Dr. Phil's Home
Updated: 01 May 2012 Tuesday.
FINAL COURSE GRADES AND BREAKDOWN BY CATEGORY FOR PHYS-1070 Spring 2012. Estimated Pre-Finals Grades can be found here. NOTE: I've posted the Revised Exam 2 curve here.
Reminder that ICES Student Course Evaluations are available now online via GoWMU .
Monday 4/23: Office Hours.
Wednesday 4/25: FINAL EXAM (12:30pm-2:30pm)
Thursday 4/26: Dr. Phil does not plan on coming in today.
Friday 4/27: LAST DAY TO MAKE UP EXAMS.
Monday 4/30: Office Hours.
Tuesday 5/1: Grades due at Noon.
Monday 1/9: Class begins. The nature of studying Physics. Science education in the United States. Natural Philosophy. The Circle of Physics.
Tuesday 1/10: Aristotle and the Greek Philosophers. Observation vs. Experiment - Dropping the book and the piece of paper (2 views). Mechanics is the study of motion. So what is motion? Zeno of Elea -- Zeno's Paradoxes. Distribute syllabus.
Wednesday 1/11: To understand the underlying concepts we need to Simplify The Universe. "Speed Limit 70" -- what does it really mean? First Equation: Speed = Distance / Time. v = d/t . Development of Speed equation for Constant or Average Speed. delta-x = xf - xi , x = x0 + v t .
Thursday 1/12: English system of measurement. SI Metric System. Prefixes. What do we mean by Measurements? "Units will save your life." What is "1 m/s"? We need a few benchmark values to compare English and SI Metric quantities. NOTE: English-to-Metric conversions will NOT, with two exceptions, be tested on in this course. 1.00 m/s = slow walking speed. 10.0 m/s = World Class sprint speed (The 100 meter dash -- Usain Bolt is the current Olympic (9.683 seconds) and World (9.58 seconds) record holder. He also has the World Record in the 200 meter dash (19.19 seconds).) Q1 and your PID number. Quiz 1 was given in-class on Thursday 12 January 2012, for attendance purposes. If you missed class on that day, you will be able to get some of the points by downloading Quiz 1A from the website and turning it in. (Click here for a copy.)
Friday 1/13: What is "1 m/s"? We need a few benchmark values to compare English and SI Metric quantities. NOTE: English-to-Metric conversions will NOT, with two exceptions, be tested on in this course. 60 m.p.h. = 26.8 m/s. 1.00 m/s = slow walking speed. 10.0 m/s = World Class sprint speed (The 100 meter dash -- Usain Bolt is the current Olympic (9.683 seconds) and World (9.58 seconds) record holder.) 26.8 m/s = 60 m.p.h.. 344 m/s = Speed of sound at room temperature. 8000 m/s = low Earth orbital speed. 11,300 m/s = Earth escape velocity. 300,000,000 m/s = speed of light in vacuum (maximum possible speed). Speed. 60 m.p.h. = "A Mile A Minute". It's a nice alliterative phrase and wasn't possible for Man to move at 60 mph until 1848: The Antelope, but it really isn't a special speed, just an accident of the English system of measurement. Significant Figures -- Although our calculators typical work with 12 digits and display 10 digits, a 10 digit measurement would have 10 significant figures. Such a measurement has to cost at least a million dollars to make. A meter stick measured to 10 significant figures requires us to know where the last few atoms are on the ends! We'll talk more about this on Tuesday. Topic 1 assigned. (Updated Searchable booklist available online here .)
NOTE: Monday 16 January 2012 is Dr. Martin Luther King, Jr. Day and while WMU holds no classes, there are many MLK Day activities going on around campus.
Monday 1/16: MLK Day to Honor Dr. Martin Luther King, Jr. -- Classes Do Not Meet at WMU -- University-wide activities.
Tuesday 1/17: PTPBIP - Putting The Physics Back Into The Problem. Handout on (1) Prefixes for moving the decimal place for larger and smaller powers of ten in the SI metric system, (2) Scientific Notation, as in 1.23 × 1012 and using the"EE" key on your calculator, and (3) Dr. Phil's Simplified Significant Figures for multiplication, division and trig functions. (Click here if you need a copy.) A simplified trip to the store -- The S-Shaped Curve. Acceleration. Physics Misconceptions: Things you think you know, are sure you know, or just assume to be true in the back of your mind... but aren't true. Aristotle was sure that heavier objects always fell faster than lighter objects, but we did a demostration on Tuesday which showed that wasn't always true. Example: You're driving a car. To speed up, you need to put your foot on the accelerator (gas pedal), so YES, you are accelerating -- True. To drive at a constant speed, you must still have your foot on the accelerator, so YES, you are accelerating -- Not True because constant v means a = 0. To slow down, you must take your foot off the accelerator and put it on the brake pedal, so NO, you are not accelerating -- Not True because v is changing, so a < 0 (negative).Q2 Take-Home quiz on speed = distance / time, due on Thursday 19 January 2012, in class or by 5pm.
Wednesday 1/18: A simplified trip to the store -- The S-Shaped Curve. Acceleration. Just as the equation v = d / t is for constant or average speed, the equation a = delta-v / delta-t is for constant or average acceleration. Finding the set of Kinematic Equations for Constant Acceleration. The Equation Without Time -- Avoiding the Quadradic Formula. To aid in setting up problems with the kinematic equations, you might try to list all six kinematic variables (x0, x, v0, v, a and t) and give the values for those you know, those you don't know and those you want to find out. This will help you choose which kinematic equation(s) you'll need. Finishing The S-Shaped Curve: plotting x-vs-t gives straight line in Region II, but parabolic curves for Regions I and III.
Thursday 1/19: Problem: A rifle bullet is fired from rest to faster than the speed of sound, 415 m/s, in a distance of 1.00 m. Find a. Answer, a = 86,110 m/s². This is huge, which is why we don't fire people out of rifle barrels. Find t = 0.004819sec. Again, we could solve for t using two different equations, but will still get the same result because there is one Physics. To aid in setting up problems with the kinematic equations, you might try to list all six kinematic variables (x0, x, v0, v, a and t) and give the values for those you know, those you don't know and those you want to find out. This will help you choose which kinematic equation(s) you'll need. What do we mean by a = 1 meter/sec² ? You cannot accelerate at 1 m/s² for very long. Types of Motion: No Motion (v=0, a=0), Uniform Motion (v=constant, a=0), Constant Acceleration (a=constant). We generally cannot accelerate for very long. Free-Fall: If we ignore air resistance, all objects near the surface of the Earth fall towards the Earth at the same rate. a = g = 9.81 m/s². That's nearly ten times the acceleration a = 1 m/s² we just talked about. With these two known acceleratoins, we can now have something to compare our accelerations a. Q3 Take-Home quiz on the Kinematic Equations for Constant Acceleration, due on Tuesday 24 January 2012, in class or by 5pm.
