Dr. Phil's Home

## Lectures in PHYS-1130 (4)

Updated: 9 December 2006 Saturday.

Correction: 27 March 2007 Tuesday.

### Week of December 11-15, 2006.

Monday 12/11: Office Hours

Tuesday 12/12: FINAL EXAM 8:00-10:00am

Wednesday 12/13: Office Hours

Thursday 12/14: Office Hours

Friday 12/15: Dr. Phil is not planning on coming in to campus today -- contact at home or prior to 12/15.

### Week of September 4-8, 2006.

Monday 9/4: LABOR DAY -- No Classes.

Tuesday 9/5: Class begins. The nature of studying Physics. Science education in the United States. Natural Philosophy. The Circle of Physics. Distribute syllabus.

Wednesday 9/6: Aristotle and the Greek Philosophers. Observation vs. Experiment - Dropping the book and the piece of paper (2 views). Zeno's Paradoxes.

Thursday 9/7: "Speed Limit 70" First Equation: Speed = Distance / Time. Development of Speed equation for Constant or Average Speed. Q1 and your PID number. (If you missed class on this day, check with Dr. Phil sometime soon.)

Friday 9/8: More about speed = distance / time. 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. SI Metric System.

### Week of September 11-15, 2006.

Monday 9/11: SI Metric System. What do we mean by Measurements? "Units will save your life." What is "1 m/s"? We need a few benchmark values to compare English and SI Metric quantities. 60 m.p.h. = 26.8 m/s. 1.00 m/s = slow walking speed. 10.0 m/s = World Class sprint speed. NEWS: Saturday 5/13/2006 new World Record in 100m dash -- 9.76 seconds. Speed. 60 m.p.h. = "A Mile A Minute". (1848: The Antelope)

Tuesday 9/12: The P-O-R (Press-On-Regardless) road rally problem. "You can't average averages." What do we mean by a = 1 meter/sec² ? You cannot accelerate at 1 m/s² for very long. Q2 in-class quiz. Handout about SI metric system prefixes and Dr. Phil's Practical Significant Figures. Distribute Topic 1 Handout. (Searchable Web Page; Downloadable PDF File)

Wednesday 9/13: Discuss Topic 1. Is 1 m/s² a large or small acceleration? Free fall (near Earth's surface, neglecting air resistance) acceleration is g = 9.81 m/s². Example: bullet fired down a rifle barrel, solve for "a" using the Equation Without Time. Story of Scott Crossfield, the X-15 and the exploding fuel tank -- momentary 1000 m/s² acceleration with no safety equipment.

Thursday 9/14: Types of Motion: No Motion (v=0, a=0), Uniform Motion (v=constant, a=0), Constant Acceleration (a=constant). The consequences of Falling Down... ...and Falling Up. The Turning Point ( v=0 but a = -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. (The guy with the fedora and the cigar.) Q3 Take-Home, due Tuesday 19 September 2006.

Friday 9/15: The guy with the fedora and the cigar. (con't.) Now we need to start dealing with two-dimensional problems in general. 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). Practical Trigonometry. SOHCAHTOA. Hand out 1st Sample Exam 1.

### Week of September 18-22, 2006.

Monday 9/18: Vectors and Vector Addition (con't.) 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.

Tuesday 9/19: Finding the final vector velocity of The guy with the fedora and the cigar problem. Classical/Galilean/Newtonian Relativity: Two observers may see something different. A person on a train tosses a ball straight up. A person watching the train go by see the same ball arc through the air in a parabola. Using Vector Addition for Velocities: Upstream, downstream (rivers), Headwind, tailwind, crosswind (airplanes). Hand back Q2. Q4 Take-Home, due Thursday 21 September 2006.

Wednesday 9/20: 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.

Thursday 9/21: Example: Cannon shot at 222m/s @ 30°. Same Range if launched at 60°. Example: Rifle fired horizontally and a bullet dropped from the same height as the muzzle -- both bullets will hit level ground at the same time, since both have the same y-problem. Classic Simple Pursuit (Cop and the Speeder). Same Place at the Same Time. Our algebra for car 1 and car 2, we cancelled a factor of t at one point -- this represents t = 0, which by definition is also a solution. But... because our problem is Simple Pursuit, when the car 2 reaches car 1, the cop is traveling at twice the speed of the speeder. Hand out 2nd Sample Exam 1. (Click here for a copy.) Q5 Take-Home, due Tuesday 26 September 2006. Read this NOTE about Q5.

