## Lectures in PHYS-205 (12)

Updated: 18 April 2003 Friday.

### Week of April 14-18, 2003.

Monday 4/14: 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. S.H.O. & S.H.M. Simple Pendulum. Q19 take-home quiz, now due Tuesday 15 April 2003.

Tuesday 4/15: 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). Damped harmonic oscillators. Q20 tak-home quiz, due Wednesday 16 April 2003.

Wednesday 4/16: Q1 (Part III of III) (5000 points automatically for participating.) Handout: "The Lost Lectures"

Thursday 4/17: 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. Volume Expansion of Solids and Liquids. 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 18 April 2003. Q23 THE LAST QUIZ take-home quiz, due at Your Final Exam.

Friday 4/18: THE LAST CLASS. Demo: 2-liter bottle of water with holes drilled in the side. Review.

### Week of January 6-10, 2003.

Monday 1/6: OFFICE DAY. No Classes.

Tuesday 1/7: Class begins. Distribute syllabus. The nature of studying Physics. Science education in the United States.

Wednesday 1/8: Q1 (Part I of III) (5000 points automatically for participating.)

Thursday 1/9: 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. First Equation: Speed = Distance / Time.

Friday 1/10: Development of Speed equation for Constant or Average Speed. 60 m.p.h. = "A Mile A Minute". (1848: The Antelope)

### Week of January 13-17, 2003.

Monday 1/13: The P-O-R (Press-On-Regardless) road rally problem. "You can't average averages." SI Metric System. Q2 in-class.

Tuesday 1/14: SI vs. mks and cgs metric systems. "Units will save your life." Dr. Phil's Reasonable Significant Figures. 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.

Wednesday 1/15: Q1 (Part II of III) (5000 points automatically for participating.)

Thursday 1/16: A simplified trip to the store. Acceleration. Physics misconceptions. Integrating to find the set of Kinematic Equations for constant acceleration. Kinematic Equations for Constant Acceleration. The Equation Without Time -- Avoiding the Quadradic Formula.

Friday 1/17: What is "1 m/s²"? You cannot accelerate at 1 m/s² for very long. So far we are doing motion in just one dimension. But that one direction can be vertical instead of horizontal. All objects near the surface of the Earth, in the absence of air resistance, fall and accelerate at the same rate, g = 9.81 m/s². That's nearly ten times the rate from before! (No wonder it hurts to fall out of a tree -- you get going really fast very quickly.) Jerk is a change in the acceleration.

### Week of January 20-24, 2003.

Monday 1/20: Dr. Martin Luther King, Jr. memorial observance [No Class Today]

Tuesday 1/21: Continuing with the Kinematic Equations for constant acceleration. (Acceleration down a rifle barrel.) The consequences of Falling Down...

Wednesday 1/22: ...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. (The guy with the fedora and the cigar.) First set of Sample Exam pages for Exam 1. (Solutions will NOT be provided for these handouts.) Q3 in class.

Thursday 1/23: 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°. Second set of Sample Exam pages for Exam 1. Q4 in class. NOTE: No Thursday afternoon office hours.

Friday 1/24: 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. Q5 Take-Home Quiz, Due Monday 27 January 2003 by 5pm.

### Week of January 27-31, 2003.

Monday 1/27: [Recall, I asked you to find my acceleration when I got off the roof that time...] Finding the final vector velocity of The guy with the fedora and the cigar problem. Q5 due by 5pm.

Tuesday 1/28: Sample Star Problems. What we already know about Ballistics. You cannot jump a gap without some postive v-naught-y. Q5 now due Tuesday by 5pm.

Wednesday 1/29: Exam 1.

Thursday 1/30: Ballistic Motion. 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.

Friday 1/31: Movie clip: Speed (You have to have some positive v0y if you want to jump a gap -- even with a bus.). Demo: Monkey Hunter problem.Classic pursuit problem: Two cars (1st v=constant, 2nd a=constant), same place at same time (2 solutions! t=0 is a solution!). Q6 take-home quiz, due Tuesday 4 February 2003. (Click here for a copy.)

