Dr. Phil's Home

Lectures in PHYS-2050 (17)

Updated: 03 July 2006 Monday.

Week of June 26-30, 2006.

Monday 6/26: LAST CLASS. 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. Return X3. Quiz 22 Take-Home, due at Final Exam (or by Friday 30 June 2006 at NOON).

Tuesday 6/27: FINAL EXAM. TWO HOURS: 2:00 to 4:00pm, 1110 Rood Hall.

Wednesday 6/28: Office Hours - Noon to 3pm.

Thursday 6/29: Not on campus today.

Friday 6/30: Office Hours - Noon to 3pm.

Monday 7/3: Grades due by NOON to Registrar. Do NOT call me in the morning.

Week of May 8-12, 2006.

Monday 5/8: 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). Distribute syllabus.

Tuesday 5/9: "Speed Limit 70" First Equation: Speed = Distance / Time. Development of Speed equation for Constant or Average Speed. Topic 1 assigned. (Searchable booklist available online here --or-- the entire handout in .pdf format here.)

Wednesday 5/10: No class.

Thursday 5/11: 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. A simplified trip to the store -- The S-Shaped Curve. Acceleration. Integrating to find the set of Kinematic Equations for constant acceleration. Kinematic Equations for Constant Acceleration. The Equation Without Time -- Avoiding the Quadradic Formula. Q1 and your PID number. (If you missed class on this day, check with Dr. Phil sometime soon.)

Friday 5/12: Dr. Phil's Reasonable Significant Figures. What do we mean by a = 1 meter/sec² ? You cannot accelerate at 1 m/s² for very long. Types of Motion: No Motion (v=0, a=0), Uniform Motion (v=constant, a=0), Constant Acceleration (a=constant). We generally cannot accelerate for very long. 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.) Q2 in-class quiz. Q3 Take-Home handed out.

Week of May 15-18, 2006.

Monday 5/15: NEWS: Saturday new World Record in 100m dash -- 9.76 seconds. 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." 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. 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.

Tuesday 5/16: 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. Finding the final vector velocity of The guy with the fedora and the cigar problem. Sample Star Problems. Q3 due by 5pm. Q4 take-home handed out, due Thursday 18 May 2006 by 5pm.

Wednesday 5/15: No class.

Thursday 5/18: Exam 1

Friday 5/19: 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. 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. (There's still gravity up there!). Q5 take-home handed out, due Tuesday 23 May 2006 by 5pm.

Week of May 22-26, 2006.

Monday 5/22: Classic Simple Pursuit (Cop and the Speeder). 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. Zeroeth Law - There is such a thing as mass. First Law - An object in motion tends to stay in motion, or an object at rest tends to stay at rest, unless acted upon by a net external force. Second Law - F=ma. Third Law - For every action, there is an equal and opposite reaction, acting on the other body. (Forces come in pairs, not apples.)

Tuesday 5/23: 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.). 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. First sample example pages for Exam 2. Q6 in-class. Q7 take-home, due Thursday 25 May 2006.

Wednesday 5/24: No class.

Thursday 5/25: Still waiting on solution to the Sign hanging from two cables. Atwood's Machine: Two blocks whose motion is link via a common cable and a pulley. 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. Change the co-ordinate system, change the rules. In the tilted x'-y' coordinates, this is a one-dimensional problem, not two-dimensional. 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.

Friday 5/26: Tires rolling with friction on good roads -- this is static friction not kinetic friction because the tires aren't sliding on the pavement. Linear momentum: p = m v. This is a vector. 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. 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. Q8 in-class. Q9 Take-Home, due Tuesday 30 May 2006.

Week of May 29 - June 2, 2006.

Monday 5/29: MEMORIAL DAY. No classes.

Tuesday 5/30: 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. How airbags work. 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). The Rocket Equation -- use conservation of momentum.

Wednesday 5/31: No class.

Thursday 6/1: 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). 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.). 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".NOTE: Exam 2 has been moved to Monday 5 June 2006. Quiz 10 ended up as a Take-Home, due Friday 2 June 2006.

Friday 6/2: Potential Energy: Storing energy from applied work for later. Gravitational P.E. = mgh. 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. 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. Review for Exam 2. Quiz 11 take-home, due Tuesday 6 June 2006.

Week of June 5-9, 2006.

Monday 6/5: Exam 2 today!

Tuesday 6/6: Power = Work / time. Resistive Forces: 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. 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". The need for "Artificial Gravity" using UCM in long duration space missions. 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.). Quiz 12 Take-Home, due Thursday 8 June 2006.

Wednesday 6/7: No class.

Thursday 6/8: The story of the 50,000 rpm Ultra-Centrifuge and the Fresh Rat's Liver. Centripetal Force. Examples: Minimum radius for safe turns at given speed v (level ground with friction, banked curved without friction). 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. The problem of determining G and the mass of the Earth. The four fundamental forces in nature, from weakest to strongest: Gravity, Electromagnetism, Weak Nuclear Force, Strong Nuclear Force. g(r). The Shuttle in Low Earth Orbit (Revisited). Tides (high/low, spring/neap). First Sample Exam 3 handed out. Quiz 13 Take-Home, due Friday 9 June 2006.

Friday 6/9: 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. Newton's 3 Laws of Motion applied to rotations. Rotational Work, rotational K.E., angular momentum. Why we need a "rotational mass". Moment of Inertia. Moment of Inertia of a long thin rod: (1) axis about center of mass, (2) axis about end. Parallel Axis Theorem. Q14 Take-Home, due Tuesday 13 June 2006.

Week of June 12-16, 2006.

Monday 6/12: 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. 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. The Cross Product and Right-Hand Rule (R.H.R.). Real pulleys vs. Perfect Massless Pulleys. The "Free Rotation Diagram". 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. Second set of three Sample Exam 3's. Q15 Take-Home, due Thursday 15 June 2006. NOTE: Move Exam 3 to Friday 16 June 2006.

Tuesday 6/13: Moment of Inertia by Integration, Double- and Triple-Integrals in Rectangular, Polar, Cylindrical and Spherical Co-ords. 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. Conservation of Angular Momentum -- the ice skater spins. Extended Objects -- Allowing for Deformation. Young's Modulus. Tension, Compression.

Wendesday 6/14: No class.

Thursday 6/15: Extended Objects -- Allowing for Deformation. Young's Modulus. Tension, Compression. Simulating years of service of a device by cycling under load. Pre-Stressed Concrete. Shear Modulus, Bulk Modulus. Some review for X3. Q16 in-class. Q17 Take-Home, says it's due Friday 16 June 2006, but you can have til Monday if you want.

Friday 6/16: Exam 3.

Week of June 19-23, 2006.

Monday 6/19: 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. Physical Pendulum. Uniform Circular Motion (U.C.M.) as two S.H.O.'s (x- and y-components). Three Classical States of Matter: Solid, Liquid, Gas. Combinations: Condensed Matter (covers both Solids and Liquids) and Fluids (covers both Liquids and Gasses). Two Extreme States of Matter: Plasma (electrons stripped off, high temperature), Cryogenics (extreme cold, odd behavior).

Tuesday 6/20: 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. 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. Q18 in-class. Q19 Take-Home, due Thursday 22 June 2006.

Wednesday 6/21: No class, but special office hours: Noon to 3pm.

Thursday 6/22: 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. 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. Second set of Sample Final Exams. Double-Take-Home Q20+21, due Monday 26 June 2006.

Friday 6/23: 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). Hand out solution to X3. (Exam 3 will be returned on Monday.) All-Titanic Sample Final Exam.