Friday 9/22: Types of Motion studied so far: No motion, Uniform motion (v=constant, a=0), Constant Acceleration. 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. Read this NOTE about Q5. Go over some Sample Exam Problems

### Week of September 25-29, 2006.

Monday 9/25: Read this NOTE about Q5. 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!)

Tuesday 9/26: Space Shuttle stories. Recap: Our studies so far have described "How" things move, and allow to say "When" and "Where" things move, but not "Why" things move. For that we have to start talking about Forces -- and that means Newton. Some stories about Sir Isaac Newton. Newton's Three Laws of Motion: Zeroeth Law - There is such a thing as mass. First Law - An object in motion tends to stay in motion, or an object at rest tends to stay at rest, unless acted upon by a net external force. Second Law - F=ma. SI unit of force: Newton (N) = (kg·m/s²). Q6 in-class quiz. Hand out 3rd Sample Exam 1. (Click here for a copy.)

Wednesday 9/27: 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.) Force is a vector. Free Body Diagrams. Normal Force (Normal = Perpendicular to plane of contact). Sum of forces in x or y equations. Example of 125 kg crate sitting there. 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.) "Last" review question for X1...

Thursday 9/28: Exam 1.

Friday 9/29: YES! WE HAVE CLASS TODAY! Example of 125 kg crate being dragged/pushed around. Variations as we allow for an applied force that it at an angle. "You can't push on a rope." Since the force from a wire/string/rope/chain/thread/etc. can only be in one direction, Dr. Phil prefers to call such forces T for Tensions rather than F for Forces. If you are hanging from a wire and are not in contact with the ground, there is NO Normal Force.

### Week of October 2-6, 2006.

Monday 10/2: 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. Atwood's Machine -- two masses connected by a single cable via a simple pulley. 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.

Tuesday 10/3: The importance of Putting The Physics Back Into The Problem (PTPBIP): Example problem with suspended sign -- some overnight solutions do not meet requirements of Newton's 1st Law in x- or y-directions. 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. Friction is both a pain and a curse. Attempt by state to "repeal the law of friction" was an April Fool's joke. (Unlike the legislation making pi = 3 during the Homesteading era, which had practical value in squaring the circle.) Q7 in-class.

Wednesday 10/4: Two kinds of Friction: Static (stationary) and Kinetic (sliding). For any given contact surface, there are two coefficients of friction, µ, one for static and one for kinetic. Static is always greater than kinetic for any given pair of materials in contact with each other. Static & Kinetic Friction. 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. Tires rolling with friction on good roads -- this is static friction not kinetic friction because the tires aren't sliding on the pavement. 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.

Thursday 10/5: X1 Returned. (Click here for a solution.) First Sample Exam 2 handed out. (Click here for a copy.) Anti-Lock Brakes and Traction Control. Static Friction can vary from zero to its max value in either direction. Q8 Take-Home, due Tuesday 10 October 2006.

Friday 10/6: Air Resistance. Low speed (Fdrag = - bv) and high speed (Fdrag = - cv2)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. Tied up in the coefficients for drag are things like shape, air, cross-section area, surface type, etc. Terminal velocity of a person depends on clothes and orientation (which way they are pointing and whether they are stretched out or trying to be compact).

### Week of October 9-13, 2006.

Monday 10/9: Columbus Day (Observerd) -- not a WMU Holiday. Objects in Free-Fall with air resistance may reach a Terminal Velocity (Force of gravity down canceled by Drag force up) and doesn't accelerate any more. (Aside on Chuck Yeager and the first supersonic aircraft, the X-1) World's Record Free-Fall. Work: A Physics Definition (Work = Force times distance in the same direction). You can do no work, but that doesn't mean you aren't exherting an effort -- only that you aren't applying a force in the direction of a motion. SI unit for Work & Energy is the Joule (J). Though technically (N·m) = (kg·m²/s²) = (J), Dr. Phil reserves (N·m) for torque (a rotational force).

Tuesday 10/10: Q8 Take-Home now due Thursday 12 October 2006. 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.

