Dr. Phil's Home
Updated: 30 April 2013 Tuesday.
Reminder that ICES Student Course Evaluations are available now online via GoWMU .
Monday 4/15: How does q1 know that q2 is there? -- "Action at a Distance" -- Gravity and the Electric Force are not contact forces. The mathematical construct of the Electric Field. E is not an observable quantity. (Side example: Methods of measuring speed v, do not directly measure speed v.) Electric Fields, E = k q / r² (E-field from one point charge) and FE = q E (Electric Force = charge times E-field the charge is emersed in). Maximum E-field in air, E-max. Electric Potential (Voltage). Spark gaps. Voltage can be measured, then used to find strength of E-field. SI units: E-field is (N/C) or (V/m) - both work. Charges tend to accumulate on long pointy things, which explains why church steeples get hit by lightning. Or why it's your fingertips which can get shocked when reaching for the light switch after walking on carpet in the wintertme. Last Day to turn in Topic 1 paper.
Tuesday 4/16: The Simplest Circuit: Battery, wires, load (resistor). Conductors (metals) versus non-conductors (insulators). Semi-Conductors sit in the middle. Sometimes they conduct and sometimes they don't. This means they act like a switch or valve, and this is the basis for the entire electronics semi-conductor industry. D.C. Electrical circuits. Ohm's Law. V=IR form. (Ohm's "3 Laws"). Power dissipated by Joule heating in a resistor. P = I V (3 forms of Power equation to with Ohm's "3 Laws").
Wednesday 4/17: The Simplest Circuit: Battery, wires, load (resistor). Series and Parallel Resistors. Two devices connected together in a circuit can only be connected two ways: series or parallel. In Series, same current, share voltage. Equivalent resistance is always larger. In Parallel, same voltage, share current. Equivalent resistance is always smaller. Resistor Network Reduction. The battery only "sees" an equivalent resistor, which controls its current. So we could (but won't) reduce a resistor network to a single equivalent resistance, go back and fill in the table for V = I R and then P = I V. In the example sketched in class, Resistor R1 sees the largest current and dissipates the largest amount of energy per second (Power in Watts). This means it is also the most vulnerable. Story of radio "repair" call from 4,000,000,000 miles. Electricity and Magnetism Together Can Create Light. The Great 19th Century Debate: Is Light a Particle or a Wave? (Wave-Particle Duality did not seem obvious at the time. Later on, deBroglie showed that even matter has both a wave and a particle nature.) Q13 Take-Home on Simple Circuits and Resistors, due on Friday 19 April 2013. (Click here for a copy.)
Monday 1/7: Class begins. The nature of studying Physics. Science education in the United States. Natural Philosophy. The Circle of Physics. "Speed Limit 70" First Equation: Speed = Distance / Time. In terms of variables, a classic three-variable equation: v = d / t .
Tuesday 1/8: To understand the underlying concepts we need to Simplify The Universe. Aristotle and the Greek Philosophers. Observation vs. Experiment - Dropping the book and the piece of paper (2 views). Theory and Measurement.
Wednesday 1/9: First Equation: Speed = Distance / Time. v = d/t . Development of Speed equation for Constant or Average Speed. delta-x = ´x = xfinal - xinitial = xf - xi , x = x0 + v t . Discussion of formula cards. Distribute Syllabus.
Thursday 1/10: Speed. 60 m.p.h. = "A Mile A Minute". It's a nice alliterative phrase and wasn't possible for Man to move at 60 mph until 1848: The Antelope, but it really isn't a special speed, just an accident of the English system of measurement. English system of measurement. SI Metric System. Prefixes. What do we mean by Measurements? "Units will save your life." What is "1 m/s"? We need a few benchmark values to compare English and SI Metric quantities. NOTE: English-to-Metric conversions will NOT, with two exceptions, be tested on in this course. 60 m.p.h. = 26.8 m/s. 1.00 m/s = slow walking speed. 10.0 m/s = World Class sprint speed (The 100 meter dash -- Usain Bolt is the current Olympic (9.683 seconds) and World (9.58 seconds) record holder.) 26.8 m/s = 60 m.p.h.. 344 m/s = Speed of sound at room temperature. 8000 m/s = low Earth orbital speed. 11,300 m/s = Earth escape velocity. 300,000,000 m/s = speed of light in vacuum (maximum possible speed).
Friday 1/11: Topic 1 assigned. (Updated Searchable booklist available online here .) Quiz 1 In-Class.
