Dr. Phil's Home
Updated: 05 July 2011 Tuesday.
Final Course Grades and Breakdown by Category 7/5/2011 Tuesday
Final Exam Stats XF raw curved n 37 37 hi 197 199 lo 135 137 ave 169.4 171.4 s.d. 15.07 15.07
Estimated Mid-Term Grades can be found here. Reminder that ICES Student Course Evaluations are available online via GoWMU .
Monday 6/27: Three Last Topics: Optics, Atomic Physics, Nuclear Physics. Real Mirrors: Backcoated, Frontcoated (expensive) and One-Way Glass. 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".) 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. A Taste of Modern Physics" -- goes to size/time/length scales far outside our normal experience. The point of today's lecture is to give you a taste for how strange things get in the real world. Quantum Mechanics. ... the Bohr Atom (derivation on the reverse side Dr. Phil's Periodic Table) to see how Coulomb's Law combines with Uniform Circular Motion and the Modern Physics concepts of the deBroglie wavelength (matter also has wave-particle duality) and quantum physics (like the stepped terraces of our lecture hall, 1110 Rood, the electron cannot exist at just any energy level or radius from the nucleus). In effect, the allowed electron orbitals in the Bohr Atom are standing waves set on a circular string. (ooh!) The deBroglie wavelength -- Wave/Particle Duality for Matter. Planck's constant -- a very small number, but it is NOT zero ( h = 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. Nuclear Physics. A brief look at Atomic and Nuclear Physics. The Einstein relation, E=mc2. Fission, fusion, matter/anti-matter anhiliation. (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 closed the book on the Final Exam on Friday. Quiz 22 was an In-Class attendance sheet for Monday 27 June 2011.
Tuesday 6/28: FINAL EXAM from 2pm to 4pm (2 Full Hours).
Wednesday 6/29: Not on campus today.
Thursday 6/30: Office Hours. Noon to 3pm -- 2203 Everett Tower.
Friday 7/1: Not on campus today.
Monday 7/4: Fourth of July holiday. Not on campus today.
Tuesday 7/5: Grades due by NOON to Registrar. Do NOT call me in the morning. Dr. Phil will not be on campus today. Office Hours webpage will be updated for Grading Week and Beyond.
Monday 5/9: Class begins. The nature of studying Physics. Science education in the United States. Natural Philosophy. The Circle of Physics. 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. To understand the underlying concepts we need to Simplify The Universe. "Speed Limit 70" -- what does it really mean? First Equation: Speed = Distance / Time.
Tuesday 5/10: 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 . English system of measurement. SI Metric System. Prefixes. What do we mean by Measurements? "Units will save your life." What is "1 m/s"? We need a few benchmark values to compare English and SI Metric quantities. NOTE: English-to-Metric conversions will NOT, with two exceptions, be tested on in this course. 60 m.p.h. = 26.8 m/s. 1.00 m/s = slow walking speed. 10.0 m/s = World Class sprint speed (The 100 meter dash -- Usain Bolt is the current Olympic (9.59 seconds) and World (9.58 seconds) record holder.) 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). Distribute syllabus.
Wednesday 5/11: No class.
Thursday 5/12: PTPBIP - Putting The Physics Back Into The Problem. A simplified trip to the store -- The S-Shaped Curve. Acceleration. 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. Problem: A rifle bullet is fired from rest to nearly twice the speed of sound, 444 m/s, in a distance of 1.00 m. Find a. Answer, a = 98,570 m/s². This is huge, which is why we don't fire people out of rifle barrels. Find t = 0.004504sec. Again, we can 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. Topic 1 assigned. (Updated Searchable booklist available online here .) Q1 and your PID number. Quiz 1 was given in-class on Thursday 12 May 2011, 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 5/13: Friday the Thirteenth is neither a WMU holiday nor a reason not to attend class (grin). What do we mean by a = 1 meter/sec² ? You cannot accelerate at 1 m/s² for very long. 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 earlier. 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. Problem: A car starts at rest, then accelerates to a speed of 26.8 m/s (60 mph) in 12.0 sec. (a) Find acceleration a. (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.) 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. Q2 in-class quiz on speed = distance / time. Q3 Take-Home quiz on the Kinematic Equations, due on Monday 16 May 2011, in class or by 5pm.