Wednesday 10/11: 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.) Continue with Conservation of T.M.E. (P.E. + K.E.). Total energy limits maximum height. Lose angle and directional information because energy is a scalar, not a vector. Example: Roller-Coaster. 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. Hooke's Law (Spring force) is a second conservative force, which we can also write as a P.E.

Thursday 10/12: Using Conservation of Energy (P.E. + K.E.) with a spring. Linear Momentum ( p = mv ) is a vector quantity. Newton's form of the 2nd Law. Two extremes in collisions: Totally Elastic Collision (perfect rebound, no damage) and Totally Inelastic Collision (stick together, take damage). The forces in collisions are complicated and always changing. Linear momentum is conserved in all types of collisions . Totally Inelastic Collisions. Example: The Yugo and the Cement Truck. Q9 in-class quiz postponed until Tuesday 17 October 2006. Q10 Take-Home quiz, due Tuesday 17 October 2006.

Friday 10/13: Friday the Thirteenth -- not a WMU Holiday. Totally Inelastic Collisions (con't.) Three example collisions: head-on, rear-end, 2-D. (The Non-Collision -- if the car following is going slower, it isn't going to run into the car ahead. PTPBIP.) What happens in a wreck. The myth of "better to be thrown from the wreck." Seat belts, shoulder belts, steel beams in doors and crumple zones. Second Sample Exam 2 handed out. (Click here for a copy.)

### Week of October 16-20, 2006.

Monday 10/16: NOTE: Dr. Phil late to class due to US-131 being closed southbound between 100th Street in Kent County and Wayland in Allegan County. What happens in a wreck. How airbags work.

Tuesday 10/17: The Ballistic Pendulum -- We can find the speed of a projectile through an Inelastic Collision followed by Conservation of TME. Totally Elastic Collisions. Close approximations: The Executive Time Waster, the Physics of pool shots. Q9 in-class quiz.

Wednesday 10/18: Why you want inelastics collisions in a wreck. 5 mph versus 3 mph impact bumpers. "Adobe: The Little Car Made of Clay". What's the opposite of a collision? An explosion. Or recoil. Example: A pitcher on ice skates at rest -- when he hurls a fastball to the right, he goes to the left. Total momentum of the system remains constant (in this case, zero).

Thursday 10/19: UCM Revisited. Centripetal Force. No such thing as Centrifugal Force. Only the Centrepital Force, which points radial inward, just like the centripetal acceleration. Note that the Centripetal Force is an ANSWER to the sum of forces equation -- it does not show up in the F.B.D. directly -- something has to CAUSE the Centripetal Force, such as a tension, normal force or a combination of forces. Although a loop-the-loop is not a proper UCM problem, we can apply UCM at the top of the loop and determine the minimum safe speed for going around the loop without falling off. At the minimum speed, the Normal Force between the wheels and rail goes to zero (the wheels just "kiss" the track), so the centripetal force is just equal to the weight, w = mg. Making "artificial gravity" for long-duration space flight by living in a rotating object. Third Sample Exam 2 handed out. (Click here for a copy.) Q11 Take-Home, due Tuesday 24 October 2006.

Friday 10/20: Some considerations of using UCM for "artificial gravity" in space. The story of the 50,000 rpm Ultra-Centrifuge and the Fresh Rat's Liver. Review some Sample Exam 2 problems and Q10.

### Week of October 23-27, 2006.

Monday 10/23: Translating Linear physics to Rotational physics (as "easy" as changing Roman/English variables to Greek), because we already know the Physics of the first six chapters. The radian is a "quasi-unit" -- it's not really a unit, but represents a fraction of a circle. (We can "wish" it away when we need to.) We are building a table with three columns: Linear Physics on the left, Rotational Physics on the right and the conversion between linear and rotational variables in the center. Angular position, angular velocity, angular acceleration, angular kinematic equations for constant angular acceleration, angular force = torque. Newton's 3 Laws of Motion applied to rotations.

Tuesday 10/24: Translating Linear physics to Rotational physics (con't.). Torque = r F, when applying a linear force perpendicular to a radius line to the axis of rotation. (Most torques we apply are done this way.) Using Right Hand Rule to assign directions to x,y,z coordinates and the sense of rotations for theta, omega, alpha and tau (torque). Rotational Work, rotational K.E., angular momentum. Why we need a "rotational mass". An ice skater spinning, bringing her arms closer to her axis of rotation -- this in an internal motion which means Newton's First Law. But Newton's version of the law looks at L, the change in the angular momentum. So L is constant, but her moment of inertia decreases (mass closer to body/axis), so therefore her angular velocity increases.