[Still haven't gotten people to find my acceleration.]

### Week of February 3-7, 2003.

Monday 2/3: 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. Space Shuttle in Low-Earth Orbit. Q6 take-home quiz, still due Tuesday 4 February 2003.

Tuesday 2/4: UCM continued. Space Shuttle in Low-Earth Orbit (There's still gravity up there!). Q6 take-home now due Wednesday 5 February 2003.

Wednesday 2/5: Relative motion (Classical Relativity): Headwind, tailwind, crosswind examples. Problem of motor boat crossing a river with a current. Q7 in-class.

Thursday 2/6: Ballistic problem: Dropping "rescue supplies" from an airplane. 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.

Friday 2/7: 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. 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.). 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.)

### Week of February 10-14, 2003.

Monday 2/10: More pushing the 125 kg crate 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. 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. 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.

Tuesday 2/11: Exam 1 returned. Q8 in-class.

Wednesday 2/12: ***Unofficial SN*W Day*** Dr. Phil apologizes for being unable to get down to Kalamazoo due to weather, roads and the snow in his driveway that took two hours to dig out from under. These things happen.

Thursday 2/13: Atwood's Machine: Two masses, one pulley, one cable = two problems linked together with same magnitude of speed and acceleration. 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. 1st Sample Exams for Exam 2 handed out.

Friday 2/14: Continue with tilted x'-y' coordinates, block sliding down the inclined plane. [Something to consider: 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.] 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. Example: NASA's VC-135 "Vomit Comet", which flies in parabolic arcs to gain about 30 seconds of free-fall at a time for experiments and training. Quiz 9 take-home, due Tuesday 18 February 2003.

### Week of February 17-21, 2003.

Monday 2/17: [President's Day -- NOT a WMU holiday -- Classes will meet] 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. 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.

Tuesday 2/18: Friction continued. Friction and our crate problem: Now have to TEST static friction, if at rest, to see if we even move. Inclined plane problem: Static friction can be anything up to ±maximum value. Revisiting UCM, now with the Centripetal Force, using F=ma. The Centrifuge and possible reasons why people talk of a "centifugal force" -- No such thing as Centrifugal Force. Why old-timers talk about "getting flung safely from a wreck". Quiz 9 take-home, due Tuesday 18 February 2003.

Wednesday 2/19: The story of the 50,000 rpm Ultra-Centrifuge and the Fresh Rat's Liver. The need for "Artificial Gravity" using UCM in long duration space missions. Q10 in-class.

Thursday 2/20: Centripetal Force. Examples: Minimum radius for safe turns at given speed v (level ground with friction, banked curved without friction). 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. Q11 take-home, due Friday 21 February 2003.

Friday 2/21: 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: Dr. Phil is considering moving Exam 2 from Wednesday 26 February 2003 to Thursday 27 February 2003 to give everyone an extra day of studying. This would inconvenience those students who unilaterally decided that Spring Break starts before our Thursday class. Q11 take-home due (today) Friday 21 February 2003 by 5pm.

### Week of February 24-28, 2003.

Monday 2/24: 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.). Work & Energy continued. Dot products: run through two 3-dimensional vector case. 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. IMPORTANT NOTE: Exam 2 moved from Wednesday 2/26 to Thursday 2/27.

Tuesday 2/25: 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. Power = Work / time. Q12 take-home, due Tuesday 25 February 2003.

Wednesday 2/26: 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. Work done by non-conservative forces, like friction.

Thursday 2/27: Exam 2 moved to THURSDAY from WEDNESDAY.

Friday 2/28: WMU Spirit Day [No Classes Today] [Effective Start to Spring Break]

### Week of March 3-7, 2003.

[SPRING BREAK - NO CLASSES THIS WEEK]

### Week of March 10-14, 2003.

Monday 3/10: Linear momentum: p = m v. This is a vector. More 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.

