 9.83m/s², which turns out to be only off by 0.2%. Why is it off? Because using Univeral Gravity in this manner makes the assumption that the entire Earth is uniform and homogenous from the surface to the core -- which it is not. We would need calculus to integrate over layers to get the observed value of 9.81m/s². The Shuttle in Low Earth Orbit (Revisited). Four Fundamental Forces in Nature: Gravity, E & M, Weak Nuclear Force, Strong Nuclear Force. Second set of Sample Exam 2's handed out. (Click here and here for a copy.) Q12 Take-Home, due Tuesday 21 October 2008. (Click here for a copy.)
Friday 10/17: YES! WE HAVE CLASS TODAY! Newton's Universal Law of Gravity (or Newton's Law of Universal Gravity). Tides (high/low, spring/neap). Though we are calculating anything with tides, it is interesting to see how Newton's equations for gravity apply. With this discussion, we close the book on material eligible for Exam 2. Discussion of studying for Exam 2 -- Dr. Phil speaks from experience. We now need to add attributes to our objects more than just mass and kinematic variables, forces, momentum, energy. Need to start considering type and shapes. Three Classical States of Matter: Solid, Liquid, Gas. Combinations: Condensed Matter (covers both Solids and Liquids) and Fluids (covers both Liquids and Gasses). Two Extreme States of Matter: Plasma (electrons stripped off, high temperature), Cryogenics (extreme cold, odd behavior).
Monday 10/20: Review for X2 from some of our Sample Exam 2 problems. Up until now, our objects really haven't had any dimensions. 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.
Tuesday 10/21: Comments on the FBD for Q12. Mass-to-Volume Ratio (Density). NOTE: Do not confuse the Density of the Materials with the Mass-to-Volume Ratio of the OBJECT. 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. Q13 Take-Home, due Friday 24 October 2008. (Click here for a copy.)
Wednesday 10/22: Why Boats Float. Example: Front lab table as a 250 kg boat with 4.00 m³ volume. Buoyant Force = Weight of the Boat = Weight of the Water Displaced by the Submerged Part of the Boat. Calulating the amount of the boat submerged, by using the fact that the mass of the boat and the mass of the displaced water are the same. Archimedes and Eureka! (I found it!)
Thursday 10/23: Pressure = Force / Area. SI unit: Pascal (Pa). Example: Squeezing a thumbtack between thumb and forefinger. 1 Pa = 1 N/m², but Pascals are very small, so we get a lot of them. One Atmosphere standard air pressure = 1 atm. = 14.7 psi = 101,300 Pa. Pressure at a depth due to supporting the column of liquid above. Absolute (total) Pressure vs. Gauge Pressure (difference between two readings). Smooth Fluid Flow. Bernoulli's Equation and the Continuity Equation. Water Tower and the Faucet Problem. Why the water tower needs a vent.
Friday 10/24: Pressure at a depth due to supporting the column of liquid above. Water pressure = 1 atm = 101,300 Pa at depth h = 10.33 m = 33.86 feet. How a straw work. 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. The perils of SCUBA diving. Why you need a qualified SCUBA instructor.
Monday 10/27: Return X1.
MOVE EXAM 2 TO THURSDAY 30 October
2008. Bernoulli's Equation and the
Continuity Equation. With smooth constant flow, the flow rate (m³/sec)
must remain constant -- hence the Continuity Equation. The faster the fluid
flow, the lower the Pressure. Example: The aspirator -- a vacuum pump with no
Tuesday 10/28: Bernoulli continued. The faster the fluid flow, the lower the Pressure. Example: Air flow around a wing. (Faster air over top means lower pressure on top, so net force is up -- Lift.) 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).
Wednesday 10/29: Temperature Scales: °F, °C and K (Kelvins). Linear Expansion: Most objects expand when heated, shrink when cooled. Use logic to figure out equation for Length Expansion. alpha = coefficient of linear expansion for a material.