Wednesday 10/25: Q7-11 Solution is now online. (Click here for a copy.) Recall Atwood's Machine: Two masses suspended by a cable looped over a simple pulley. Two F.B.D.'s give us 2 equations in 2 unknowns: the common tension T1 and the common acceleration a. In the Real Pulley case, we have to also rotate the physical pulley, which has a mass, radius and a moment of inertia I. For a solid disk of mass M and radius R, the moment of inertia is Isolid-disk = ½MR². Now we have two F.B.D.'s and an F.R.D. (Free Rotation Diagram), giving us 3 equations in 3 unknowns: the two separate tensions T1 and T2 and the common acceleration a, after we use the conversion between linear and rotational acceleration. Last review for Exam 2. Q12 Take-Home, due Tuesday 31 October 2006.

Thursday 10/26: Exam 2.

Friday 10/27: Physics Help Room moved to 2202 Everett through Friday 11/3. Table 8-1: Some Moments of Inertia of Standard Shapes. Moment of Inertia of Ring, Solid Disk. Moment of Inertia of Solid Cylinder, Hollow Sphere, Solid Sphere. Rotational K.E., Rolling objects down an incline (rolling without slipping). mgh = ½ mv² + ½ Iw², the energy available from the P.E. is split between linear K.E. and rotational K.E. Depending on the moment of inertia of the rolling object, the final speed at the bottom of the incline varies. Demo: A "race" between aluminum rings of different sizes (R and L do not show up in the final solution, so don't matter), between two steel balls (again, radius R is not a factor), and finally between a metal ring, a solid disk, a hollow ball and a solid ball (here the finish order depends on the I used).

### Week of October 30-November 3, 2006.

Monday 10/30: Statics: objects not translating in any direction and objects not rotating in any direction. Free Body Diagrams, Free Rotation Diagrams (sum of forces, sum of torques). Simple bridges, unloaded and loaded. The Diver and the Springboard.

Tuesday 10/31: Extended Objects: We have been treating our objects really as dimensional dots, that have been allowed to have mass. Now we want to start considering how that mass is distributed. An airplane with mass unevenly concentrated in front, back or to one side, may not be flyable. Center of mass and Center of gravity are usually the same thing. Both are a "weighted average", meaning it combines a position with how much mass (weight) is involved. Center of mass in the x-direction: discrete case (Example: A meter stick balances at the 50 cm mark.) We have been calculating the motion of the center of mass all this time. Demo: Suspending real objects from different points to find the center of mass -- hung from the center of mass, the object is perfectly balanced. Include: irregular plate, rectangular plate, triangular plate, Michigan (Lower Pennisula), Florida. The center of mass does NOT have to be located ON the object -- the obvious example is a ring or hoop, where the center is empty. Demo: The toy that "rolls uphill" -- actually, whether with the cylinder or the double-cone, the center of mass is going downhill. Another classic statics problem: The ladder leaning on the wall. Choose pivot point at floor to eliminate two of the three unknown forces from the sum of torques equation. Homework: Figure out whether the perpendicular components of the weight and the wall (normal) force use sin or cos of theta, the angle the ladder makes with the floor. Q14 Take-Home, due Thursday 2 November 2006. NOTE: Extending deadline for Q12 Take-Home til at least Wednesday 1 November 2006. If you've done Q12 correctly, then you should get the same answers for (b) and (e) because Newton's 2nd Law is the same no matter what form you use, and the same answers for (c) and (d) because of the Work-Energy Theorem.

Wednesday 11/1: Stability of objects -- not tipping over. Rollovers, "J-Turns" (a U-turn with a rollover), Jeep CJ vs. Jeep YJ. Ground clearance and the HUMVEE. The formula w=mg gives us the gravitational force near the surface of the Earth. Newton had to work out gravity for anywhere, hence "Universal Gravity." Specifically Newton was working on trying to solve the problem of the motion of Mars in the night sky.

Thursday 11/2: 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. The problem of determining G and the mass of the Earth. g(r). The Shuttle in Low Earth Orbit (Revisited). Q15 Take-Home, due Tuesday 7 November 2006.

