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Updated: 01 May 2012 Tuesday · 6:30pm.
FINAL COURSE GRADES AND BREAKDOWN BY CATEGORY FOR PHYS-1000 Spring 2012. Estimated Pre-Finals Grades can be found here.
Reminder that ICES Student Course Evaluations are available now online via GoWMU .
Monday 4/23: Office Hours.
Tuesday 4/24: FINAL EXAM (2:45pm-4:45pm)
Wednesday 4/25: Office Hours.
Thursday 4/26: Dr. Phil does not plan on coming in today.
Friday 4/27: LAST DAY TO MAKE UP EXAMS.
Monday 4/30: Office Hours.
Tuesday 5/1: Grades due at Noon.
Monday 1/9: Class begins. Why are you here? "They" made you take this -- or at least a science course with a lab. Why? Science literacy. The nature of studying Physics. Science education in the United States. HOW THINGS WORK -- Macro/Gross versus Micro/Detailed analytical model. We're looking at the bigger picture. Much of what we know is Black Box stuff. (We can drive a car without knowning what those dark greasy shapes under the hood are.) (We can use a computer or a cellphone without knowing how to build a computer chip or program it.) "Speed Limit 70" -- what does it really mean? First Equation: Speed = Distance / Time. v = d/t . Physics - Numbers - Equations - Calculations. We can use the equations in Physics to (a) Predict the future (how far will this go?) or (b) "Predict" the past (where was this when it started? how fast was it going?) These are Powerful Tools
Wednesday 1/11: Distribute syllabus. Speed = Distance / Time. v = d/t . What is measurement? Systems of units need to have a Standard. Why the metric system? Because the old units don't make much sense in turns of numbers and conversions. In the metric system, once you've defined something, like The Meter is the standard unit of length, you can make larger or smaller units by the use of prefixes. A centimeter (cm) is 1/100th of a meter, while a kilometer (km) is 1000 meters.
Friday 1/13: The Simplest Types of Motion: (1) No motion. (v = 0) ; (2) Moving at a constant speed. (v = constant) ; (3) Moving with a changing speed. (v is not constant) What is "1 m/s"? We need a few benchmark values to compare English and SI Metric quantities. Converting Units: Multiply a number by "1", where the numbers in the top and bottom of the fraction represent the same quantity, just in different units, hence the fraction equals 1. So... 60 m.p.h. = ( 60 miles/hour ) × ( 1 hour / 3600 sec ) × ( 1609 m / 1 mile) = 26.8 m/s. A Table of m/s Comparisons: 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). Remember PTPBIP! Q1 and your PID number. Quiz 1 was given in-class on Friday 13 January 2012, for attendance purposes. If you missed class on that day, you will be able to get some of the points by downloading Quiz 1A from the website and turning it in. (Click here for a copy.) Topic 1 assigned. (Updated Searchable booklist available online here .)
NOTE: Monday 16 January 2012 is Dr. Martin Luther King, Jr. Day and while WMU holds no classes, there are many MLK Day activities going on around campus.
Monday 1/16: MLK Day to Honor Dr. Martin Luther King, Jr. -- Classes Do Not Meet at WMU -- University-wide activities.
Wednesday 1/18: Textbook example of Skating. Moving at a constant speed. INERTIA = Momentum. "A relentless quality of motion that it the result of an object having mass." External Forces push or pull on objects. Internal Forces hold objects together. Some stories about Sir Isaac Newton. Newton's Three Laws of Motion: Zeroeth Law - There is such a thing as mass. The Zeroeth Law represents the underlying assumption that the Three Laws require, in this case, that objects have mass, a measure of how much "stuff" (matter) they contain. 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. In real life, "an object in motion tends to slow to a stop" -- that's because there ARE external forces, such as friction, in play. If there is a change in speed, then we have an acceleration. Second Law - F=ma. 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).
Friday 1/20: Acceleration a = delta-v / delta-t -- a change in speed divided by the time. If we have an acceleration, then we must have an external force and vice versa. F=ma allows us to think about what is happening. If we want a larger acceleration, we need a bigger force. If you apply the same force to a smaller mass, we get a bigger acceleration. If we want the same acceleration for two objects, then the force will be larger or smaller if the mass is larger or smaller. Etc. Comparisons: 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. 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. Aristotle and the Greek Philosophers. Observation vs. Experiment - Dropping the book and the piece of paper (2 views)
Monday 1/23: 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. Since F = ma , then we get weight due to acceleration of gravity, w = mg. Note that weight is a force and weight is not the same as mass -- we only talk about kilograms and pounds interchangeably, because we only ever live near the surface of the Earth. 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.). The consequences of Falling Down... ...and Falling Up. The Turning Point (y = ymax , vy = 0, but ay = -g during whole flight). The illusion of "hanging up there in the air" at the turning point. When you fall back down to the original height, if you ignore air resistance, you are moving at the same speed as when you started falling up, just opposite direction. Q2 Take-Home quiz due Wednesday 25 January 2012 in class or by 5pm.