Friday 1/20: Free-Fall: If we ignore air resistance, all objects near the surface of the Earth fall towards the Earth at the same rate. ay = -g ; g = 9.81 m/s². That's nearly ten times the acceleration a = 1 m/s² we talked about last week. Rewriting the Kinematic Equations for motion in the y-direction, pre-loading them for free-fall. Example: Falling off a ten-foot roof (3.00 meters). The consequences of Falling Down... ...and Falling Up. The Turning Point ( vy = 0, but ay = -g during whole flight). The illusion of "hanging up there in the air" at the turning point.
Monday 1/23: The P-O-R (Press-On-Regardless) road rally problem. "You can't average averages." Comments on Q2 -- solution already posted on class webpage. Note that part (c) is just like the P-O-R problem. Motion in Two-Dimensions: You may be able to break it down into two one-dimensional problems, connected by time, which you can already solve. Example: The guy with the fedora and the cigar. There are 6 variables from the first dimension (x0, x, v0x, vx, ax, t), but only 5 from the second (y0, y, v0y, vy, ay), because time is the same. Remarkably, with a couple of reasonable assumptions, there are only 3 unknown variables (v0x, t, vy). Time links the two one-dimensional problems together. We need to find v0x , but we don't know the time. So we can find the time it takes to fall from the top of the building in the y-problem, then use that in the x-problem.
Tuesday 1/24: Demo: These class webpages online. How much acceleration can a human take? See story of Scott Crossfield below. Two kinds of numbers: Scalars (magnitude and units) and Vectors (magnitude, units and direction). Adding and subtracting vectors: Graphical method. Q4 Take-Home quiz on Falling Up and Falling Down, due on Thursday 26 January 2012, in class or by 5pm.
Wednesday 1/25: Two kinds of numbers: Scalars (magnitude and units) and Vectors (magnitude, units and direction). Adding and subtracting vectors: Graphical method. To generate an analytical method, we first need to look at some Trigonometry. Right Triangles: Sum of the interior angles of any triangle is 180°, Pythagorean Theorem (a² + b² = c²). Standard Angle (start at positive x-axis and go counterclockwise). Standard Form: 5.00m @ 30°. Practical Trigonometry. SOHCAHTOA. Adding and subtracting vectors: Analytical method. (Check to make sure your calculator is set for Degrees mode. Try cos 45° = sin 45° = 0.7071) Why arctangent is a stupid function on your calculator.
Thursday 1/26: Standard Form: Vector-A = 5.00m @ 30°, Vector-B = 7.00m @ 120°. Adding and subtracting vectors: Analytical method. (Check to make sure your calculator is set for Degrees mode. Try cos 45° = sin 45° = 0.7071) Why arctangent is a stupid function on your calculator. Examples: vector C = vector A + vector B, vector D = vector A - vector B. Use you sketche to check your work.
Friday 1/27: Ballistic or Projectile Motion 2-D problem where ax = 0 and ay = -g. Covers anything shot, thrown or kicked into the air which is unpowered and where we can ignore air resistance. Ancient cannons. Two Dangerous Equations. You can only use the Range Equation if the Launch Height = Landing Height. But the sin (2*theta) term in the Range Equation means that (1) 45° gives the maximum range for a given initial velocity and (2) that all other angles have a complementary angle (90° - theta) that gives the same range (but a different time and height). High and low trajectories for Range Equation. Sample Exam 1: First Set here (includes pp. 5-6, handed out in class). Quiz 5 is a Take-Home quiz on Vectors, handed out on Friday 27 January 2012 , and due on Tuesday 24 January 2012, in class or by 5pm.
Monday 1/30: Ballistic / Projectile Motion: You can only use the Range Equation if the landing height is the same at the launch height. If it is not, you can still break the problem into two pieces and find the t and height h at the turning point, then solve for the time from rest in the y-direction down to the landing point, no matter whether it is above or below the launch height. Classic Simple Pursuit (Cop and the Speeder). Starting from rest, the contant accelerating cop ends up with a final speed twice that of the uniform motion speeder -- because they both have to have the same average speed (same place, same time). There are two times when they are in the same place and the same time -- the other solution is at t=0.
Tuesday 1/31: Types of Motion: No Motion (v=0, a=0), Uniform Motion (v=constant, a=0), Constant Acceleration (a=constant). Uniform Circular Motion (UCM): speed is constant, but vector velocity is not; magnitude of the acceleration is constant, but the vector acceleration is not. Velocity is tangent to circle, Centripetal Acceleration is perpendicular to velocity and points radial INWARD. ac = v²/r. You can generate very large centripetal acclerations very quickly. Example: A hard disk drive spinning at 3600 rpm (60 times a second, time for one revolution = 1/60th of a second). Q6 Take-Home quiz on Projectile Motion, due on Thursday 2 February 2012, in class or by 5pm.
Wednesday 2/1: Using Vector Addition for Velocities: Upstream, downstream (rivers), Headwind, tailwind, crosswind (airplanes). Uniform Circular Motion (UCM): speed is constant, but vector velocity is not; magnitude of the acceleration is constant, but the vector acceleration is not. Velocity is tangent to circle, Centripetal Acceleration is perpendicular to velocity and points radial INWARD. ac = v²/r. Space Shuttle in Low-Earth Orbit. (There's still gravity up there!)
Thursday 2/2: Demo: Rodney Reindeer and U.C.M. The moment the centripetal acceleration is zero, Rodney travels ballistically with an initial velocity that is the last tangential velocity. The guard around a circular saw blade takes the sawdust and broken bits which shoot out tangentially from the blade and redirects them to a bucket -- improves safety and makes less of a mess. Recap: Our studies so far have described "How" things move, and allow to say "When" and "Where" things move, but not "Why" things move. For that we have to start talking about Forces -- and that means Newton. Some stories about Sir Isaac Newton. (Falling apple and Mars.) Review for X1. Return Q3.
Friday 2/3: Exam 1.
Monday 2/6: Recap: Our studies so far have described "How" things move, and allow to say "When" and "Where" things move, but not "Why" things move. For that we have to start talking about Forces -- and that means Newton. Some stories about Sir Isaac Newton. (Reeding on the edge of the silver shilling or a U.S. dime/quarter, "mad as a hatter" from mercury poisoning.) Newton's Three Laws of Motion: Zeroeth Law - There is such a thing as mass. First Law - An object in motion tends to stay in motion, or an object at rest tends to stay at rest, unless acted upon by a net external force. Second Law - F=ma. Third Law - For every action, there is an equal and opposite reaction, acting on the other body. (Forces come in pairs, not apples.)