Monday 1/14: The P-O-R (Press-On-Regardless) road rally problem. "You can't average averages." Comments on Q1½ -- solution already posted on class webpage. Note that part (c) is just like the P-O-R problem. A simplified trip to the store -- The S-Shaped Curve. Acceleration. Physics Misconceptions: Things you think you know, are sure you know, or just assume to be true in the back of your mind... but aren't true. Aristotle was sure that heavier objects always fell faster than lighter objects, but we did a demostration on Tuesday which showed that wasn't always true. Example: You're driving a car. To speed up, you need to put your foot on the accelerator (gas pedal), so YES, you are accelerating -- True. To drive at a constant speed, you must still have your foot on the accelerator, so YES, you are accelerating -- Not True because constant v means a = 0. To slow down, you must take your foot off the accelerator and put it on the brake pedal, so NO, you are not accelerating -- Not True because v is changing, so a < 0 (negative). Just as the equation v = d / t is for constant or average speed, the equation a = delta-v / delta-t is for constant or average acceleration. Finding the set of Kinematic Equations for Constant Acceleration.
Tuesday 1/15: PTPBIP - Putting The Physics Back Into The Problem. Handout on (1) Prefixes for moving the decimal place for larger and smaller powers of ten in the SI metric system, (2) Scientific Notation, as in 1.23 × 1012 and using the "EE" key on your calculator, and (3) Dr. Phil's Simplified Significant Figures for multiplication, division and trig functions. (Click here if you need a copy.) Finding the set of Kinematic Equations for Constant Acceleration. The Equation Without Time -- Avoiding the Quadradic Formula. To aid in setting up problems with the kinematic equations, you might try to list all six kinematic variables (x0, x, v0, v, a and t) and give the values for those you know, those you don't know and those you want to find out. This will help you choose which kinematic equation(s) you'll need. 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.
Wednesday 1/16: Return Q1½. Finish car acceleration problem from yesterday -- t = 19.03 sec. Problem: A rifle bullet is fired from rest to faster than the speed of sound, 415 m/s, in a distance of 1.00 m. Find a. Answer, a = 86,110 m/s². This is huge, which is why we don't fire people out of rifle barrels. Find t = 0.004819sec. Again, we could solve for t using two different equations, but will still get the same result because there is one Physics. To aid in setting up problems with the kinematic equations, you might try to list all six kinematic variables (x0, x, v0, v, a and t) and give the values for those you know, those you don't know and those you want to find out. This will help you choose which kinematic equation(s) you'll need. Free-Fall: If we ignore air resistance, all objects near the surface of the Earth fall towards the Earth at the same rate. ay = -g ; g = 9.81 m/s². That's nearly ten times the acceleration a = 1 m/s² we just talked about. With these two known accelerations, we can now have something to compare our accelerations a. How much acceleration can a human take? See story of Scott Crossfield below.
|t (seconds)||v = a t (m/sec)||x = ½ a t² (meters)|
Thursday 1/17: Prepping for 2-D Motion: We can look at motion in 1-dimension in different directions. We usually use x in the horizontal. y can either be another horizontal dimension or in the vertical. We can rewrite the Kinematic Equations for constant acceleration for x or y. It turns out that if x and y are perpendicular to each other, then they are independent, so we will be able to break down 2-D motion into two 1-D motion problems. Free-Fall: If we ignore air resistance, all objects near the surface of the Earth fall towards the Earth at the same rate. ay = -g ; g = 9.81 m/s². That's nearly ten times the acceleration a = 1 m/s² we talked about last week. With these two known acceleratoins, we can now have something to compare our accelerations a. Rewriting the Kinematic Equations for motion in the y-direction, pre-loading them for free-fall. Example: Falling off a ten-foot roof (3.00 meters). The consequences of Falling Down... ...and Falling Up. The Turning Point ( vy = 0, but ay = -g during whole flight). The illusion of "hanging up there in the air" at the turning point.
Friday 1/18: Quiz 2 in-class.
Monday 1/21: MLK Day to Honor Dr. Martin Luther King, Jr. -- Classes Do Not Meet at WMU -- University-wide activities.
Tuesday 1/22: The consequences of Falling Down... ...and Falling Up. The Turning Point ( vy = 0, but ay = -g during whole flight). The illusion of "hanging up there in the air" at the turning point. Motion in Two-Dimensions: You may be able to break it down into two one-dimensional problems, connected by time, which you can already solve. Example: The guy with the fedora and the cigar. There are 6 variables from the first dimension (x0, x, v0x, vx, ax, t), but only 5 from the second (y0, y, v0y, vy, ay), because time is the same. Remarkably, with a couple of reasonable assumptions, there are only 3 unknown variables (v0x, t, vy). Time links the two one-dimensional problems together. We need to find v0x , but we don't know the time. So we can find the time it takes to fall from the top of the building in the y-problem, then use that in the x-problem.
A slice of Pi at ConFusion 2013. (Click on photo for larger.) ©2013 Dr. Philip Edward Kaldon (All Rights Reserved)
Wednesday 1/23: Another problem solved by using two linked 1-D problems: Classic Simple Pursuit (Cop and the Speeder). Starting from rest, the contant accelerating cop ends up with a final speed twice that of the uniform motion speeder -- because they both have to have the same average speed (same place, same time). There are two times when they are in the same place and the same time -- the other solution is at t=0. Two kinds of numbers: Scalars (magnitude and units) and Vectors (magnitude, units and direction). Compass directions (N, S, E, W, NE, SE, SW, NW).