Thursday 10/30: Length Expansion. Example: One 39 ft. (12.0m) steel rail expands 2.88 mm for a 20°C change in temperature, or nearly a centimeter from the dead of winter to the height of summer, but that's nearly a meter for a hundred pieces of railroad track -- about ¾-mile. Expansion joints. I-57 in Chicago and the expanding asphault. 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?)
Friday 10/31: Volume Expansion of Solids and Liquids. Coefficient of Volume Expansion usually given for liquids; for solids, beta = 3 × alpha. Beta for liquids usually larger than beta for solids. Why you need an overflow tank for your radiator. Why you shouldn't fill your gas tank completely full, especially as the weather changes. Ideal Gas Law (PV/T = constant). Review of some Sample Exam 2 problems.
Monday 11/3: Exam 2.
Tuesday 11/4: Election Day! The Laws of Thermodynamics. Heat Energy (Q). The Heat Engine and Three Efficiencies (Actual, Carnot and 2nd Law). Fuel Economy (miles per gallon) is not an Efficiency. Q14 Take-Home, due Thursday 6 November 2008.
Wednesday 11/5: The Laws of Thermodynamics. Heat Energy (Q). 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. Smaller, lighter cars with smaller, lighter engines. To improve efficiency, can reduce TC or raise TH .
Thursday 11/6: When a heat engine is cold, TC = TH . Can't get any useful work done. Reverse the arrows in the Heat Engine and you get a Refrigerator. Cannot place an open refrigerator or a window air conditioner in the middle of a room and cool the room, because the exhaust heat to the hot side includes the heat pulled from the cold side plus the work done on the compressor. A Heat Pump is a reversible system which cools inside of the house in summer and heats the inside of the house in winter -- just because it is cold outside, doesn't mean there is not heat energy Q in the outside air. (There has to be, otherwise the air would be at 0 K.) Waves: Single Pulse vs. Repeating Waves. The motion of the material vs. the apparent motion of the wave. For Repeating Waves, we have a Repeat Length (wavelength) and a Repeat Time (Period). Frequency = 1/Period. Wave speed = frequency x wavelength. Demonstration: the Slinky shows both longintudinal (string type) and transverse waves (sound type).
Friday 11/7: 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. Standing Waves in a tube. Brass instruments start from the "natural trumpet", which can only play the fundamental and overtones for the pipe. Woodwind instruments get more complicated. Topic 2 Worksheets on taking real world data and analysing it. (Click here for a copy of Worksheet 1.) Q15 Take-Home, due Tuesday 11 November 2008.
Monday 11/10: Tuning forks, resonance boxes. The range of "normal" human hearing: 20Hz-20,000Hz (10 octaves). Artilleryman's ear -- mid-range hearing loss. NOTE: Quiz tomorrow will NOT be In-Class.
Tuesday 11/11: Veteran's Day (not a WMU holiday). Constructive and Destructive Interference. Acoustics of concert halls. dB = decibel, a logarhythmic scale. NOTE: A regular log scale is based on exponents: 100 = 1, 101 = 10, 102 = 100, etc. So log(1) = 0, log(10) = 1, log (100) = 2, etc. The dB scale is similar, but every 10 dB is a change of about 2, and ever 20 dB is a change of 10. So a 90 dB sound is 20 times louder than a 60 dB sound (90dB - 60 dB = +30dB = 20dB + 10dB or 10 ×2 = 20 times). Q16 Take-Home, due Thursday 13 November 2008. (Click here for a copy.)
Wednesday 11/12: dB = decibel, a logarhythmic scale. See tables in textbook. Why driving in around in a very quiet car and the windows rolled up tight is A Very Bad Idea. The speed of sound in air: 334 m/s @ 0°C and 344 m/s @ 20°C. Takes time for sound to travel.
NOTE: From Friday 11/7: Topic 2 Worksheets on taking real world data and analysing it. (Click here for a copy of Worksheet 1.)