Tuesday 2/7: Newton's Three Laws of Motion. SI unit of mass = kilogram (kg). SI unit of force = Newton (N). English unit of force = pound (lb.). English unit of mass = slug (Divide pounds by 32. For English units, g = 32 ft/sec².). Force is a vector. Free Body Diagrams. Normal Force (Normal = Perpendicular to plane of contact). The normal force does NOT automatically point up and it is not automatically equal to the weight -- we have to solve for the normal force. "The Normal Force is NOT automatically present -- you have to be in contact with a surface. The Normal Force does NOT automatically point up -- FN is perpendicular to the surface. The Normal Force is NOT automatically equal to the weight. FN = mg only if there are no other forces in the y-direction." Sum of forces in x or y equations -- either will be equal to 0 (Newton's 1st Law) or ma (Newton's 2nd Law). Example of 125 kg crate being dragged/pushed around. (Near the surface of the Earth, you can use the relationship that 1 kg of mass corresponds [not "equals"] to 2.2 lbs. of weight. So multiple 125 by 2 and add 10%... 250 + 25 = 275... so a 125 kg crate has a weight of mg = 1226 N or 275 lbs.). Variations as we allow for an applied force that it at an angle. Push down and Normal Force increases. Q7 Take-Home, due on Thursday 9 February 2012, in class or by 5pm.
Wednesday 2/8: Example of 125 kg crate being dragged/pushed around. (Near the surface of the Earth, you can use the relationship that 1 kg of mass corresponds [not "equals"] to 2.2 lbs. of weight. So multiple 125 by 2 and add 10%... 250 + 25 = 275... so a 125 kg crate has a weight of mg = 1226 N or 275 lbs.). Variations as we allow for an applied force that it at an angle. Push down and Normal Force increases; pull up and Normal Force decreases -- though it cannot go negative. "You can't push on a rope." Since the force from a wire/string/rope/chain/thread/etc. can only be in one direction, Dr. Phil prefers to call such forces T for Tensions rather than F for Forces. Simple pulleys (Massless, frictionless, dimensionless, only redirect the forces). "There is no free lunch." The bracket for the pulley will have to support a force greater than the weight of the hanging object. Mechanical advantage: multiple pulleys allow us to distribute the net force across multiple cables or the same cable loop around multiple times. Tension in the cable is reduced, but you have to pull more cable to move the crate. Hanging a sign with angled wires -- still the same procedure: Sketch of the problem, Free Body Diagram, Sum of Forces equations in the x- and y-directions, solve for unknowns.
Thursday 2/9: Hanging a sign with angled wires -- still the same procedure: Sketch of the problem, Free Body Diagram, Sum of Forces equations in the x- and y-directions, solve for unknowns. For the problem in class, we had a sign with m = 15.0 kg and two tension forces, T1-vector = 107.7 N @ 150° and T2-vector = 131.9 N @ 45°. You can check to make sure these forces cancel in the x-direction and support the weight of the sign in the y-direction. Discussion of "two pound test fishing line", stretching and breaking of cables, Safety Factors. Inclined plane problems: Change the co-ordinate system, change the rules. In the tilted x'-y' coordinates, this is a one-dimensional problem, not two-dimensional. Q8 Take-Home quiz on Force and Acceleration, due on Tuesday 14 February 2012, in class or by 5pm.
Friday 2/10: X1 returned. Atwood's Machine -- two masses connected by a single cable via a simple pulley. They share a common acceleration, a, with one mass going up and the other going down. Elevator Problems. The Normal Force represents the "apparent weight" of the person in the elevator. For the elevator at rest or moving at constant speed, the Normal Force = weight, and the tension of the cable = weight of loaded elevator. But if there is an acceleration vector pointing up, the apparent weight and the tension of the cable increase; if the vector points down, the apparent weight and the cable tension decrease. In true Free Fall, without any air resistance, the Normal Force = 0 and you are floating.
Monday 2/13: Two kinds of Friction: Static (stationary) and Kinetic (sliding). For any given contact surface, there are two coefficients of friction, µ, one for static (µs) and one for kinetic (µk). Static is always greater than kinetic. Rubber on concrete. Tires rolling with friction on good roads -- this is static friction not kinetic friction because the tires aren't sliding on the pavement. If velocity vector and acceleration vector point in the same direction, then the speed is increasing. If they are in the opposite direction, then the speed is decreasing. In either case, for a car the force involved must be in the same direction as the acceleration vector -- this seems to be confusing whereby the static friction force on the tires from the road points forward when you are speeding up. The conflict arises because you might be thinking "friction opposes motion" and not thinking about the motion of the tires versus the motion of the car. If object is at rest, need to "test" to see if an applied external force exceeds the maximum static friction force ("breaks the static friction barrier"). Anti-Lock Brakes and Traction Control. ABS works by monitoring the rotation of all four wheels. If one wheel begins to "lose it" and slip on the road while braking, it will slow its rotation faster than the other tires, so the computer releases the brake on that wheel only until it is rolling without slipping again. This can be done many times a second, much faster than the good old "pump your brakes to stop on ice" trick older drivers are familiar with. Traction control uses the ABS sensors to monitor the wheel slip during acceleration -- keeps the wheels from spinning.
Tuesday 2/14: Friction Examples using our 125 kg crate sliding on the floor. If object is at rest, need to "test" to see if an applied external force exceeds the maximum static friction force ("breaks the static friction barrier") and we switch to kinetic friction, or if static friction "wins" then we remain at rest. Static Friction can vary from zero to its max value in either direction. Kinetic Friction has only the one value. If you push with a force equally the kinetic friction, you will move at a constant speed. Otherwise you will either a positive or negative acceleration. Finding the coefficient of static friction by tilting: µs = tan(thetamax). Similar for kinetic friction, except one has to tap the board to "break the static friction barrier". Rubber on concrete. Can µ be greater than 1? Means thetamax greater than 45° -- rare, but yes. Q9 Take-Home quiz on Tensions and Friction, due on Thursday 16 February 2012 (?), in class or by 5pm.
Wednesday 2/15: We are not done with Forces, but some problems cannot easily be solved by using forces. Collisions, for example, are very complex if we have to put in all the forces of bending and breaking and mashing things. Need a simpler way of looking at the problem. "Inertia" is a word which isn't used much today, but it is the same as "momentum" -- represents some kind of relentless quality of movement. It takes a force to change the momentum, otherwise it just continues on, i.e., Newton's 1st Law. Linear Momentum ( p = mv ) is a vector quantity. Newton's form of the 2nd Law: F = delta-p / delta-t = change in momentum / change in time instead of F=ma, but really the same thing. Two extremes in collisions: Totally Elastic Collision (perfect rebound, no damage) and Totally Inelastic Collision (stick together, take damage). Linear momentum is conserved in all types of collisions . Totally Inelastic Collisions. Example: The Yugo and the Cement Truck with numbers. Real Head-On collisions. Three example collisions: (1) Head-on Collisions. (2) Rear-end Collisions. (Also... The Non-Collision -- if the car following is going slower, it isn't going to run into the car ahead. PTPBIP.) (3) ...