Thursday 1/24: (Apologies for being late to class due to excessive number of accidents on the icy roads.) Return Q2. Demo these class web pages. Look at Sample Exam 1s. Discuss how to use the mph and sec/mile chart seen in the multiple-guess problems.
2nd and 4th wrecks of the day -- drive careful out there! (Click on photos for larger.)
Friday 1/25: Quiz 3 in-class.
Monday 1/28: Two kinds of numbers: Scalars (magnitude and units) and Vectors (magnitude, units and direction). Adding and subtracting vectors: Graphical method. To generate an analytical method, we first need to look at some Trigonometry. Right Triangles: Sum of the interior angles of any triangle is 180°, Pythagorean Theorem (a² + b² = c²). Standard Angle (start at positive x-axis and go counterclockwise). Standard Form: 5.00m @ 30°. Practical Trigonometry. SOHCAHTOA. Adding and subtracting vectors: Analytical method. (Check to make sure your calculator is set for Degrees mode. Try cos 45° = sin 45° = 0.7071) Why arctangent is a stupid function on your calculator. Examples: vector C = vector A + vector B, vector D = vector A - vector B. Dr. Phil's Method uses a table you fill out with the x- and y-components, to allow you to easily add or subtract the columns. Then use your sketch to check your work. Q4 Take-Home on Vector Addition, due on Wednesday 30 January 2013.
Tuesday 1/29: Finishing vector problems: (1) Examples: vector C = vector A + vector B. (For studying, you might try to find vector D = vector A - vector B). (2) Finding final velocity of problem with the guy with the fedora and the cigar in Standard Form. Ballistic or Projectile Motion 2-D problem where ax = 0 and ay = -g. Covers anything shot, thrown or kicked into the air which is unpowered and where we can ignore air resistance. Ancient cannons. We can always use the Kinematic Equations, but we can also derive specialized equations: Max Height, h = v0² sin² ¸ / 2 g .
Wednesday 1/30: Return Q3. Ballistic or Projectile Motion 2-D problem where ax = 0 and ay = -g. Covers anything shot, thrown or kicked into the air which is unpowered and where we can ignore air resistance. Ancient cannons. We can always use the Kinematic Equations, but we can also derive specialized equations: Max Height, Time to Max Height, Range Equation. Two Dangerous Equations. You can only use the Range Equation if the Launch Height = Landing Height. But the sin (2 θ) 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° - θ) that gives the same range (but a different time and height). High and low trajectories for Range Equation.
Thursday 1/31: WMU Closed Today -- Classes Canceled.
Friday 2/1: Exam 1 MOVED to TUESDAY 5 February 2013. Cannonball example: if v0 is 100. m/s @ 30° and lands at launch height, y = y0. Find range R, height h, time of flight t -- note that the latter is for the full flight. What changes if you use the complementary launch angle of 60°? Types of Motion: No Motion (v=0, a=0), Uniform Motion (v=constant, a=0), Constant Acceleration (a=constant). Uniform Circular Motion (UCM): speed is constant, but vector velocity is not; magnitude of the acceleration is constant, but the vector acceleration is not. Velocity is tangent to circle, Centripetal Acceleration is perpendicular to velocity and points radial INWARD. ac = v²/r. You can generate very large centripetal acclerations very quickly.
Monday 2/4: (Apologies for being late to class due to slow speeds on the icy roads. 2½ hours isn't a record, but it's up there.) Types of Motion: No Motion (v=0, a=0), Uniform Motion (v=constant, a=0), Constant Acceleration (a=constant). Uniform Circular Motion (UCM): speed is constant, but vector velocity is not; magnitude of the acceleration is constant, but the vector acceleration is not. Velocity is tangent to circle, Centripetal Acceleration is perpendicular to velocity and points radial INWARD. ac = v²/r. You can generate very large centripetal acclerations very quickly. Space Shuttle in Low-Earth Orbit. (There's still gravity up there!) Comments on Free Fall vs. "zero gravity" in space.
Tuesday 2/5: Exam 1. (Rescheduled from 2/1.)
Wednesday 2/6: Demo: Rodney Reindeer and U.C.M. The moment the centripetal acceleration is zero, Rodney travels ballistically with an initial velocity that is the last tangential velocity. Examples: A hard disk drive spinning at 3600 rpm (60 times a second, time for one revolution = 1/60th of a second). The guard around a circular saw blade takes the sawdust and broken bits which shoot out tangentially from the blade and redirects them to a bucket -- improves safety and makes less of a mess. 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. (Reeding on the edge of the silver shilling or a U.S. dime/quarter.) (Mad as a hatter -- from mercury poisioning.)
