## Lectures in PHYS-205 (11)

Updated: 8 December 2002 Sunday

### Week of December 2-6, 2002.

THE LAST WEEK OF CLASS!

Monday 12/2: 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. DVD: Titanic Physics.

Tuesday 12/3: Demonstration: 2-liter bottle with holes drilled. 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. 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. Question: Does the material expand into a hole when heated, or does the hole expand?

Wednesday 12/4: Length Expansion. Volume Expansion of Solids and Liquids. Q1 (Part III of III) (5000 points automatically for participating.) Exam 3 handed back.

Thursday 12/5: Ideal Gas Law (PV/T = constant). The 1st and 2nd Laws of Thermodynamics. Heat Energy (Q). The Heat Engine and Three Efficiencies (Actual, Carnot and 2nd Law). Fuel Economy (miles per gallon) is not an Efficiency. There is no conspiracy to keep big 100 m.p.g. cars out of our hands. To use less fuel, do less work. Q21-22 take-home quiz, due Friday 6 December 2002.

Friday 12/6: COURSE REVIEW. Q23 take-home quiz, due at Your Final Exam.

### Week of September 2-6, 2002

Monday 9/2: LABOR DAY

Tuesday 9/3: OFFICE DAY

Wednesday 9/4: Class begins. Quick roll-call (we're stuffed in here). Distribute syllabus. The nature of studying Physics. Science education in the United States.

Thursday 9/5: Q1 (Part I of III) (5000 points automatically for participating.)

Friday 9/6: Natural Philosophy. The Circle of Physics. Aristotle and the Greek Philosophers. Observation vs. Experiment - Dropping the book and the piece of paper (2 views). Zeno's Paradoxes.

### Week of September 9-13, 2002

Monday 9/9: Q1 (Part II of III) (5000 points automatically for participating.)

Tuesday 9/10: First Equation: Speed = Distance / Time.

Wednesday 9/11: Development of Speed equation for Constant or Average Speed. 60 m.p.h. = "A Mile A Minute". (1848: The Antelope) The P-O-R (Press-On-Regardless) road rally problem. "You can't average averages."

Thursday 9/12: SI Metric System. 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. Q2 in-class.

Friday 9/13: A simplified trip to the store. Acceleration. Physics misconceptions. Integrating to find the set of Kinematic Equations for constant acceleration. Q3 Take-Home Due Monday.

### Week of September 16-20, 2002

Monday 9/16: Kinematic Equations for Constant Acceleration. The Equation Without Time -- Avoiding the Quadradic Formula. (Acceleration down a rifle barrel.) (The guy with the fedora and the cigar.)

Tuesday 9/17: The consequences of Falling Down -- and Falling Up. The Turning Point ( v=0 but a = -g during whole flight). First set of Sample Exam pages for Exam 1. (Solutions will NOT be provided for these handouts.)

Wednesday 9/18: The illusion of "hanging up there in the air" at the turning point. Two kinds of numbers: Scalars (magnitude and units) and Vectors (magnitude, units and direction). Right Triangles: Sum of the interior angles of any triangle is 180°, Pythagorean Theorem (a² + b² = c²). Trigonometry: SOHCAHTOA Rule. Standard Angle (start at positive x-axis and go counterclockwise). Standard Form: 5.00m @ 30°. Q2 returned. Q4 in-class.

Thursday 9/19: Adding and subtracting vectors: Graphical method and Analytical method. (Check to make sure your calculator is set for Degrees mode.) Why arctangent is a stupid function on your calculator.

Friday 9/20: Finding the final vector velocity of The guy with the fedora and the cigar problem. Classic pursuit problem: Two cars (1st v=constant, 2nd a=constant), same place at same time (2 solutions! t=0 is a solution!). Ballistics: You cannot jump a gap without some postive v-naught-y. Q5 take-home on vectors, due Monday 9/23.

### Week of September 23-27, 2002

Monday 9/23: Movie clip: Speed (You have to have some positive v0y if you want to jump a gap -- even with a bus.). Ballistic Motion. Handout: 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). Q5 take-home quiz due.

Tuesday 9/24: High and low trajectories for Range Equation. Start problem of kicking a stone down a set of stairs. Third set of sample exams for Exam 1 handed out. Q4 returned. Q6 in-class.

Wednesday 9/25: Ballistic problems. Relative motion (Classical Relativity): Headwind, tailwind, crosswind examples. Problem of motor boat crossing a river with a current.

Thursday 9/26: 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. Some Exam 1 review.

Friday 9/27: UCM continued. Space Shuttle in Low-Earth Orbit (There's still gravity up there!). More Exam 1 review. (No take-home quiz this weekend - Dr. Phil snowed under with some other paperwork.)