Thursday 2/16: Three example collisions: Head-on Collisions. Rear-end Collisions. (The Non-Collision -- if the car following is going slower, it isn't going to run into the car ahead. PTPBIP.) 2-D Side Impact (vector) collision. Real crashes. Interactions of safety systems: Seat belts, shoulder belts, steel beams in doors and crumple zones. The myth of it being better to be "thrown clear from the wreck". What happens in a wreck. How airbags work. Note: We do NOT want our cars to have Totally Elastic Collisions -- the whiplash on our fragile bodies would be awful. Instead, our cars are designed to crumple and "die" for us.
Friday 2/17: What's the opposite of a collision? An explosion. Or recoil. Example: A clown on roller skates at rest -- when he hurls a pie to the left, he goes to the right. Total momentum of the system remains constant (in this case, zero). We've talked about How things move (Kinematic Equations) and Why things move (Forces, momentum). Now we want to talk about the Effort to make things move. Work: A Physics Definition (Work = Force times distance in the same direction). Work = Energy. Kinetic Energy -- an energy of motion, always positive, scalar, no direction information. Work-Energy Theorem (net Work = Change in K.E.). Using the Work-Energy Theorem to find a final speed. Q10 Take-Home quiz on Total Inelastic Collisions, due on Tuesday 21 February 2012, in class or by 5pm.
Monday 2/20: Work: A Physics Definition (Work = Force times distance in the same direction). Work = Energy. Power = Work / time. Kinetic Energy -- an energy of motion, always positive, scalar, no direction information. Work-Energy Theorem (net Work = Change in K.E.). Using the Work-Energy Theorem to find a final speed. Potential Energy: Storing energy from applied work for later. Gravitational P.E. = mgh. Location of h=0 is arbitrary choice. Conservation Laws are very important in Physics. Conservation of Total Mechanical Energy (T.M.E. = K.E. + P.E.). Lose angle and directional information because energy is a scalar, not a vector. We can change height for speed and vice versa. Conservation of T.M.E. (P.E. + K.E.) on a roller coaster. Total energy limits maximum height. If speed at top of the first hill is about zero, then this P.E. is all we have. Cannot get higher, but we can change height for speed. The Loop-the-Loop on the roller coaster requires that there be sufficient speed v (or K.E.) such that we meet the conditions of Uniform Circular Motion at the top. The minimum speed occurs when the downward pointing normal force from the track on the upsidedown cars goes to zero, and the centripetal force, Fc = mac = mv²/r , comes only from the weight, w = mg. Remember, that the centripetal force is a NET force, i.e., F = ma is Newton's 2nd Law, so the net external force goes on the right side of the sum of forces equations.
Tuesday 2/21: Example: Rollercoaster with h1 = 45.0 m, v1 = 0, h2 = 0, h3 = 12.0 m, h4 = 0 (bottom of loop-the-loop), h5 = 12.0 m (top of loop-the-loop, making D = 12.0 m and r = D/2 = 6.00 m). Results: v2 = 29.xx m/s, v3 = 25.44 m/s. v5 = v3 is well above the minimum speed to safely do the loop-the-loop. Exchanging height for speed with conservation of T.M.E. -- because energy is a scalar, we lose all directional information, so the path taken between points 1 and 2, and the initial/final directions do not matter. Work = Energy. Power = Work / time. Power is rate that work can be done. 1 horsepower = 1 h.p. = the amount of work that one man, one horse and one plow can do in a day. An engine with "more power" can either do the same work in less time, or do more work. Q11 Take-Home quiz on Conservation of Energy, due on Thursday 23 February 2012, in class or by 5pm.
Wednesday 2/22: Return Q2/4/5/6/7. The Ballistic Pendulum -- Old School Physics, in the days before all our modern electronics: We can find the speed of a projectile through an Inelastic Collision into a block of wood, followed by Conservation of TME, as the block+projectile swings up and comes to a stop. Newton's Universal Law of Gravity (or Newton's Law of Universal Gravity). Use Universal Gravity to check "g". The value we calculate is close, 9.83m/s², which turns out to be only off by 0.2%. Why is it off? Because using Univeral Gravity in this manner makes the assumption that the entire Earth is uniform and homogenous from the surface to the core -- which it is not. We would need calculus to integrate over layers to get the observed value of 9.81m/s². UCM Revisited. The Shuttle in Low Earth Orbit (Revisited). Calculating g(r) for r = 6,770,000 m (the radius of the Earth plus the height of 400 km for Low Earth Orbit), we get a value somewhat different than we found for the centripetal acceleration.
Thursday 2/23: Four Fundamental Forces in Nature: Gravity, E & M, Weak Nuclear Force, Strong Nuclear Force. Surprisingly, gravity is the weakest of these, but it holds the universe together because things like planets, stars and galaxies have so much mass. The Shuttle in Low Earth Orbit (Revisited). Calculating g(r) for r = 6,770,000 m (the radius of the Earth plus the height of 400 km for Low Earth Orbit), we get a value somewhat different than we found for the centripetal acceleration. Working backwards, we discover for this radius that the period T = 5542 sec and NOT the estimated 5400 sec (90 minutes) we had started with before. Each radius of circular orbit has a different value of g(r). As r increases, v decreases and T increases. Orbital mechanics: Speed up and radius decreases, slow down and radius increases. For the Moon, the period is around 28 days at a quarter of a million miles away. Geosynchronous orbits occur when T = 1 day exactly, and for geosynchronous communications sattelites, the orbit must be directly over the equator -- hence all sattelite dishes in the U.S. face south. Newton's Law of Universal Gravity and Tides (high/low, spring/neap). Q12 is a Take-Home quiz on Newton's Law of Universal Gravity, and due on Monday 27 February 2012, in class or by 5pm.
Friday 2/24: Dr. Phil has canceled today's classes due to weather / illness. Updates later today. NOTE: Exam 2 has been moved to TUESDAY 28 February 2012.
Monday 2/27: Review for X2. We've asked: How do things move? (kinematics) Why do things move? (forces) What effort does it take to move? (work and energy) Now we ask -- What moves? Three Classical States of Matter: Solid, Liquid, Gas. Combinations: Condensed Matter (covers both Solids and Liquids) and Fluids (covers both Liquids and Gasses). Two Extreme States of Matter: Plasma (electrons stripped off, high temperature), Cryogenics (extreme cold, odd behavior).
Tuesday 2/28: Exam 2.
Wednesday 2/29: Extended Objects: Mass occupies a volume and shape. Mass-to-Volume Ratio (Density). NOTE: Do not confuse the Density of the Materials with the Mass-to-Volume Ratio of the OBJECT. Density of Water built into the SI metric system (1 gram/cm³ = 1000 kg/m³). Floating on the Surface: Mass-to-Volume Ratio of the boat < Mass-to-Volume Ratio of the Liquid. Why Boats Float. Example: Front lab table as a 250 kg boat with 4.00 m³ volume. Buoyant Force = Weight of the Boat = Weight of the Water Displaced by the Submerged Part of the Boat. Calulating the amount of the boat submerged, by using the fact that the mass of the boat and the displaced water are the same.