Thursday 2/7: Newton's Three Laws of Motion: Zeroeth Law - There is such a thing as mass. First Law - An object in motion tends to stay in motion, or an object at rest tends to stay at rest, unless acted upon by a net external force. Second Law - F=ma. Third Law - For every action, there is an equal and opposite reaction, acting on the other body. (Forces come in pairs, not apples.) SI unit of mass = kilogram (kg). SI unit of force = Newton (N). English unit of force = pound (lb.). English unit of mass = slug (Divide pounds by 32. For English units, g = 32 ft/sec².). Force is a vector.
Friday 2/8: Quiz 5 in-class.
Monday 2/11: Newton's Three Laws of Motion. SI unit of mass = kilogram (kg). SI unit of force = Newton (N). English unit of force = pound (lb.). English unit of mass = slug (Divide pounds by 32. For English units, g = 32 ft/sec².). Force is a vector. Free Body Diagrams. Normal Force (Normal = Perpendicular to plane of contact). The normal force does NOT automatically point up and it is not automatically equal to the weight -- we have to solve for the normal force. "The Normal Force is NOT automatically present -- you have to be in contact with a surface. The Normal Force does NOT automatically point up -- FN is perpendicular to the surface. The Normal Force is NOT automatically equal to the weight. FN = mg only if there are no other forces in the y-direction." Sum of forces in x or y equations -- either will be equal to 0 (Newton's 1st Law) or ma (Newton's 2nd Law). Example of 125 kg crate being dragged/pushed around. (Near the surface of the Earth, you can use the relationship that 1 kg of mass corresponds [not "equals"] to 2.2 lbs. of weight. So multiple 125 by 2 and add 10%... 250 + 25 = 275... so a 125 kg crate has a weight of mg = 1226 N or 275 lbs.). Variations as we allow for an applied force that it at an angle. Push down and Normal Force increases; pull up and Normal Force decreases -- though it cannot go negative. "You can't push on a rope." Since the force from a wire/string/rope/chain/thread/etc. can only be in one direction, Dr. Phil prefers to call such forces T for Tensions rather than F for Forces.
Tuesday 2/12: "You can't push on a rope." Since the force from a wire/string/rope/chain/thread/etc. can only be in one direction, Dr. Phil prefers to call such forces T for Tensions rather than F for Forces. Simple pulleys (Massless, frictionless, dimensionless, only redirect the forces). "There is no free lunch." The bracket for the pulley will have to support a force greater than the weight of the hanging object. Mechanical advantage: multiple pulleys allow us to distribute the net force across multiple cables or the same cable loop around multiple times. Tension in the cable is reduced, but you have to pull more cable to move the crate. 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. Article on the 1945 crash of a B-25 bomber into the Empire State Building and subsequent elevator free fall.
Wednesday 2/13: 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. 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. Discussion of guy wires to help support a very tall antenna. Atwood's Machine -- two masses connected by a single cable via a simple pulley. They share a common acceleration, a, with one mass going up and the other going down. More Elevator Comments. The Normal Force represents the "apparent weight" of the person in the elevator. Like Atwood's Machine, we can hang a counterweight on a cable and a pulley and support all or some of hte weight of the elevator. The elevator will go one way and the counterweight will go the other way.
Thursday 2/14: Return X1. Two kinds of Friction: Static (stationary) and Kinetic (sliding). For any given contact surface, there are two coefficients of friction, µ, one for static (µs) and one for kinetic (µk). Static is always greater than kinetic.
Friday 2/15: Quiz 6.
Monday 2/18: 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. Inclined plane with and without friction. Finding the coefficient of static friction by tilting: μs = tan(θmax). Similar for kinetic friction, except one has to tap the board to "break the static friction barrier". Rubber on concrete. Can μ be greater than 1? Means θmax greater than 45° -- rare, but yes. Anti-Lock Brakes and Traction Control. ABS works by monitoring the rotation of all four wheels. If one wheel begins to "lose it" and slip on the road while braking, it will slow its rotation faster than the other tires, so the computer releases the brake on that wheel only until it is rolling without slipping again. This can be done many times a second, much faster than the good old "pump your brakes to stop on ice" trick older drivers are familiar with. Traction control uses the ABS sensors to monitor the wheel slip during acceleration -- keeps the wheels from spinning.
Tuesday 2/19: Dr. Phil canceled drive in and office hours due to slippery conditions + crosswinds. Prof. Michael Famiano came in to pinch hit and do some friction problems.
Wednesday 2/20: We are not done with Forces, but some problems cannot easily be solved by using forces. Collisions, for example, are very complex if we have to put in all the forces of bending and breaking and mashing things. Need a simpler way of looking at the problem. "Inertia" is a word which isn't used much today, but it is the same as "momentum" -- represents some kind of relentless quality of movement. It takes a force to change the momentum, otherwise it just continues on, i.e., Newton's 1st Law. Linear Momentum ( p = mv ) is a vector quantity. Newton's form of the 2nd Law: F = δp / δt = change in momentum / change in time instead of F=ma, but really the same thing. Impulse Equation: δp = F δt .Two extremes in collisions: Totally Elastic Collision (perfect rebound, no damage) and Totally Inelastic Collision (stick together, take damage). Linear momentum is conserved in all types of collisions . Totally Inelastic Collisions. Example: The Yugo and the Cement Truck with numbers. Real Head-On collisions.