Monday 5/16: The P-O-R (Press-On-Regardless) road rally problem. "You can't average averages." Demo: These class webpages online. Comments on Q2 -- solution already posted on class webpage. Note that part (c) is just like the P-O-R problem. 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. 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. First set of Sample Exam 1's handed out. (Click here and here for a copy.) Q4 Take-Home quiz on Falling Up and Falling Down, due on Thursday 19 May 2011, 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.
Tuesday 5/17: 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.
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. 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 quiz on Vectors and Standard Angle, due on
Friday 20 May
2011 Monday 23 May 2011, in class or by 5pm.
Wednesday 5/18: No class.
Thursday 5/19: 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. Demo: Toss a piece of chalk horizontally and drop a second piece -- they both hit the table at the same time, because they have the same y-problem of free-fall in the vertical. Cannot aim directly at an object, have to allow for the drop. That's why the javelin in Q6 is launched at an angle in order to reach the target at the launch height. 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. Space Shuttle in Low-Earth Orbit. (There's still gravity up there!) Second set of Sample Exam 1's handed out. (Click here and here for a copy.) Q6 Take-Home on Ballistic/Projectile Motion, due on Monday 23 May 2011, in class or by 5pm.
Friday 5/20: Demo: Rodney Reindeer and U.C.M. 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. UCM can generate some very large accelerations. How large? 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. A 13.0 cm diameter hard disk drive spinning at 3600 RPM (revolutions per minute, so T = 1/60th second) sees a speed along the outside edge of over 20.0 m/s and a centripetal acceleration of over 9000 m/s² -- that's nearly a thousand gees. Fighter jet pilots can pass out in turns with 9-10 gees. Race car drivers, too. 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. (Falling apple and Mars, reeding on the edge of the silver shilling, "mad as a hatter" from mercury poisoning.) Return Q2/Q3. Third set of Sample Exam 1's handed out. (Click here and here for a copy.) Q7 In-Class quiz on Uniform Circular Motion.
Monday 5/23: 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. A final note on ballistic motion: You have to have some positive v0y if you want to jump a gap, because otherwise you start falling immediately once you are no longer supported. Newton's Three Laws of Motion: Zeroeth Law - There is such a thing as mass. First Law - An object in motion tends to stay in motion, or an object at rest tends to stay at rest, unless acted upon by a net external force. Second Law - F=ma. Third Law - For every action, there is an equal and opposite reaction, acting on the other body. (Forces come in pairs, not apples.) SI unit of mass = kilogram (kg). SI unit of force = Newton (N). English unit of force = pound (lb.). English unit of mass = slug (Divide pounds by 32. For English units, g = 32 ft/sec².). Force is a vector. Dr. Phil's request for questions on Sample Exam 1's -- no questions. Class ended early. Q8 Take-Home quiz on Forces, due Friday 27 May 2011, in class or by 5pm.
Tuesday 5/24: Exam 1.
Wednesday 5/25: No class.
Thursday 5/26: Return X1. Newton's 3 Laws continued. Force is a vector. Free Body Diagrams. Normal Force (Normal = Perpendicular to plane of contact). The normal force does NOT automatically point up and it is not automatically equal to the weight -- we have to solve for the normal force. "The Normal Force is NOT automatically present -- you have to be in contact with a surface. The Normal Force does NOT automatically point up -- FN is perpendicular to the surface. The Normal Force is NOT automatically equal to the weight. FN = mg only if there are no other forces in the y-direction." Sum of forces in x or y equations -- either will be equal to 0 (Newton's 1st Law) or ma (Newton's 2nd Law). Example of 125 kg crate being dragged/pushed around. (Near the surface of the Earth, you can use the relationship that 1 kg of mass corresponds [not "equals"] to 2.2 lbs. of weight. So multiple 125 by 2 and add 10%... 250 + 25 = 275... so a 125 kg crate has a weight of mg = 1226 N or 275 lbs.). Variations as we allow for an applied force that it at an angle. Push down and Normal Force increases; pull up and Normal Force decreases -- though it cannot go negative. "You can't push on a rope." Since the force from a wire/string/rope/chain/thread/etc. can only be in one direction, Dr. Phil prefers to call such forces T for Tensions rather than F for Forces. 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.