Q13 In-Class. Example: Front lab table
as a 250 kg boat with 4.00 m³ volume. Buoyant Force = Weight of the Boat =
Weight of the Water Displaced by the Submerged Part of the Boat. Calulating the
amount of the boat submerged, by using the fact that the mass of the boat and
the displaced water are the same. Water is unusual in that the
mass-to-volume ratio of ice (solid) is LESS than liquid water, so ice floats.
Ice which floats doesn't add to volume of water when it melts, but grounded ice
(non-floating) does. This is one of the reasons why people worry about what
global warming might do to the great ice sheets around the world. Sinking
of the RMS Titanic; Edmund Fitzgerald. Archimedes and Eureka! (I found
it!) Pressure = Force / Area. SI unit: Pascal
(Pa). Example: Squeezing a thumbtack between thumb and forefinger. 1 Pa = 1
N/m², but Pascals are very small, so we get a lot of them. One Atmosphere
standard air pressure = 1 atm. = 14.7 psi = 101,300 Pa. Pressure at a depth due
to supporting the column of liquid above. Absolute (total) Pressure vs. Gauge
Pressure (difference between two readings). Pressure due to a column of water =
1 atm. at h = 10.33m = 33.86 feet. The perils of SCUBA diving.
Friday 3/2: WMU SPIRIT DAY -- No Classes.
SPRING BREAK -- NO CLASSES.
Monday 3/12: Reset. One Atmosphere standard air pressure = 1 atm. = 14.7 psi = 101,300 Pa. Pressure at a depth due to supporting the column of liquid above. Absolute (total) Pressure vs. Gauge Pressure (difference between two readings). Pressure due to a column of water = 1 atm. at h = 10.33m = 33.86 feet. Absolute (total) Pressure vs. Gauge Pressure (difference between two readings). Using a column of liquid to make a barometer to measure air pressure. Switch from water to mercury changes h at 1 atm. from 10.33 m to 0.759m. The aneroid barometer. How to get liquid out of a cup using a straw -- or why Physics does not "suck", but pushes using a pressure difference.
Tuesday 3/13: Water is unusual in two ways: (1) Water is relatively incompressible. If the depth h isn't too deep, then the Mass-to-Volume ratio for water is constant. For great depths, such as the bottom of the oceans, we can't use our simple equation because rho is not constant. Air and gasses are compressible, so we can't use our pressure from a column of fluid equation either, though the air pressure here on the surface of the Earth is based on supporting the weight of the column of air above us. (2) The mass-to-volume ratio of ice (solid) is LESS than liquid water, so ice floats. Ice which floats doesn't add to volume of water when it melts, but grounded ice (non-floating) does. This is one of the reasons why people worry about what global warming might do to the great ice sheets around the world. Smooth Fluid Flow: Pressure from a column of liquid looks like P.E. Create a Kinetic Pressure term which looks like K.E. and add in the base pressure for total pressure to create Bernoulli's Equation and the Continuity Equation. Water Tower and the Faucet Problem. Why the water tower needs a vent. Q13 Take-Home quiz on Pressure and Bernoulli's Equation, due on Thursday 15 March 2012, in class or by 5pm.
Wednesday 3/14: (Happy Pi Day! 3.14...) Bernoulli's Equation and the Continuity Equation. Want Smooth Continuous Flow, not Turbulent Flow or Viscous Flow. Flow rate = Volume / time = Cross-sectional Area × Speed. The faster the fluid flow, the lower the Pressure. Example: The aspirator -- a vacuum pump with no moving parts. Example: Air flow around a wing. (Faster air over top means lower pressure on top, so net force is up -- Lift.) Spoilers -- doors open in wing to allow air to pass between upper and lower surfaces, thus "spoiling the lift" by eliminating the pressure difference. Why the Mackinac Bridge has grates on the inside north- and soundbound lanes. Air Resistance. Low speed and high speed air resistance. If allowed to drop from rest, then a real object may not free fall continuously, but may reach a Terminal Velocity (Force of gravity down canceled by Drag force up) and doesn't accelerate any more. Ping-pong balls versus turkeys (or pennies).
Thursday 3/15: Air Resistance: Low speed and high speed air resistance. If allowed to drop from rest, then a real object may not free fall continuously, but may reach a Terminal Velocity (Force of gravity down canceled by Drag force up) and doesn't accelerate any more. Ping-pong balls in free-fall, vs. being hit with a paddle in a world-class table tennis match. What is the terminal velocity of a falling person? It depnds on clothing and orientation -- aerodynamics, streamlining, cross-sectional area, composition of the air are all part of the drag coefficients b and c. World's Record Free-Fall. Why the steel bands wrapped around an old fashioned water tower or a farm silo are closer together at the bottom than at the top. A farm silo holds grain, which like sand, etc., is made up of solids but in small particles. Such flowable solids or fluidized solids can act like fluids and be piped around.
Friday 3/16: Return X2. Temperature & Heat. Heat = Energy. Two objects in thermal contact, exchange heat energy, Q. If net heat exchange is zero, the two objects are at the same temperature. Temperature Scales: °F, °C and K (Kelvins). Q14 Take-Home on Air Resistance and Drag, due on Tuesday 20 March 2012, in class or by 5pm.
Monday 3/19: Linear Expansion: Most objects expand when heated, shrink when cooled. Length Expansion. Example: One 39 ft. (12.0m) steel rail expands 5.88 mm from winter to summer, but that's 0.75 meters for every mile of railroad track. Expansion joints. Bridge expansion joints. Pavement expansion joints. I-57 in Chicago and the expanding asphault in 1983.
Tuesday 3/20: Linear Expansion: Why "Bridge Freezes Before Roadway" signs. Question: Does the material expand into a hole when heated, or does the hole expand? (Think about what happens to the disk removed from the hole -- does it expand or contract when heated?) Volume Expansion of Solids and Liquids. Coefficient of Volume Expansion usually given for liquids; for solids, beta = 3 × alpha. Ideal Gas Law (PV/T = constant or our form: P1V1/T1 = P2V2/T2) -- must use Kelvins for temp and absolute Pressures, because neither P or T can be zero or negative. Q15 Take-Home on Linear and Volume Expansion, due on Thursday 22 March 2012, in class or by 5pm.