Thursday 2/21: Linear momentum is conserved in all types of collisions .Three example collisions: Head-on Collisions. Rear-end Collisions. (The Non-Collision -- if the car following is going slower, it isn't going to run into the car ahead. PTPBIP.) 2-D Side Impact (vector) collision. Real crashes. Interactions of safety systems: Seat belts, shoulder belts, steel beams in doors and crumple zones. The myth of it being better to be "thrown clear from the wreck". What happens in a wreck.
Quiz 7. Course Reset... Discussion and Q&A
session of problems and communications issues in PHYS-1070 this semester.
Monday 2/25: An explosion. Or recoil. Example: A clown on roller skates at rest -- when he hurls a pie to the left, he goes to the right. Total momentum of the system remains constant (in this case, zero). We've talked about How things move (Kinematic Equations) and Why things move (Forces, momentum). Now we want to talk about the Effort to make things move (Work and Energy). Work: A Physics Definition (Work = Force times distance in the same direction). Work = Energy. SI units: (N)(m) = (kg·m²/s²) = (Joule) = (J). 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.
Tuesday 2/26: Return Q6. Work: A Physics Definition (Work = Force times distance in the same direction). Work = Energy. Power = Work / time. Kinetic Energy -- an energy of motion, always positive, scalar, no direction information. Work-Energy Theorem (net Work = Change in K.E.). Using the Work-Energy Theorem to find a final speed. Potential Energy: Storing energy from applied work for later. Gravitational P.E. = mgh. Location of h=0 is arbitrary choice. Conservation Laws are very important in Physics. Conservation of Total Mechanical Energy (T.M.E. = K.E. + P.E.). Lose angle and directional information because energy is a scalar, not a vector. We can change height for speed and vice versa. Conservation of T.M.E. (P.E. + K.E.) on a roller coaster. Total energy limits maximum height. If speed at top of the first hill is about zero, then this P.E. is all we have. Cannot get higher, but we can change height for speed.
Wednesday 2/27: Demo: a suspended bowling ball shows conservation of T.M.E. All P.E. when swings up to a stop on either side, all K.E. at bottom of swing. (There must be non-conservative forces, such as air resistance and friction in the pivot point on the ceiling -- because the bowling ball never quite gets up as high as it starts.) Totally Elastic Collisions:-- perfect rebound, no damage, conserve both momentum and K.E. The equations get messy because each object has both an vi and a vf. Worse, momentum is a vector and can have components, while K.E. is a scalar and a square (½mv²). Two special cases: (1) m1 = m2 , v2i = 0, so v2f = v1i and v1f = 0. All the momentum and K.E. transfer from object 1 to object 2. (2) m1 = m2 , v1i = - v2i , so they just bounce off each other and go the other way. Close approximations, Demo: The Executive Time Waster. Why you want inelastics collisions in a wreck. 5 mph versus 3 mph impact bumpers.
Thursday 2/28: Exam 2.
Friday 3/1: WMU SPIRIT DAY -- No Classes.
SPRING BREAK -- NO CLASSES.
Monday 3/11: Work = Energy. Power = Work / time. Power is rate that work can be done. 1 horsepower = 1 h.p. = the amount of work that one man, one horse and one plow can do in a day. An engine with "more power" can either do the same work in less time, or do more work. Conservation of T.M.E. (P.E. + K.E.) on a roller coaster. Total energy limits maximum height. If speed at top of the first hill is about zero, then this P.E. is all we have. Cannot get higher, but we can change height for speed. The Loop-the-Loop on the roller coaster requires that there be sufficient speed v (or K.E.) such that we meet the conditions of Uniform Circular Motion at the top. The minimum speed occurs when the downward pointing normal force from the track on the upsidedown cars goes to zero, and the centripetal force, Fc = mac = mv²/r , comes only from the weight, w = mg. Remember, that the centripetal force is a NET force, i.e., F = ma is Newton's 2nd Law, so the net external force goes on the right side of the sum of forces equations. Example: Rollercoaster with h1 = 30.0 m, v1 = 0, h2 = 0 (bottom of loop-the-loop), h3 = 12.0 m (top of loop-the-loop, making D = 12.0 m and r = D/2 = 6.00 m). Results: v2 = 24.26 m/s, v3 = 18.79 m/s. v3 is well above the minimum speed to safely do the loop-the-loop (7.672 m/s from FN = 0 and mv²/r = mg )
Tuesday 3/12: 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. UCM Revisited. The Shuttle in Low Earth Orbit (Revisited). Calculating g(r) for r = 6,770,000 m (the radius of the Earth plus the height of 400 km for Low Earth Orbit), we get a value somewhat different than we found for the centripetal acceleration. Working backwards, we discover for this radius that the period T = 5542 sec and NOT the estimated 5400 sec (90 minutes) we had started with before. Newton's Law of Universal Gravity + U.C.M: Each radius of circular orbit has a different value of g(r). As r increases, v decreases and T increases. Orbital mechanics: Speed up and radius decreases, slow down and radius increases. For the Moon, the period is around 28 days at a quarter of a million miles away. Geosynchronous orbits occur when T = 1 day exactly, and for geosynchronous communications sattelites, the orbit must be directly over the equator -- hence all sattelite dishes in the U.S. face south.