### Week of September 30 - October 4, 2002

Monday 9/30: Some stories about Sir Isaac Newton. Newton's Three Laws of Motion: Zeroeth Law - There is such a thing as mass. First Law - An object in motion tends to stay in motion, or an object at rest tends to stay at rest, unless acted upon by a net external force. Second Law - F=ma. Third Law - For every action, there is an equal and opposite reaction, acting on the other body. (Forces come in pairs, not apples.) SI unit of force: Newton (N).

Tuesday 10/1: Exam 1.

Wednesday 10/2: Newton's Three Laws continued. Force is a vector. Free Body Diagrams. Normal Force (Normal = Perpendicular to plane of contact). Sum of forces in x or y equations. 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.).

Thursday 10/3: Pushing a 125 kg crate 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. "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. 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.

Friday 10/4: 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. 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. Double-Quiz 7 & 8 take-home, due Monday 10/7.

### Week of October 7-11, 2002

Monday 10/7: Continue with tilted x'-y' coordinates, block sliding down the inclined plane. Though the time to slide down the incline is different from just dropping the block from the same height, the final speed v is the same in both problems -- just in different directions.

Tuesday 10/8: 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. 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. Double Quiz Q7/8 due today (moved from Monday).

Wednesday 10/9: Friction continued. Static Friction is "magic", varying between zero and its maximum value of µ times the Normal Force. Kinetic Friction is always µ times the Normal Force. Demonstration of Book sliding down inclined plane with friction. Tires rolling with friction on good roads -- this is static friction not kinetic friction because the tires aren't sliding on the pavement.

Thursday 10/10: Resistive Forces: Friction and 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. World's Record Free-Fall. Newton's Universal Law of Gravity (or Newton's Law of Universal Gravity). Q9 ended up as a take-home quiz due Monday 14 October 2002.

Friday 10/11: Movie Clip: Apollo 13 and The Making of Apollo 13. 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 to integrate over layers to get the observed value of 9.81m/s². Revisit Space Shuttle in Low-Earth Orbit and use UCM and Universal Gravity to set it right.

### Week of October 14-18, 2002.

Monday 10/14: The Centrifuge and possible reasons why people talk of a "centifugal force" -- No such thing as Centrifugal Force. Examples: Minimum radius for safe turns at given speed v (level ground with friction, banked curved without friction). The story of the 50,000 rpm Ultra-Centrifuge and the Fresh Rat's Liver. Q9 take-home due today.

Tuesday 10/15: The need for "Artificial Gravity" using UCM in long duration space missions. Loop-the-loop using UCM. Q10 in-class.

Wednesday 10/16: Work: A Physics Definition (Work = Force times distance in the same direction). Work = Energy. Pay particular attention to Units. Dot products: one of two methods of multiplying two vectors -- this method generates a scalar, which is a good thing because Work happens to be a scalar, which is Work's virtue (i.e. why we care). IMPORTANT NOTE: Exam 2 moved from Tuesday 10/22 to Thursday 10/24.

Thursday 10/17: Exam 1 returned (FINALLY).Q11 in-class.

Friday 10/18: Work & Energy continued. Kinetic Energy -- an energy of motion, always positive, scalar, no direction information. Work-Energy Theorem (net Work = Change in K.E.). Potential Energy: Storing energy from applied work for later. Gravitational P.E. = mgh.

### Week of October 21-25, 2002.

Monday 10/21: 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. 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. Revisit example of the loop-the-loop from U.C.M. and determine height of Hill 1 in order to safely loop-the-loop.

Tuesday 10/22: More Conservation of T.M.E. problems. You can recover the vector force from a scalar Potential Energy by taking minus the partial derivatives. Q12 in-class.

Wednesday 10/23: Movie clip: 2001: A Space Odyssey (What would it look like to have use centripetal force for artificial gravity? Stanley Kubrick's 1968 movie showed us a large rotating space station and a smaller rotating carousel on a ship to Jupiter.). Demo: a suspended bowling ball shows conservation of T.M.E. Hooke's Law (Spring force) is a second conservative force, which we can also write as a P.E. Power = Work / time. 1 h.p. = 746 W.

Thursday 10/24: Exam 2 moved to Thursday 24 October 2002.

Friday 10/25: Conservation Laws in Physics. 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. Example: The Yugo and the Cement Truck. Head-on Collisions.

### Week of October 28-November 1, 2002.

Monday 10/28: Three example collisions: head-on, rear-end, 2-D. What happens in a wreck. How airbags work. Q13 Take-Home, now due Thursday 31 October 2002.