Wednesday 3/21: Heat Energy (Q) and Temperature Change & Phase Change. Add/remove Heat Energy Q will raise/lower the temperature of a material using the Specific Heat (J/kg·°C) for objects of mass m, or the Heat Capacity (J/mole·K) for objects with n moles of atoms or molecules. Add/remove Heat Energy Q will change its phase between solid-liquid-gas using the Latent Heat of Fusion, Lf, between solids and liquids, or the Latent Heat of Vaporization Lv, between liquids and gasses. Example: Take a 1.00 kg block of ice from the freezer (T = -20°C, about 0°F) and heat it in a pan until it is all boiled away. (1) Heat ice from -20°C to ice at 0°C; (2) melt ice to water at 0°C; (3) heat water from 0°C to 100°C, (4) boil water into steam at 100°C. Using Power = Work/time, we can apply heat at the rate of 1000 W = 1000 J/sec, and estimate how long each of these steps take. Ice has a low specific heat, 2000 J/kg·°C-1, so ice very quickly warms up to the melting point. The latent heat of fusion for melting ice / freezing water is 336,000 J/kg. Wet ice is at T = 32°F = 0°C = 273K. The specific heat of water is 4186 J/kg·°C-1 = 1 Calorie (1 "Big C" Calorie = 1 Food Calorie). This is the energy it takes to raise the temperature of 1 kg of water by 1°C. (In the English system, we have the British Thermal Unit, where 1 BTU is the energy it takes to raise the temperature of 1 pound of water by 1°F. You see BTU ratings on air conditioners and furnaces, for example.) "A watched pot never boils". Water will boil in a pan for a long time. Indeed, the latent heat of vaporization of water, 2,260,000 J/kg is huge and important for cooking and putting out many fires. Water doesn't drown the fire, it removes heat from the fire, lowering its temperature eventually below the ignition point. Can't use water on all fires. Class D (magnesium) fires, electrical fires. Halon gas fire supression systems protect computer hardware in a big data center, but displace the breathable air -- get out when alarm sounds!
Thursday 3/22: Heat content versus Thermal conductivity. Leidenfrost Effect. Thermodyanmics (Heat + Motion) -- Moving heat energy Q around. The Laws of Thermodynamics. Zeroeth Law -- There is such a thing as temperature. First Law -- Conservation of energy. Second Law -- One cannot extract useful work from a cyclic mechanical system without wasting some energy. Entropy examples -- It takes work to clean or restore things. Left to themselves, everything falls apart. Heat Energy (Q). The Heat Engine and Three Efficiencies (Actual, Carnot and 2nd Law).
Friday 3/23: The Heat Engine and Three Efficiencies (Actual, Carnot and 2nd Law). Fuel Economy (miles per gallon) is not an Efficiency. There is no conspiracy to keep big 100 m.p.g. cars out of our hands. To use less fuel, do less work. Q16 Take-Home quiz on the Heat Engine, due on Tuesday 27 March 2012, in class or by 5pm.
Monday 3/26: Reverse the arrows in the Heat Engine and you get a Refrigerator. NOTE: Cannot place an open refrigerator or a window air conditioner in the middle of a room and cool the room, because the exhaust heat to the hot side includes the heat pulled from the cold side plus the work done on the compressor. Waves: Single Pulse vs. Repeating Waves. The motion of the material vs. the apparent motion of the wave. For Repeating Waves, we have a Repeat Length (wavelength) and a Repeat Time (Period). Frequency = 1/Period. Wave speed = frequency x wavelength. The speed of sound in air: 334 m/s @ 0°C and 344 m/s @ 20°C. Waves and Resonance. Standing Waves on a string. Fundamental, First Overtone, Second Overtone, etc.
Tuesday 3/27: [TODAY ONLY -- Meet in 1110 Rood at 1pm.] Waves: Single Pulse vs. Repeating Waves. The motion of the material vs. the apparent motion of the wave. For Repeating Waves, we have a Repeat Length (wavelength) and a Repeat Time (Period). Frequency = 1/Period. Wave speed = frequency x wavelength. Demonstration: the Slinky shows both longintudinal (string type) and transverse waves (sound type). Waves and Resonance continued. Standing Waves on a string. Fundamental, First Overtone, Second Overtone, etc. Demonstration: First and higher overtones on a string driven by a saber saw. (Can't see the Fundamental on the saber saw demo, because the tension required usually breaks the string.) Standing Waves in a tube. Demo: Getting Fundamental and overtones from twirling a plastic tube open at both ends. Demo: Variable length organ pipe -- Fundamental and First Overtone (overblowing), varying pitch (musical note) by changing length of tube open at only one end. Tuning forks, resonance boxes. Demo: Tuning forks require both tines to work -- the "sound of a tuning fork with one tine" is that of silence. Musical instruments: Accoustic string instruments have a resonance box. Brass instruments start from the "natural trumpet", which can only play the fundamental and overtones for the pipe. Woodwind instruments get more complicated. Beat frequencies occur when two sounds have almost the same frequency -- get a distinctive wah-wah-wah sound, whose beat frequency = | f1 - f2 | .
Wednesday 3/28: Waves and Resonance continued. Standing Waves on a string. Fundamental, First Overtone, Second Overtone, etc. Standing Waves in a tube. Beat frequencies occur when two sounds have almost the same frequency -- get a distinctive wah-wah-wah sound, whose beat frequency = | f1 - f2 | . Takes time for sound to travel over a distance. Constructive and Destructive Interference. Acoustics of concert halls. The range of "normal" human hearing: 20Hz-20,000Hz (10 octaves). Artilleryman's ear -- mid-range hearing loss. Topic 2 Worksheets (Click here for 1st Worksheet and Directions). Q17 is a Take-Home quiz on Standing Waves, due on Thursday 29 March 2012, in class or by 5pm. Note the short due date so I can post the solution after 5pm for your studying purposes.
Thursday 3/29: Review for X3. The speed of sound in air. Sonic Booms and other shockwaves. Bullwhip stories. Waves take time to travel. Sound takes time to travel. An echo takes times to get to the reflecting surface and travel back -- to and fro. The reflected wave can arrive in phase and constructively interfere, or out of phase and destructively interfere, based on the distance traveled divided by the wavelength. Also, there are some Sample Exam 3 problems which involve ratios -- finding V2/V1 from the Ideal Gas Law, so that you find how many times larger (or smaller) V2 is than V1, rather than giving you a specific value for V1. Or finding the ratio of the speeds v2/v1 from the Continuity Equation or even Bernoulli's.
Friday 3/30: Exam 3.
Monday 4/2: The Realization that Electricity and Magnetism were part of the
same Electromagnetic Force was a great triumph of 19th century physics. Greeks
knew about static electricity -- build up charge and get sparks.
Static electricity. The Two-Fluid Model of Static Electricity (A &
B), to account for the two types of behavior noted. Franklin's One-Fluid Model
of Electricity. Occam's Razor: If you can't decide between two competing ideas
for how Nature works, take the simpler model. Four Fundamental Forces in
Nature: Gravity, E & M, Weak Nuclear Force, Strong Nuclear Force.