Wednesday 3/13: Newton's Law of Universal Gravity and Tides (high/low, spring/neap). Water is more flexible than land, so it can be influenced by the weak gravitational forces from the Moon (a quarter million miles away) and the Sun (93 million miles away). We've asked: How do things move? (kinematics) Why do things move? (forces) What effort does it take to move? (work and energy) Now we ask -- What moves? Three Classical States of Matter: Solid, Liquid, Gas. Combinations: Condensed Matter (covers both Solids and Liquids) and Fluids (covers both Liquids and Gasses). Note than in the absense of chemical reactions, that the progression from Solid to Liquid to Gas for a material goes from lower temperatures to higher temperatures. Two Extreme States of Matter: Plasma (electrons stripped off, high temperature), Cryogenics (extreme cold, odd behavior).
Thursday 3/14: Return Q7, Q8. Extended Objects: Mass occupies a volume and shape. Mass-to-Volume Ratio (Density). NOTE: Do not confuse the Density of the Materials with the Mass-to-Volume Ratio of the OBJECT. Density of Water built into the SI metric system (1 gram/cm³ = 1000 kg/m³). Sea water is 1030 kg/m³ ; sugar water is 1060 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. Q9 Take-Home on Newton's Law of Universal Gravity, due on Monday 18 March 2013.
Friday 3/15: Return X2. Water is unusual in two ways: (1) Water is relatively incompressible. If the depth h isn't too deep, then the Mass-to-Volume ratio for water is constant. For great depths, such as the bottom of the oceans, we can't use our simple equation because rho is not constant. Air and gasses are compressible, so we can't use our pressure from a column of fluid equation either, though the air pressure here on the surface of the Earth is based on supporting the weight of the column of air above us. (2) The mass-to-volume ratio of ice (solid) is LESS than liquid water, so ice floats. Ice which floats doesn't add to volume of water when it melts, but grounded ice (non-floating) does. This is one of the reasons why people worry about what global warming might do to the great ice sheets around the world.
Monday 3/18: Archimedes and Eureka! (I found it!) Using mass-to-volume ratio and water displacement to determine if gold crown was solid gold or not. 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. Calculating the amount of the boat submerged, by using the fact that the mass of the boat and the displaced water are the same. Water is unusual in that the mass-to-volume ratio of ice (solid) is LESS than liquid water, so ice floats. Ice which floats doesn't add to volume of water when it melts, but grounded ice (non-floating) does. This is one of the reasons why people worry about what global warming might do to the great ice sheets around the world. Sinking of the RMS Titanic; Edmund Fitzgerald. Pressure = Force / Area. SI unit: Pascal (Pa). Example: Squeezing a thumbtack between thumb and forefinger. 1 Pa = 1 N/m², but Pascals are very small, so we get a lot of them. One Atmosphere standard air pressure = 1 atm. = 14.7 psi = 101,300 Pa.
Tuesday 3/19: Water is unusual in two ways: (1) Water is relatively incompressible. If the depth h isn't too deep, then the Mass-to-Volume ratio for water is constant. For great depths, such as the bottom of the oceans, we can't use our simple equation because rho is not constant. Air and gasses are compressible, so we can't use our pressure from a column of fluid equation either, though the air pressure here on the surface of the Earth is based on supporting the weight of the column of air above us. (2) The mass-to-volume ratio of ice (solid) is LESS than liquid water, so ice floats. Ice which floats doesn't add to volume of water when it melts, but grounded ice (non-floating) does. This is one of the reasons why people worry about what global warming might do to the great ice sheets around the world. Reset: One Atmosphere standard air pressure = 1 atm. = 14.7 psi = 101,300 Pa. Pressure at a depth due to supporting the column of liquid above. Absolute (total) Pressure vs. Gauge Pressure (difference between two readings). Pressure due to a column of water = 1 atm. at h = 10.33m = 33.86 feet. Absolute (total) Pressure vs. Gauge Pressure (difference between two readings). The perils of SCUBA diving. 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.