Wednesday 1/25: Two kinds of numbers: Scalars (magnitude and units) and Vectors (magnitude, units and direction). Velocity is the vector version of speed. Combining motion in the x (costant speed) and y (free fall) gives us Projectile Motion. The ojbect moves in a parabolic arc. High and low trajectories: (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). Example: Cannon shot at 100.m/s @ 30°. Same Range if launched at 60°, but the time of flight is longer for the 60°. 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.) What keeps a book from free falling when it comes in contact with the table? There is a Support or Normal Force from the table on the book -- leaving us with no net external force. (1st Law). Why should there be a Normal Force? Because the book is pushing on the table and the table is pushing on the book. (3rd Law). 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. Ramps or Inclined Planes support some but not all of the weight of an object. So it takes less force to move an object up a ramp of height h, than to lift an object directly to a height h. How things move (constant speed, constant acceleration) and Why things move (Forces, momentum). Now we want to talk about the Effort to make things move. Work: A Physics Definition (Work = Force times distance in the same direction). Work = Energy. For the object on the ramp, if we ignore friction, then while the force applied to slide the object up a ramp is less than the force to lift it, the force for the ramp must be applied for a longer distance -- in this case the total work being done is the same.
Friday 1/27: Work: A Physics Definition W = F d. (Work = Force times distance in the same direction). Work = Energy. SI Units are (N)(m) = (Joule) = (J). English Units for energy include the footpound and the Calorie. There are 4196 J in 1 food Calorie. Graviational Potential Energy PE = mgh. Location of h=0 is arbitrary choice. If I do work on an object to raise it to a height h above the ground, the object gains a PE which is then available to turn into falling motion when I let it go. If I want something to go higher, I must do more work on it. Rotational Motion -- In a sense, rotational physics is just like linear (straight-line) physics. Have a version of Newton's Laws of Motion. The rotational force is the Torque. There is a "rotational mass", as we have to worry about not just the mass, but how it is distributed about the axis of rotation. Q3 Take-Home quiz due Monday 30 January 2012 in class or by 5pm.
Monday 1/30: Review of what we have done so far. Just a few equations -- v = d/t , x = vt , a = delta-v/delta-t , x = x0 + v0t + ½at² , F = ma , w = mg , g = 9.81 m/s² , W = Fd , PE = mgh . More concepts, including Newton's 3 Laws -- always watch out for the 3rd Law, which involves equal and opposite forces acting on the other object, rather than the same object.
Wednesday 2/1: Exam 1.
Friday 2/3: Translating Linear physics to Rotational physics (as "easy" as changing Roman/English variables to Greek), because we already know the Physics of Chapter 1. 360° = 2 pi radians. We are building a table with two columns: Linear Physics on the left, Rotational Physics on the right. Angular position, angular velocity, angular acceleration, angular force = torque. Newton's 3 Laws of Motion applied to rotations. "Rotational Mass" Moment of Inertia, I. Angular momentum.
Monday 2/6: Why is it important that the wind turbine blades used as the first example in Chapter 2 be balanced? If balanced, then the center-of-mass is at the rotation axis. Otherwise, the center-of-mass will be moving as the blades turn -- wobbling and shaking -- which will require a force -- this force adds stress to the bearings and the support structure, weakening it and eventually causing it to fail. Note that center-of-mass and center-of-gravity are not the same thing. The c.m. is based on how the mass is distributed, the c.g. requires gravity. Rotational mass (moment of interia), I, has units of kg·m². Angles in degrees or radians are "quasi-units", which can be "wished" away as opposed to meters or seconds -- radians and degrees are really talking about how much of a fraction of a circle you're dealing with. Force versus Torque. Torque = radius arm × force, but the force must be perpendicular to the radius arm or lever arm. Torque has units of N·m. Work = torque × theta (angle), which still has units of N·m or Joules. As with the work from a force, you do know work unless there is (a) a torque and (b) a change in angular position in the same direction. Mechanical advantage, pp. 59-60. Pulling a nail out with a claw hammer -- the curve in the claw provides the pivot point, the long handle gives you the mechanical advantage. Next up: Wheels. But before we can go rolling along, we have to talk about friction...