Friday 11/3: X2 Returned. (Click here for a solution.) First Sample Exam 3 handed out. (Click here for a copy.) Newton's Law of Universal Gravity. Tides (high/low, spring/neap).

### Week of November 6-10, 2006.

Monday 11/6: Planetary Orbits. Ptolemy to Copernicus to Johannes Kepler. Epicycles, elliptical orbits and Occam's Razor.

Tuesday 11/7: Kepler's First Law -- All orbits are ellipses, with the larger mass at one focus. Circular orbits are a special case where the semi-major axis is the same as the semi-minor asix: a = b = R. Kepler's Second Law -- The Equal Area Law is equivalent to a statement of Conservation of Angular Momentum. Kepler's Third Law -- T² = C R³ or T² = C a³. There is one value for the constant C for every orbital system, i.e. one C for objects orbiting the Earth, another C for objects orbiting the Sun. Example: Using our data from the Space Shuttle's Low Earth Orbit, we can calculate C for Earth. Then plug in the R for the Moon's orbit and get an orbital period of 27 days, which is essentially correct.Extended Objects: Mass occupies a volume and shape. 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). Extended Objects -- Allowing for Deformation. Stress and Strain. Q16 Take-Home, due Thursday 9 November 2006.

Wednesday 11/8: Extended Objects -- Allowing for Deformation. Stress versus Strain graph. Linear region (no damage), elastic limit, plastic deformation, brittle and ductile failures. Tensile Strength, necking, voids, failure. Young's Modulus. Tension, Compression, Shear. Example: Our demo with the bowling ball hanging from the steel wire in 1110 Rood -- L0 = 2.00m, delta-L = 0.1 mm. Pre-Stressed Concrete.

Thursday 11/9: Bulk Modulus, for compression of bulk material due to applied Pressure (also equals Force/Area). 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. Q17 Take-Home, due Tuesday 14 November 2006.

Friday 11/10: Finding the submerged depth h of our front lab table "boat". Archimedes and Eureka! (I found it!) Water displacement and buoyant force still exist even for things which are completely submerged, they just don't cancel. Demo: Aluminum cylinder displaces water and weighs less. The Wreck of the Edmund Fitzgerald. Lighter-than-air aircraft (balloons, blimps, zeppelins, etc.) do the same thing in air (density = 1.29 kg/m³). Second Sample Exam 3 handed out. (Click here for a copy.)

### Week of November 13-17, 2006.

Monday 11/13: Pressure = Force / Area. SI unit: Pascal (Pa). Example: Squeezing a thumbtack between thumb and forefinger. 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. Water pressure = 101,300 Pa at depth h = 10.33 m. Why you need a qualified SCUBA instructor. The difference between Gauge Pressure (pressure difference inside and out, can be positive, negative or zero) and Absolute Pressure (total pressure, always positive or zero only for vacuum). LAST DAY TO TURN IN DRAFT PAPERS TO DR. PHIL.

Tuesday 11/14: 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. 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. Q18 in-class quiz.

Wednesday 11/15: Bernoulli's Equation and the Continuity Equation. Water Tower and the Faucet Problem. Why the water tower needs a vent. When speed goes up, pressure goes down. The aspirator, a vacuum pump with no moving parts. 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. This should close the book on Exam 3 topics.

Thursday 11/16: Pressure matters, as does force. Example: Squeezing a thumbtack between thumb and forefinger. 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). First day to turn in Topic 1 Papers -- continues through Monday 20 November 2006 at 5pm. (Draft papers get extended deadline.) Q19 in-class quiz.

Friday 11/17: Topic 2 Worksheets assigned, due Monday 4 December 2006. (Click here for a set.) Review problems from first two Sample Exam 3's. Third Sample Exam 3 handed out. (Click here for a copy.)

### Week of November 20-24, 2006.

Monday 11/20: 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. I-57 in Chicago and the expanding asphault. Last Day to turn in Topic 1 Papers if you didn't turn in a Draft Paper.

Tuesday 11/21: Exam 3.

Wednesday 11/22: Class cancelled.

Thursday 11/23: <Thanksgiving Day> No classes.

Friday 11/24: No classes.

### Week of November 27-December 1, 2006.

Monday 11/27: Classes resume. Question: Does the material expand into a hole when heated, or does the hole expand? Bimetalic strip uses two coefficients of linear expansion to curve one way or the other when heated or cooled. Can be used in a thermostat. 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).