Friday 5/27: YES! We have class on Friday. There is not an early start to the Memorial Day Weekend. We do get Monday 30 May 2011 off as a holiday. 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. 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. 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. 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. Hand out first sample exam pages for Exam 2. (Click here and here for a copy.)
Monday 5/30: Memorial Day (Observed) -- No classes.
Tuesday 5/31: 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. 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. 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. Second set of Sample Exam 2's handed out. (Click here and here for a copy.) Q10 Take-Home quiz on Friction, due Friday 3 June 2011, in class or by 5pm. NOTE: For each part you want to think about what kind of friction you are using and whether v is constant or changing.
Wednesday 6/1: No class.
Thursday 6/2: 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: 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. Third set of Sample Exam 2's handed out. (Click here for a copy.) Q11 Take-Home quiz on Totally Inelastic Collisions (2-D), due Monday 6 June 2011, in class or by 5pm.
Friday 6/3: Return Q5,6,8,9. 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. 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. 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. Q12 In-Class quiz on T.I.C. (1-D). Q13 Take-Home quiz on Conservation of Energy, also due on Monday 6 June 2011, in class or by 5pm.
Monday 6/6: Demo: a suspended bowling ball shows conservation of T.M.E. All P.E. when swings up to a stop on either side, all K.E. at bottom of swing. (There must be non-conservative forces, such as air resistance and friction in the pivot point on the ceiling -- because the bowling ball never quite gets up as high as it starts.) Totally Elastic Collisions:-- perfect rebound, no damage, conserve both momentum and K.E. The equations get messy because each object has both an vi and a vf. Worse, momentum is a vector and can have components, while K.E. is a scalar and a square (½mv²). Two special cases: (1) m1 = m2 , v2i = 0, so v2f = v1i and v1f = 0. All the momentum and K.E. transfer from object 1 to object 2. (2) m1 = m2 , v1i = - v2i , so they just bounce off each other and go the other way. Close approximations: The Executive Time Waster. Why you want inelastics collisions in a wreck. 5 mph versus 3 mph impact bumpers. "Adobe: The Little Car Made of Clay". 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. The difficulty in finding the universal constant G. How do you find the mass of the planet you're standing on? Tides (high/low, spring/neap). Short review of some Sample Exam 2 problems. Tarzan and Jane Collision = 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.
Tuesday 6/7: Exam 2.
Wednesday 6/8: No class.
Thursday 6/9: Use Universal Gravity to check "g". The value we calculate is close, 9.83m/s², which turns out to be only off by 0.2%. Why is it off? Because using Univeral Gravity in this manner makes the assumption that the entire Earth is uniform and homogenous from the surface to the core -- which it is not. We would need calculus to integrate over layers to get the observed value of 9.81m/s². UCM Revisited. The Shuttle in Low Earth Orbit (Revisited). Calculating g(r) for r = 6,770,000 m (the radius of the Earth plus the height of 400 km for Low Earth Orbit), we get a value somewhat different than we found for the centripetal acceleration. Working backwards, we discover for this radius that the period T = 5542 sec and NOT the estimated 5400 sec (90 minutes) we had started with before. 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. 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). Up until now, our objects really haven't had any dimension. Topic 2 Worksheet 1 (Click here for a copy and directions.) Q14 Take-Home quiz on Newton's Law of Universal Gravity, due Monday 13 June 2011, in class or by 5pm.
Friday 6/10: 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. 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. First Set of Sample Exam 3s. (Click here and here for a copy.) Q15 Take-Home quiz on Boats. It says it's due on Monday 13 June 2011 -- but we didn't cover the material to answer the last couple of parts, so it WILL NOT be due on Monday. (Click here for a copy.)