Wednesday 2/8: To understand wheels and how they work, we have to look at friction. Two kinds of Friction: Static (stationary) and Kinetic (sliding). For any given contact surface between two materials, there are two coefficients of friction, µ, one for static (µs) and one for kinetic (µk). Static is always greater than kinetic. If I push on a book lying on a table with a small force, it does not move -- static friction will oppose the attempt to move up to a maximum value. After that, kinetic friction will oppose the motion. If I push on a book and it moves across the table at a constant speed, it is not accelerating. The postive work I am doing on the book (force and movement in same direction) is exactly canceled by the negative work that kinetic friction does on the book (force and movement in opposite directions). Hence the total or net work done on the book is zero, which makes sense because the book is not accelerating. On An Inclined Ramp, a book will not slide until the angle is steep enough. Static friction can vary its value up to a maximum -- kinetic friction is a single value. Traction is the available friction force. Rubber on concrete. Tires rolling with friction on good roads -- this is static friction not kinetic friction because the tires aren't sliding on the pavement. 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.
Friday 2/10: Return X1. Friction and Traction and Wheels: If your wheels are rolling without slipping, that is you are in control and have good traction, then a there is a connection between the rotational motion of the wheels and the linear motion of the vehicle. Position: d = r × theta. Speed: v = r × omega. Acceleration: a = r × alpha. A computer hard drive might spin at 3600 RPM. An RPM is a revolution per minute. 3600 RPM is 60 revolutions per second. Each revolution is 2 pi radians. So... omega = 2 × pi × 60 (rad/sec) = 377 rad/sec. You can end up with very large speeds very quickly with rotating systems. Q4 Take-Home quiz on Rotational Motion, due on Monday 13 February 2012, in class or by 5pm.
Monday 2/13: Q4 questions. Inertia = momentum. Linear momentum, p = m v . Angular momentum, L = I × omega . It takes a force to change linear momentum, or a torque to change angular momentum. Kinetic Energy is the energy of motion. K.E. = ½mv² . Note that if you double the speed of an object, say a car goes from 25mph to 50mph, the linear momentum is doubled, but the K.E. is quadrupled. This is one of the reasons why it is so hard to increase speed -- it takes much more work to put in that kinetic energy. Likewise, if you want to slow down, you have to do negative work and remove the K.E. Brakes typically turned the K.E. into heat energy. Unfortunately that means you can burn out your brakes, especially if you're driving a big rig. Example of Runaway Truck Ramps on mountain roads to stop trucks speeding downhill with no brakes safely. Conserved Quantities in Physics: linear momentum, angular momentum and energy (K.E. + P.E.) are examples of quantities which must be conserved in Physics. This means we have to account for them. Collisions are very complicated, for example, but the total momentum of "the system" must be conserved in a collision. "The system" is the combined momentum of two vehicles, for example. If two identical cars traveling at identical speeds are heading towards each other, then they have ptotal = +mv - mv = 0 before the collision, and after a head-on collision where they form one wreck of mass (m+m), the system still has 0 momentum, so the wreck does not move. To change the total momentum or energy of a system, one much do work from an external force.
Wednesday 2/15: A System is a group of objects taken together. So while two cars are two objects, in order to understand what happens in a collision we can take the two cars as a system. Now any forces doing any damage to the two cars are internal to the system and don't change the motion of the system. Two extremes in collisions: Totally Elastic Collision (perfect rebound, no damage) and Totally Inelastic Collision (stick together, take damage). The Linear momentum of the system is conserved in all types of collisions. Totally Inelastic Collisions: Two identical cars heading towards each other at the same speed, while each have momentum, the total momentum of the system is zero. So when they smash into one wreck, the wreck has the same momentum as the system, which is zero, so the wreck's speed is zero. Totally Elastic Collisions:-- perfect rebound, no damage, conserve both momentum and K.E. Two special cases: (1) same mass , v2i = 0, so v2f = v1i and v1f = 0. All the momentum and K.E. transfer from object 1 to object 2. (2) same mass, v1i = - v2i , so they just bounce off each other and go the other way. Close approximations: The Executive Time Waster. Why you want inelastics collisions in a wreck. 5 mph versus 3 mph impact bumpers. Impulse: Instead of writing F=ma for Newton's 2nd Law, we can change it to F = delta-p/delta-t, and talk about the change in the initeria (momentum). The Impulse equation is delta-p = F × delta-t. So you can get the same change in motion by applying a large force for a short time, or a short force for a long time. Hooke's Law (Spring force) -- Springs exhibit a linear restoring force if you don't stretch them too far. It's linear, so that means stretching the spring twice as far will give you twice the force. It's a restoring force, which means the force points back to the original position. Example: A meter stick supported on two chalkboard erases. Like a floor, if you push down on the middle, it will bend. Release it and it will spring back to its original position.