The Hydrogen Atom. Real Electric
Charges. Two charges: like charges repel, unlike (opposite) charges
attract. Coulomb's Law looks like
Newton's Law of Universal Gravity.
Tuesday 4/3: Real Electric Charges. Two charges: like charges repel, unlike (opposite) charges attract. Coulomb's Law looks like Newton's Law of Universal Gravity. 1 Coulomb of charge is an enormous amount of charge. Two 1.00 C charges separated by 1.00 meters have a force of nine-billion Newtons acting on each other. A Nickel coin has a mass of 5 grams, so about 1/10th of a mole. Find number of Coulombs of positive and negative charges. It's over 200,000 C! But... at the atomic level, each nickel atom has the same number of electrons and protons, so overall each atom and the whole nickel coin is charge neutral -- so not dangerous. Four Fundamental Forces in Nature: Gravity, E & M, Weak Nuclear Force, Strong Nuclear Force. The Hydrogen Atom. Gravity loses to Electric Force by a factor of 200 million dectillion (!!!). Likewise, the two protons in the nucleus of the Helium Atom require the Strong Nuclear Force to overcome the 231 N electric repulsion. Isotopes are the same element (proton number Z), but with different numbers of neutrons (N). Some isotopes are stable, some are unstable and undergo radioactive decay. If we didn't have the Strong Nuclear Force making the Electric Force irrelevent inside the nucleus, then the only element in the universe would be hydrogen.
Wednesday 4/4: Discussion of Topic 1 Book Report. How does q1 know that q2 is there? -- "Action at a Distance" -- Gravity and the Electric Force are not contact forces. The mathematical construct of the Electric Field. E is not an observable quantity. (Side example: Methods of measuring speed v, do not directly measure speed v.) Electric Fields, E = k q / r² (E-field from one point charge) and FE = q E (Electric Force = charge times E-field the charge is emersed in). Maximum E-field in air, E-max. Electric Potential (Voltage). Spark gaps. Voltage can be measured, then used to find strength of E-field. SI units: E-field is (N/C) or (V/m) - both work. Charges tend to accumulate on long pointy things, which explains why church steeples get hit by lightning. Or why it's your fingertips which can get shocked when reaching for the light switch after walking on carpet in the wintertme.
Thursday 4/5: Charges tend to accumulate on long pointy things, which explains why church steeples get hit by lightning. Or golfers and trees on golf courses. Conductors (metals) versus non-conductors (insulators). Semi-Conductors sit in the middle. Sometimes they conduct and sometimes they don't. This means they act like a switch or valve, and this is the basis for the entire electronics semi-conductor industry. D.C. Electrical circuits. Ohm's Law. V=IR form. (Ohm's "3 Laws"). The Simplest Circuit: Battery, wires, load (resistor). Q18 In-Class quiz on Real Electric Charges and Coulomb's Law. (Solution already posted.) Q19 Take-Home quiz on Series and Parallel Resistors, due on Tuesday 10 April 2012, in class or by 5pm. NOTE: We handed it out on Thursday, but haven't covered all the material on this yet in class.
Friday 4/6: D.C. and A.C. circuits. Ohm's Law. V=IR form. (Ohm's "3 Laws"). The Simplest Circuit: Battery, wires, load (resistor). Power dissipated by Joule heating in a resistor. P = I V (3 forms of Power equation to with Ohm's "3 Laws"). The Simplest Circuit: Battery, wires, load (resistor). Series and Parallel Resistors. Reminder of Significant Figures again. Two devices connected together in a circuit can only be connected two ways: series or parallel. In Series, same current, share voltage. Equivalent resistance is always larger. In Parallel, same voltage, share current. Equivalent resistance is always smaller. Resistor Network Reduction. The battery only "sees" an equivalent resistor, which controls its current. So we could (but won't) reduce a resistor network to a single equivalent resistance, go back and fill in the table for V = I R and then P = I V. In the example sketched in class, Resistor R1 sees the largest current and dissipates the largest amount of energy per second (Power in Watts). This means it is also the most vulnerable. Story of radio "repair" call from 4,000,000,000 miles.
Reminder that ICES Student Course Evaluations are available now online via GoWMU .
Monday 4/9: "Magnetism is just like Electricity, only different." Real Magnets are dipoles (North and South ends, linked). Break a magnet in half, and you either get two new magnets -- or nothing. So far, there is no evidence that there are Magnetic Monopoles (magnetic charges: isolated North or South poles). Rules similar to Electric Charges: Unlike poles attract, like poles repel. Dropping a permanent magnet can result in a reduction of its magnetic field (B-field) as the shock allows some iron atoms to flip 180° and therefore cancel instead of add to an adjacent iron atom's magnetic field. The horizontal compass needle rotates until its North end points North (or rather to the North Magnetic Pole, which is of course a South pole of the Earth's magnetic core); the vertical compass rotates so that it lines up with the B-field along the surface of the Earth at the point. At the Equator, the vertical magnetic should be parallel to the ground, at the magnetic poles, it should be perpendicular to the ground. Is the Earth's magnetic field going to flip some day? And what about Mars? SI Units for B-field: (1 Tesla = 1 T). "Other" unit for B-field: ( 1 Gauss = 1 G ; 1 T = 10,000 G ). Earth's B-field is about 1 Gauss at the Earth's surface. Example of the 4T NMR magnet at Michigan Tech and the 10-foot radius line on the floor and erasing ATM cards within that circle. The Great 19th Century Debate: Is Light a Particle or a Wave? (Wave-Particle Duality did not seem obvious at the time.)
Tuesday 4/10: The Electromagnetic Wave travels at the speed of light. c = 300,000,000 m/s = 186,000 miles/sec. Electromagnetic Spectrum: Visible light (ROYGBIV=red orange yellow green blue indigo violet). Visible light is 400nm to 750nm (4000 angstroms to 7500 angstroms). Cannot "see" atoms with visable light, because the atom is about 1 angstrom across (1.00E-10 meters). The visible light wave is too large to see something that small. Frequences LOWER and wavelengths LONGER than visible light (IR infrared, Microwave, Radio waves, ELF extremely low frequency). Microwave ovens have metal screens in their windows -- the centimeter-range sized EM waves cannot see the "small" holes in the screen, so they bounce off the window as if it were just like the metal in the other five walls. Discussion of how microwave ovens "cook" food. Frequencies HIGHER and wavelengths SHORTER than visible light (UV ultraviolet, X-rays, Gamma rays). Q20 Take-Home quiz on Light as Waves, due Thursday 12 April 2012, in class or by 5pm.
Wednesday 4/11: Return X3. Update on remaining class time, discussion of format of the Final Exam. Visible light (ROYGBIV=red orange yellow green blue indigo violet). Frequencies HIGHER and wavelengths SHORTER than visible light (UV ultraviolet, X-rays, Gamma rays). UV-A and UV-B, tanning and the problem of cheap sunglasses. Images inside object using X-rays passing through or scattering or being absorbed by the object. Why Superman's X-ray vision cannot work -- because everyday situations are "dark" in the X-ray band, thankfully!