Tuesday 10/29: Totally Elastic Collisions. Close approximations: The Time Waster, the Physics of pool shots. More on car safety systems. Why you want inelastics collisions in a wreck. "Adobe: The Little Car Made of Clay". 5mph impact bumpers vs. 3mph impact bumpers. The Ballistic Pendulum (Inelastic Collision followed by Conservation of TME).

Wednesday 10/30: Newton's Form of the Second Law (differential form). Impulse (integral form). NOTE: The difference between Work and Impulse, is that one integrates the Force over distance, the other Force over time. Explosions = Backwards Collisions. Recoil. 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 is a "weighted average", meaning it combines a position with how much mass is involved. Center of mass in the x-direction: discrete case and 1-D uniformly distributed mass (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: Tossing a stick across the room (1) javelin style and (2) with rotation -- in both cases the center of mass roughly follows the ballistic curve.

Thursday 10/31: 2-D uniformly distributed mass -- Center of mass in x-direction and in y-direction. Rectangular plate. Note that the center of mass value depends on the coordinate system, but the center of mass point remains in the same place. Triangular plate -- parameterizing y = y(x) (y as a function of x). Mass per unit length (lamda), mass per unit area (sigma). 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.

Friday 11/1: The Rocket Equation -- use conservation of momentum. Rotational Motion is really the same physics as Linear Motion -- we just change the co-ordinate system. Q14 take-home handed out. See Monday 11/4.

### Week of November 4-8, 2002.

Monday 11/4: Translating Linear physics to Rotational physics (as "easy" as changing Roman/English variables to Greek). 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.) Angular position, angular velocity, angular acceleration, angular force = torque. Q14 Take-Home, now due Wednesday 6 November 2002. Hand out first Sample Exam 3 problems (plus the leftovers from Exam 2 on collisions and momentum conservation).

Tuesday 11/5: Connecting the linear and rotational motion: Problem of a car at rest accelerating to final speed, tires not slipping. Force applied perpendicular to a radius line from the axis of rotation. Why we need a "rotational mass": Example of Ice Skater. Moment of Inertia. The Cross Product and Right-Hand Rule (R.H.R.).

Wednesday 11/6: Moment of Inertia of a long thin rod: (1) axis about center of mass, (2) axis about end. A ring must have I = MR².

Thursday 11/7: Exam 2 Returned.

Friday 11/8: Moment of Inertia by Integration, Double- and Triple-Integrals in Rectangular, Polar, Cylindrical and Spherical Co-ords. Moment of Inertia of Ring, Solid Disk, Solid Cylinder.

### Week of November 11-15, 2002.

Monday 11/11: Moment of Inertia of Solid Disk, Hollow Sphere, Solid Sphere.

Tuesday 11/12: Rotational K.E., Rolling objects down an incline. Q15 Take-Home due.

Wednesday 11/13: 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.

Thursday 11/14: More Statics Examples (see-saw/teeter-totter, ladder), "The Best Angular Momentum Story Ever". Q16 Take-Home, due Monday 18 November 2002.

Friday 11/15: AV clips: NASA Skylab Missions. Parallel Axis Theorem.

### Week of November 18-22, 2002.

Monday 11/18: Elastic Deformation. Stress, Strain. Review Exam 3 star problems. Last day to turn in Draft papers for free evaluation (not required) by 5pm.

Tuesday 11/19: Exan 3.

Wednesday 11/20: Young's Modulus. Tension, Compression. Simulating years of service of a device by cycling under load.

Thursday 11/21: Shear Modulous, Bulk Modulus. Pre-Stressed Concrete.Oscillatory Motion. Revisit Mass on a spring. F = -kx = ma. Generates a 2nd Order Differential Equation - 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. Topic 1 papers due starting today. (Last day to turn in without penalty, unless you had a Draft paper evaluation, is Monday 11/25 by 5pm.)

Friday 11/22: 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). Q18 take-home quiz, due Monday 25 November 2002.

### Week of November 25-29, 2002.

Monday 11/25: Uniform Circular Motion (U.C.M.) as two S.H.O.'s (x- and y-components). Damped Oscillations (underdamped, critically damped and overdamped) and Driven Oscillations. Short film on the Tacoma Narrows Bridge.

Tuesday 11/26: 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). 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). 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. Bernoulli's Equation and the Continuity Equation. Water Tower and the Faucet Problem. Why the water tower needs a vent. 1st Sample Final Exam. Q19/20 take-home quiz, now due Tuesday 3 December 2002.

Wednesday 11/27: WMU closes at Noon. Our class meets at 2pm. You're an advanced math student -- do the math.

Thursday 11/28: It's Thanksgiving. Go eat something. Be Thankful.

Friday 11/29: No classes.