Wednesday 3/20: How to get liquid out of a cup using a straw -- or why Physics does not "suck", but pushes using a pressure difference. Smooth Fluid Flow: Pressure from a column of liquid looks like P.E. Create a Kinetic Pressure term which looks like K.E. and add in the base pressure for total pressure to create Bernoulli's Equation and the Continuity Equation. The Water Tower and the Faucet Problem. Why the water tower needs a vent.
Thursday 3/21: Bernoulli's Equation and the Continuity Equation. Want Smooth Continuous Flow, not Turbulent Flow or Viscous Flow. Flow rate = Volume / time = Cross-sectional Area × Speed. The faster the fluid flow, the lower the Pressure. Example: The aspirator -- a vacuum pump with no moving parts. Example: Air flow around a wing. (Faster air over top means lower pressure on top, so net force is up -- Lift.) Spoilers -- doors open in wing to allow air to pass between upper and lower surfaces, thus "spoiling the lift" by eliminating the pressure difference. Why the Mackinac Bridge has grates on the inside north- and soundbound lanes. 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).
Friday 3/22: 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 in free-fall, vs. being hit with a paddle in a world-class table tennis match. What is the terminal velocity of a falling person? It depnds on clothing and orientation -- aerodynamics, streamlining, cross-sectional area, composition of the air are all part of the drag coefficients b and c. World's Record Free-Fall (old). (NEW Sunday 10/14/2012) Problem: Spray can. (Inside: P1 = 200,000 Pa, v1 = 0, h1 = h2. Outside: P2 = 100,000 Pa. Find v2.) Problem: RMS Titanic is on the bottom of the Atlantic, about 2½ miles down. When James Cameron made his movie, he rode the Mir submersibles to the wreck. Find the speed of the water shooting into the sub if there is a leak. Find the water pressure at that depth. (P1 = P2, v1 (on surface) = 0, h1 = 3821 m, h2 = 0, ρseawater = 1030 kg/m³.) Actually the water pressure is higher, due to the fact that with hundreds of atmospheres of pressure, the seawater is slightly compressed and so the mass-to-volume ratio isn't constant, but increasing. Q10 Take-Home on Mass-to-Volume Ratio and Bernoulli's Equation, due Tuesday 26 March 2013. (Click here for a copy.)
Monday 3/25: 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).
Tuesday 3/26: 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. Linear Expansion: Why "Bridge Freezes Before Roadway" signs. Bridge expansion joints. Pavement expansion joints.
Wednesday 3/27: Linear Expansion: Pavement expansion joints. I-57 in Chicago and the expanding asphault in 1983. Question: Does the material expand into a hole when heated, or does the hole expand? (Think about what happens to the disk removed from the hole -- does it expand or contract when heated?) Volume Expansion of Solids and Liquids. Coefficient of Volume Expansion usually given for liquids; for solids, β = 3α. Ideal Gas Law (PV/T = constant or our form: P1V1/T1 = P2V2/T2) -- must use Kelvins for temp and absolute Pressures, because neither P or T can be zero or negative.
Thursday 3/28: 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. Q11 Take-Home on Expansion,
Monday 1 April 2013 Tuesday 2 April
2013. (Click here for a copy.)
Friday 3/29: Problem: A steel tea kettle has a volume of 2.00 L. At 20.0°C, is is half filled with water or 1.00 L. The kettle is sealed and heated to 80.0°C. Using the equatinon volume expansion, ²steel = 3±steel and ²water = 207 × 106 °C-1, find the new volume of the kettle and the volume of the water. Finally, consider the air sealed above the water. Initially, it's volume is 1.00 L, but at 80.0°C, the volume is less, because the water expands more than the kettle. Use P1V1/T1 = P2V2/T2 to find the final pressure, assuming the initial pressure was 101,300 Pa. Problem: 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. Find the heat energy Q to: (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, and estimate how long each of these steps take. Ice has a low specific heat, 2000 J/kg·°C-1, so ice very quickly warms up to the melting point. The latent heat of fusion for melting ice / freezing water is 336,000 J/kg. Wet ice is at T = 32°F = 0°C = 273K. The specific heat of water is 4186 J/kg·°C-1 = 1 Calorie (1 "Big C" Calorie = 1 Food Calorie). This is the energy it takes to raise the temperature of 1 kg of water by 1°C. (In the English system, we have the British Thermal Unit, where 1 BTU is the energy it takes to raise the temperature of 1 pound of water by 1°F. You see BTU ratings on air conditioners and furnaces, for example.) "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!
Monday 4/1: Heat content versus Thermal conductivity. Leidenfrost Effect. Thermodyanmics (Heat + Motion) -- Moving heat energy Q around. The Laws of Thermodynamics. Zeroeth Law -- There is such a thing as temperature. First Law -- Conservation of energy. Second Law -- One cannot extract useful work from a cyclic mechanical system without wasting some energy. Entropy examples -- It takes work to clean or restore things. Left to themselves, everything falls apart. The Heat Engine and Three Efficiencies (Actual, Carnot and 2nd Law).