Thursday 4/12: Return X3 (again). Electromagnetic Spectrum: Visible light (ROYGBIV=red orange yellow green blue indigo violet). Frequencies HIGHER and wavelengths SHORTER than visible light (UV ultraviolet, X-rays, Gamma rays). Optics: Geometric Optics (empirical) and Physical Optics (more wave and fieldlike). Ray Tracing: Rays from a spherical source become essentially parallel rays when you are far away. When a straight light ray hits a boundary between one material and another, three things can happen: Reflection, Absorption, Transmission. The Law of Reflection. When light rays strike a rough surface, you get Scattering, which is reflections off many different angles. People tend to not like photographs of themselves, because they are used to seeing their mirror image -- their normal image, which the rest of us sees, looks "wrong". The Optical Lever -- move a mirror by 10° and the reflected ray moves by 20°. (Dr. Phil's theory on the origin of "seven years of bad luck for breaking a mirror".) First day to accept finished Topic 1 Book Reports. (Last day to accept without penalty is Monday 16 April 2012 by 5pm.) Q21 Take-Home quiz on Reflection and Refraction, and due Tuesday 17 April 2012, in class or by 5pm.
Friday 4/13: The Law of Refraction - Snell's Law. Light bent at the interface between two media, because the speed of light changes in the media. (Analogy: If you are driving along the road and your right tires go off onto the soft shoulder, they can't go as fast and the car turns towards the shoulder until all four wheels are driving off the road.) If going from an high index of refraction media to a lower index media ONLY, have a chance for Total Internal Reflection (T.I.R.). This is a "perfect" reflection, better than a mirror. Used in high-end optical systems instead of mirrors. Also useful in fiber optics cables. Second day to accept finished Topic 1 Book Reports. (Last day to accept without penalty is Monday 16 April 2012 by 5pm.)
Monday 4/16: Thin Lenses. Simplest lens surfaces are spherical (convex = bows out, concave = bows in) and flat (plano). So some lenses might appear to be biconvex, plano-convex, biconcave, convex-concave. A biconvex lens is also called a positive or converging lens. Parallel light rays coming into such a lens will all pass through the focal point, a distance f from the center of the lens. By itself, could use as a magnifying lens. Concentrating sunlight: burning paper or popping ants? Ray tracing gets same results as doing Snell's Law on mulitple curved lens surfaces. Handy not to have to do all that refraction calculations! Real image formed by passing three rays through a positive thin lens. Three cases: object distance p > 2f (real, inverted, reduced image). Last day to accept finished Topic 1 Book Reports without penalties -- unless you had Dr. Phil look at a Draft Paper.
Tuesday 4/17: Thin Lenses. Real image formed by passing three rays through a positive thin lens. Three cases: object distance p > 2f (real, inverted, reduced image), 2f < p < f (real, inverted, magnified image), p < f (virtual, upright, magnified image = magnifying glass). Quantum Mechanics. ... the Bohr Atom (derivation on the reverse side Dr. Phil's Periodic Table) to see how Coulomb's Law combines with Uniform Circular Motion and the Modern Physics concepts of the deBroglie wavelength (matter also has wave-particle duality) and quantum physics (like the stepped terraces of our lecture hall, 1118 Rood, the electron cannot exist at just any energy level or radius from the nucleus). (Click here for the Atomic & Nuclear Physics handout (not given in class) and here for the Periodic Table handout.) Q22 Take-Home quiz on Objects & Images From a Thin Lens, due Thursday 19 April 2012, in class or by 5pm.
Wednesday 4/18: "A Taste of Modern Physics" -- goes to size/time/length scales far outside our normal experience. The point of today's lecture is to give you a taste for how strange things get in the real world. Quantum Mechanics. ... the Bohr Atom (derivation on the reverse side Dr. Phil's Periodic Table) to see how Coulomb's Law combines with Uniform Circular Motion and the Modern Physics concepts of the deBroglie wavelength (matter also has wave-particle duality) and quantum physics (like the stepped terraces of our lecture hall, 1118 Rood, the electron cannot exist at just any energy level or radius from the nucleus). In effect, the allowed electron orbitals in the Bohr Atom are standing waves set on a circular string. (ooh!) The deBroglie wavelength -- Wave/Particle Duality for Matter. Planck's constant -- a very small number, but it is NOT zero ( h = 0 in Classical Physics). So the deBroglie wavelength only matters for very small objects, not Buicks. For an electron to move from one orbit to another, it must gain or lose energy. Going from a higher n to a lower n, the difference in the energy is release as a photon with E = hf. To go from a lower n to a higher n, the electron has to absorb a photon of E=hf. And now we have an explanation of the spectral lines which we had once described as "fingerprints for elements". Burn hydrogen and the light emitted, when run through a prism will split not into a rainbow, but individual lines of individual colors -- these are emission lines. Take white sunlight, shine it through a prism and look at the rainbow of colors under a microscope and you will see that individual lines of color are missing -- these are absoption lines caused by the hydrogen gas in the Sun's atmosphere removing those colors and moving their electrons to higher orbits or ionizing completely. If we try to solve the helium atom (Z=2) in a similar way, we find that with one nucleus and two electrons, we have a three-body problem and we can't solve that in closed form. However, we can use our Bohr equations for hydrogenic ions (hydrogen-like) which have only one electron, so we can solve for He+, Li+2, Be+3, B+4, C+5, ... , U+91, etc.
Thursday 4/19: Nuclear Physics. A brief look at Nuclear Physics. There are some118 Elements in the Periodic Table. For each element, there may be many Isotopes -- same Z (# of protons) but different N (# of neutrons). The atomic mass starts out as A = Z + N. The actual atomic mass numbers listed in the periodic table are averages of all the isotopes found in nature. From Hydrogen to Calcium (1-20), typically we have as many neutrons as protons. Starting with Scandium (Z=21), we need more and more neutrons to stabilize against the Coulomb repulsion of so many protons, so N > Z. By Uranium (Z=92), there are so many neutrons that nuclei are generally unstable. Radioactive particles: alpha = nucleus of a Helium atom, beta = electron or positron, gamma = high energy gamma rays from the protons and neutrons shifting in their orbitals, much like the electrons and their photons. The Einstein relation, E=mc2 -- energy can be turned in matter and matter can be turned into energy. Fission = nucleus breaking into small pieces creating smaller elements, fusion = nuclei combining to form larger elements. (Click here for the Atomic & Nuclear Physics handout (not given in class) and here for the Periodic Table handout -- with today's derivation on the back.) For all intents and purposes, we have closed the book on the Final Exam material on Thursday.
Friday 4/20: THE LAST CLASS.