Tuesday 3/11: Three example collisions: head-on, rear-end, 2-D. What happens in a wreck. How airbags work. Q14 Take-Home, due Thursday 13 March 2003.

Wednesday 3/12: Totally Elastic Collisions. Close approximations: The Executive 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.

Thursday 3/13: Explosions = Backwards Collisions. Recoil. The Ballistic Pendulum (Inelastic Collision followed by Conservation of TME). The Rocket Equation -- use conservation of momentum.

Friday 3/14: Return X2. Q14 now due today, Friday 14 March 2003.

### Week of March 17-21, 2003.

Monday 3/17: Finish up Rocket Equation and discussion of why we use multi-stage rockets. 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. 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.

Tuesday 3/18: 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. Q15 in-class.

Wednesday 3/19: Demo: The toy that "rolls uphill" -- actually, whether with the cylinder or the double-cone, the center of mass is going downhill. 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.

Thursday 3/20: Newton's 3 Laws of Motion applied to rotations. Rotational Work, rotational K.E., angular momentum. Why we need a "rotational mass": Example of Ice Skater. Q16 take-home. Due Monday 24 March 2003.

Friday 3/21: Moment of Inertia. The Cross Product and Right-Hand Rule (R.H.R.). Moment of Inertia of a long thin rod: (1) axis about center of mass, (2) axis about end.

### Week of March 24-28, 2003.

Monday 3/24: Moment of Inertia by Integration, Double- and Triple-Integrals in Rectangular, Polar, Cylindrical and Spherical Co-ords. Moment of Inertia of Ring, Solid Disk. Q16 now due Tuesday 25 March 2003.

Tuesday 3/25: Moment of Inertia by Integration, Double- and Triple-Integrals in Rectangular, Polar, Cylindrical and Spherical Co-ords. Moment of Inertia of Solid Cylinder, Hollow Sphere, Solid Sphere. Rotational K.E., Rolling objects down an incline. Q16 due today by 5pm.

Wednesday 3/26: Rotational K.E., Rolling objects down an incline (continued). The Race.

Thursday 3/27: Real pulleys vs. Perfect Massless Pulleys. The "Free Rotation Diagram". First day to turn in Topic 1 Papers. Q17 in-class.

Friday 3/28: 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.

### Week of March 31- April 4, 2003.

Monday 3/31: 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. 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 to integrate over layers to get the observed value of 9.81m/s².Topic 1 Papers due by 5pm for all Dr. Phil students, except those who had a Draft Paper evaluation.

Tuesday 4/1: Newton's Law of Universal Gravity (or Newton's Universal Law of Gravity, if you prefer). g(r). The Shuttle in Low Earth Orbit (Revisited). This closes the material that will be on Exam 3. (Young's Modulus, Stretching, Compression, Simple Harmonic Motion -- these are NOT on this Exam 3.)Some review problems.

Wednesday 4/2: Exam 3.

Thursday 4/3: Newton's Law of Universal Gravity. Tides (high/low, spring/neap). Planetary Orbits. Ptolemy to Copernicus to Johannes Kepler. Epicycles, elliptical orbits and Occam's Razor.

Friday 4/4: Extended Objects -- Allowing for Deformation. Young's Modulus. Tension, Compression. Simulating years of service of a device by cycling under load. Pre-Stressed Concrete.

### Week of April 7-11, 2003.

Monday 4/7: Shear Modulus, Bulk Modulus. 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). 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.

Tuesday 4/8: Why Boats Float (continued). 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. Q18 in class.

Wednesday 4/9: 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.

Thursday 4/10: Bernoulli's Equation and the Continuity Equation. Water Tower and the Faucet Problem. Why the water tower needs a vent. 1st Sample Final Exam.

Friday 4/11: X3 returned. DVD: Titanic Physics.