Monday 6/13: 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. How to get liquid out of a cup using a straw -- or why Physics does not "suck", but pushes using a pressure difference. Using a column of liquid to make a barometer to measure air pressure. Switch from water to mercury changes h at 1 atm. from 10.33 m to 0.759m. The aneroid barometer. Smooth Fluid Flow. Pressure from a column of liquid looks like P.E. Create a Kinetic Pressure term which looks like K.E. to create Bernoulli's Equation and the Continuity Equation. Water Tower and the Faucet Problem.
Tuesday 6/14: Bernoulli's Equation and the Continuity Equation. Water Tower and the Faucet Problem. Bernoulli continued. 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.) Why the Mackinac Bridge has grates on the inside north- and soundbound lanes. Why the water tower needs a vent. 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. 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). 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. Bridge expansion joints. Why "Bridge Freezes Before Roadway" signs. Expansion joints. Last week I-69 southbound north of Marshall MI -- heated up beyond 95°F too quickly and the concrete buckled and folded up, forming a launching ramp. Volume Expansion of Solids and Liquids. Coefficient of Volume Expansion usually given for liquids; for solids, beta = 3 × alpha. Second set of Sample Exam 3's (Click here and here for a copy.) Q16 Take-Home on Heat Expansion, due Friday 17 June 2011, in class or by 5pm. (Click here for a copy.)
Wednesday 6/15: No class.
Thursday 6/16: Return X2. (Click here for a Solution.) Remember: L = L0 + delta-L and V = V0 + delta-V. 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. The Laws of Thermodynamics. (Zeroeth Law -- There is such a thing as temperature.) 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). 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. First day to turn in Topic 1 book reports. Q17 Take-Home on Heat Engines, due Monday 20 June 2011, in class or by 5pm.
Friday 6/17: The Heat Engine and Three Efficiencies (Actual, Carnot and 2nd Law). Fuel Economy (miles per gallon) is not an Efficiency. There is no conspiracy to keep big 100 m.p.g. cars out of our hands. To use less fuel, do less work. Reverse the arrows in the Heat Engine and you get a Refrigerator. NOTE: Cannot place an open refrigerator or a window air conditioner in the middle of a room and cool the room, because the exhaust heat to the hot side includes the heat pulled from the cold side plus the work done on the compressor. 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. 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 | .Second day to turn in Topic 1 book reports. Topic 2 Worksheets 2-3-4 (Click here for remaining Worksheets and Directions) Q18 Take-Home quiz on Vibrating Strings, due Monday 20 June 2011, in class or by 5pm.
Monday 6/20: For stringed instruments, increasing the tension increases the
wave speed. Since the wavelength is fixed by the geometery of the problem,
increasing the wave speed means the frequency is increased -- and you get a
higher musical note. Lower the tension and you get a lower frequency and a
lower note. 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. Speed of
Sound (Mach 1) depends on temperature: cs = 344 m/s (20°C)
or 334 m/s (0°C). Sonic booms in air (actually get a double-boom, because
of the two V's.), wake from a boat in water. The range of "normal"
human hearing: 20Hz-20,000Hz (10 octaves). Artilleryman's ear -- mid-range
hearing loss. End of Unit 3 Material. The Realization that Electricity
and Magnetism were part of the same Electromagnetic Force was a great triumph
of 19th century physics. Greeks knew about static electricity -- build up
charge and get sparks.
Demo: Static electricity. The Two-Fluid
Model of Static Electricity (A & B), to account for the two types of
behavior noted. Franklin's One-Fluid Model of Electricity. Occam's Razor: If
you can't decide between two competing ideas for how Nature works, take the
simpler model. 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 one-billion Newtons acting on each other. 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
Tuesday 6/21: Exam 3. First set of Sample Final Exams. (Click here and here for a copy.) Q19 Take-Home Quiz on Coulomb's Law of Electric Force, due on Friday 24 June 2011, in class or by 5pm.
Wednesday 6/22: No class.
Thursday 6/23: 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. 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. 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. Discussion 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. Story of radio "repair" call from 4,000,000,000 miles. Q20 Take-Home on Circuits, due on Monday 27 June 2011, in class or by 5pm.
Friday 6/24: Return X3. 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).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 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 set of Sample Final Exams -- the All-Titanic Exam. (Click here for a copy.) Q21 Take-Home on Light & Optics, due on Monday 27 June 2011, in class or by 5pm.