Thursday 11/13: If you exceed the wave speed in a material, you get a Shock Wave -- distinctive V-shaped pattern from front and back of moving object. Sonic booms in air (actually get a double-boom, because of the two V's.), wake from a boat in water. The speed of sound in air: 334 m/s @ 0°C and 344 m/s @ 20°C. Takes time for sound to travel. The Realization that Electricity and Magnetism were part of the same Electromagnetic Force was a great triumph of 19th century physics. 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. First Set of Sample Exam 3's. (Click here for a copy.) NOTE: Some people reported problems downloading Q16 -- I checked, it's there, but already said we'd collect Q16 on Friday.
Friday 11/14: Two charges: like charges repel, unlike (opposite) charges
attract. Coulomb's Law looks like
Newton's Law of Universal Gravity. Four
Fundamental Forces in Nature: Gravity, E & M, Weak Nuclear Force, Strong
Nuclear Force. The Hydrogen Atom. Gravity loses to
Electric Force by a factor of 200 million dectillion (!!!). Q17 Take-Home,
Tuesday 18 November 2008 changed to Wednesday 19 November
2008 because I didn't get it posted over the weekend.
Monday 11/17: 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. Discussion for the future: Isotopes of the same element have different numbers of neutrons. Coulomb of charge is an enormous amount of charge. Two 1.00 C charges separated by 1.00 meters have a force of one-billion Newtons acting on each other. Real Electric Charges. Two charges: like charges repel, unlike (opposite) charges attract. A Nickel coin has a mass of 5 grams, so about 1/10th of a mole. Each Ni atom has 28 protons and 28 electrons. Or +270,000 C of positive charges and -270,000 C of negative charges. Fortunately, the net charge of a typical nickel coin is... zero.
Tuesday 11/18: 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 wintertime.
Wednesday 11/19: Return X2. 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. 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.
Thursday 11/20: D.C. and A.C. circuits. Ohm's Law. V=IR form. (Ohm's "3 Laws"). 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.
Friday 11/21: Power dissipated by Joule heating in a resistor. P = I V (3 forms of Power equation to with Ohm's "3 Laws"). Resistor Network Reduction. Having reduced the resistor network to a single equivalent resistance, go back and fill in the table for V = I R and then P = I V. 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 Voyager 2 radio "repair" call from 4,000,000,000 miles.) Topic 2 Worksheets 2-4. (Click here for a copy.)
Monday 11/24: "Magnetism is just like Electricity, only different." Real Magnets are dipoles (North and South ends, linked). Break a magnet in half, and you either get two new magnets -- or nothing. So far, there is no evidence that there are Magnetic Monopoles (magnetic charges: isolated North or South poles). Rules similar to Electric Charges: Unlike poles attract, like poles repel. Demos: Cow magnets -- powerful cylindrical, rounded end magnets which get dropped into a cow's first stomach, to collect nails, bits of barbed wire, etc. from continuing on to the cow's other stomachs. The horizontal compass needle rotates until its North end points North (or rather to the North Magnetic Pole, which is of course a South pole of the Earth's magnetic core); the vertical compass rotates so that it lines up with the B-field along the surface of the Earth at the point. At the Equator, the vertical magnetic should be parallel to the ground, at the magnetic poles, it should be perpendicular to the ground. Is the Earth's magnetic field going to flip some day? SI Units for B-field: (1 Tesla = 1 T). "Other" unit for B-field: ( 1 Gauss = 1 G ; 1 T = 10,000 G ). Earth's B-field is about 1 Gauss at the Earth's surface. Example of the 4T NMR magnet at Michigan Tech and the 10-foot radius line on the floor and erasing ATM cards within that circle. Review some Sample Exam 3 problems.
Tuesday 11/25: Exam 3.
Wednesday 11/26: <No Class> WMU Closes for Thanksgiving Holiday at Noon. Classes resume as usual on Monday 1 December 2008.
Thursday 11/27: THANKSGIVING -- No Classes --
Friday 11/28: Recovery from THANKSGIVING DINNER -- No Classes -- (grin)