Tuesday 11/28: Heat Energy (Q) and Temperature Change & Phase Change. Add/remove Heat Energy Q will raise/lower the temperature of a material using the Specific Heat (J/kg·°C) for objects of mass m, or the Heat Capacity (J/mole·K) for objects with n moles of atoms or molecules. Add/remove Heat Energy Q will change its phase between solid-liquid-gas using the Latent Heat of Fusion, Lf, between solids and liquids, or the Latent Heat of Vaporization Lv, between liquids and gasses. 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. "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! Q20 Take-Home, due Thursday 30 November 2006.

Wednesday 11/29: Dry Ice (solid CO2) at 1 atm air pressure, does not exist as a liquid, so it goes directly from solid to gas -- it would have a latent heat of sublimation. The change in the internal energy of system Uf - Ui = Q + W. 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.

Thursday 11/30: Return X3. (Click here for a copy.) Heat Energy (Q). The Heat Engine and Three Efficiencies (Actual, Carnot and 2nd Law). Fuel Economy (miles per gallon) is not an Efficiency. Q21 Take-Home, due Tuesday 5 December 2006. First Sample Final Exam. (Click here and here for copies.)

Friday 12/1: Snow Day. WMU Closed. No Class. NOTE: Topic 2 Worksheet due date extended to Wednesday 6 December 2006 to allow for questions on Monday.

### Week of December 4-8, 2006.

Monday 12/4: There is no conspiracy to keep big 100 m.p.g. cars out of our hands. To use less fuel, do less work. Smaller, lighter cars with smaller, lighter engines. To improve efficiency, can reduce TC or raise TH . Reverse the arrows in the Heat Engine and you get a Refrigerator. Cannot place an open refrigerator or a window air conditioner in the middle of a room and cool the room, because the exhaust heat to the hot side includes the heat pulled from the cold side plus the work done on the compressor. A Heat Pump is a reversible system which cools inside of the house in summer and heats the inside of the house in winter -- just because it is cold outside, doesn't mean there is not heat energy Q in the outside air. (There has to be, otherwise the air would be at 0 K.) Coming up -- Periodic Motion, Waves and Resonance.

Tuesday 12/5: Revisit Mass on a spring. F = -kx = ma. Equations for x, v and a are sine & cosine solutions. Any time you have a conservative linear restoring force that can act as periodic motion you have a Simple Harmonic Oscillator that undergoes Simple Harmonic Motion. S.H.O. & S.H.M. Simple Pendulum. Physical Pendulum. Uniform Circular Motion (U.C.M.) as two S.H.O.'s (x- and y-components).

Wednesday 12/6: 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). No volunteers for assisting with last demonstration -- so just ended class. Waves and Resonance continued. Standing Waves on a string. Fundamental, First Overtone, Second Overtone, etc. Demonstration: First and higher overtones on a string driven by a saber saw. Standing Waves in a tube. Tuning forks, resonance tubes. Titanic/Third set of Sample Final Exams. (Click here for a copy.) Q22 Take-Home, due THIS WEEK (Thursday 7 December 2006, if you aren't going to attend The Last Class on Friday 8 December 2006.)

Thursday 12/7: The speed of sound in air: 334 m/s @ 0°C and 344 m/s @ 20°C. Takes time for sound to travel. Constructive and Destructive Interference. Acoustics of concert halls. "Normal" human hearing is frequencies from 20 Hz to 20,000 Hz. Artilleryman's ear -- mid-range hearing loss. dB = decibel, a logarhythmic scale. Sound Meter: ambient noise in1110 Rood = 56 dB; Dr. Phil talking at ½ meter = 63 dB; Class shouting = 83 dB; Dr. Phil shouting at ¼ meter = 108 dB. Solutions for Q20 and Q21 up on the website. Solution for Q22 going up late on Friday.

Friday 12/8: LAST DAY OF CLASS. At this point, all outside work (Take-Home Quizzes and Worksheets, plus the Paper) has been assigned. Only outstanding item is the Final Exam, including Q23 as the Check-Out form. Course Review. Finish up the day with the course & teacher evaluations for the semester.

### NOTE: Exam 3 Solution for Problems 2b and 2c has an error. Corrected answers:

```2(b) 453.7N      2(c) 331.1 N

If you were marked off for EITHER of these answers,