Tuesday 4/2: The Heat Engine and Three Efficiencies (Actual, Carnot and 2nd Law). Fuel Economy (miles per gallon) is not an Efficiency. There is no conspiracy to keep big 100 m.p.g. cars out of our hands. To use less fuel, do less work. Reverse the arrows in the Heat Engine and you get a Refrigerator. NOTE: Cannot place an open refrigerator or a window air conditioner in the middle of a room and cool the room, because the exhaust heat to the hot side includes the heat pulled from the cold side plus the work done on the compressor.
Wednesday 4/3: Air conditioners and Heat Pumps. 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 λ (wavelength) and a Repeat Time T (Period). Frequency = 1/Period or f = 1 / T . Wave speed = frequency × wavelength ; v = f λ . The speed of sound in air: 334 m/s @ 0°C and 344 m/s @ 20°C. Waves and Resonance. Standing Waves on a string. Fundamental, First Overtone, Second Overtone, etc. Demonstration: the Slinky shows both longintudinal (string type) and transverse waves (sound type).
Thursday 4/4: Review. Topic 2 Worksheets (Click here for 1st Worksheet and Directions)
Friday 4/5: Exam 3.
Monday 4/8: Waves and Resonance continued. Standing Waves on a string. Fundamental, First Overtone, Second Overtone, etc. Demonstration: First and higher overtones on a string driven by a saber saw. (Can't see the Fundamental on the saber saw demo, because the tension required usually breaks the string.) Standing Waves in a tube. Demo: Getting Fundamental and overtones from twirling a plastic tube open at both ends. (Pink tube missing - tried to use a shop vac hose, too heavy, too slow.) Demo: Variable length organ pipe -- Fundamental and First Overtone (overblowing), varying pitch (musical note) by changing length of tube open at only one end. Tuning forks, resonance boxes. Musical instruments: Accoustic string instruments can change tuning by changing the tension of the string and the string itself can be shortened on the neck of violins, guitars, etc. Brass instruments start from the "natural trumpet", which can only play the fundamental and overtones for the pipe. Woodwind instruments get more complicated.
Tuesday 4/9: The range of "normal" human hearing: 20Hz-20,000Hz (10 octaves). Resonance boxes, accoustic guitars. Beat frequencies occur when two sounds have almost the same frequency -- get a distinctive wah-wah-wah sound, whose beat frequency = | f1 - f2 | . Takes time for sound to travel over a distance. Constructive and Destructive Interference. Acoustics of concert halls. The range of "normal" human hearing: 20Hz-20,000Hz (10 octaves). Artilleryman's ear -- mid-range hearing loss.
Wednesday 4/10: The speed of sound in air. Sonic Booms and other shockwaves. Bullwhip stories. Waves take time to travel. Sound takes time to travel. An echo takes times to get to the reflecting surface and travel back -- to and fro. The Realization that Electricity and Magnetism were part of the same Electromagnetic Force was a great triumph of 19th century physics. Greeks knew about static electricity -- build up charge and get sparks.
Thursday 4/11: The Two-Fluid Model of Static Electricity (A & B), to account for the two types of behavior noted. Franklin's One-Fluid Model of Electricity. Occam's Razor: If you can't decide between two competing ideas for how Nature works, take the simpler model. Real Electric Charges. Two charges: like charges repel, unlike (opposite) charges attract. Coulomb's Law looks like Newton's Law of Universal Gravity. 1 Coulomb of charge is an enormous amount of charge. Two 1.00 C charges separated by 1.00 meters have a force of nine-billion Newtons acting on each other. A Nickel coin has a mass of 5 grams, so about 1/10th of a mole. Find number of Coulombs of positive and negative charges. It's over 200,000 C! But... at the atomic level, each nickel atom has the same number of electrons and protons, so overall each atom and the whole nickel coin is charge neutral -- so not dangerous. Four Fundamental Forces in Nature: Gravity, E & M, Weak Nuclear Force, Strong Nuclear Force. The Hydrogen Atom. Gravity loses to Electric Force by a factor of 200 million dectillion (!!!). Q12 Take-Home on Standing Waves, due on Monday 15 April 2013. (Click here for a copy.) First Day to turn in Topic 1 paper.
Friday 4/12: Return X3. Four Fundamental Forces in Nature: Gravity, E & M, Weak Nuclear Force, Strong Nuclear Force. The Hydrogen Atom. Gravity loses to Electric Force by a factor of 200 million dectillion (!!!). Likewise, the two protons in the nucleus of the Helium Atom require the Strong Nuclear Force to overcome the 231 N electric repulsion. Isotopes are the same element (proton number Z), but with different numbers of neutrons (N). Some isotopes are stable, some are unstable and undergo radioactive decay. If we didn't have the Strong Nuclear Force making the Electric Force irrelevent inside the nucleus, then the only element in the universe would be hydrogen. Second Day to turn in Topic 1 paper.