Friday 2/17: Striking a Baseball with a Bat: If you apply a force to the center of mass, then you will cause a change in the bat's linear motion. Apply a force away from the center of mass and you will be applying a force a distance away from a pivot point and it will change its rotation. About 7" from the end of the bat is the center of percussion, a place where the linear force and rotational torque effects cancel each other out -- this is much more comfortable. In addition, a baseball bat isn't perfectly rigid. Since it can bend, it can vibrate if struck. In a vibrating object, a node is where there is no apparent vibration and an anti-node is where there is maximum vibration. If one holds the bat at a node near the handle, there will be another node right by the center of percussion. This "sweet spot" not only provides the best force on the ball, but puts less stress on the bat and on your hands. Hit the bat away from the sweet spot and it is possible to break a wooden bat. Conservation of Total Mechanical Energy (T.M.E. = K.E. + P.E.). 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. Sample Exam 2 page. (Click here for a copy.) Q5 Take-Home quiz on Total Inelastic Collisions, due on Monday 20 February 2012, in class or by 5pm.
Monday 2/20: Uniform Circular Motion -- speed is contant, velocity is not. The velocity vector is always tangent to the circle, the centripetal acceleration, ac = v²/r, and the centripetal force, Fc, are always radial inward. For a car driving around a corner on a flat road, the centripetal force comes from the static friction between tire and road. Best case, the centripetal acceleration is limited to ac = g. For any given radius curve, there is a maximum safe 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. 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. Stability: Some things easily fall down and some things are hard to knock over. An object is in Stable Equilibrium when any small shift raises its P.E. (Trying to tip over a chair will raise its center of mass, raising its P.E. -- let it go and it tends to fall back into position.) An object is in Unstable Equilibrium when any small shift lowers its P.E. (Trying to stand up my cane on the desk, results in it falling over, due to lowering its center of mass, lowering its P.E. -- the center of mass is unsupported by the bottom of the cane if moved very far from vertical.) Examples: Rollovers, "J-Turns" (a U-turn with a rollover), Jeep CJ vs. Jeep YJ. The HUMVEE, which replaced the Army Jeep, is much wider and has a low center of gravity -- very hard to rollover -- as opposed to a person on a riding lawnmower.
Wednesday 2/22: What's the opposite of a collision? An explosion. Or recoil. Example: When a gun is fired, the bullet goes one way and the gun barrel goes the other way. 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 -- uses conservation of momentum: A mass of burning fuel moves one way at an exhaust speed while the remaining mass goes the other way. Orbital mechanics: Each radius of circular orbit has a different value of g(r). As r increases, v decreases and T increases. For Low Earth Orbit, such as the International Space Station, about 250 miles up, the orbital speed is about 17,000 mph (8000 m/s) and the orbital period T is about 90 minutes. For the Moon, the period is around 28 days at a quarter of a million miles away. Geosynchronous orbits occur 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
Friday 2/24: Dr. Phil has canceled today's classes due to weather / illness. Updates later today.
Monday 2/27: Review for X2. A rocket uses conservation of momentum: A mass of burning fuel moves one way at an exhaust speed while the remaining mass goes the other way. For our typical rocket in the Topic 2 worksheet, 90% of the mass is fuel/oxidizer and 10% is the structure and engines and tanks and payload. Why multi-stage rockets? Because even 10% of the mass of a single-stage "big dumb rocket" can be a lot of dead weight to try to lift into space. So by breaking up the rocket into pieces, each one with 90% fuel and 10% structure, we can throw away an empty stage and start with a smaller, lighter rocket. Even the Space Shuttle was really a multi-stage rocket -- you had the spaceplane itself, an external fuel tank so that we didn't have to carry the fuel tank into orbit, plus the big external solid rocket boosters that only burn for the first few minutes. The deLaval Nozzle: It seems so simple at first. Just burn the fuel and convert it into flame and thrust, and away the rocket goes. But if you have a converging-diverging engine nozzle, you first compress the exhaust to make it go faster, then let it expand and push away from the rocket -- you get much better performance. The shape of the engine bell -- the cone where the exhaust comes out -- can be optimized for use in the lower, thicker atmosphere or out in the vacuum of space. So the different engines of a multi-stage rocket can be tuned to work better in their environments. Newton's Universal Law of Gravity (or Newton's Law of Universal Gravity). We have been using w=mg to find the force of gravity(weight) near the Earth's surface. But once you are no longer near the surface, gravity weakens. It turns out that gravity requires two masses, either m1 and m2 or a big mass M and a little mass m, which makes sense because of Newton's Third Law. Gravity also depends on r, the distance between the centers of the objects -- the gravitational force falls off as 1/r². So if we double the distance, the force becomes ¼ as strong. Tides: We see high and low tides at the ocean shores, because the Moon is weakly pulling on objects on Earth with its gravity, even though it is a quarter-of-a-million miles away. The ocean closest to the Moon is pulled on a little harder than the Earth, so there is a high tide bulge. The ocean on the other side of the Earth is pulled on by the Moon a little weaker, so it gets left behind with another high tide buldge. The water in the bulge comes from the oceans on the sides of the Earth, where we get a low tide depression. The Earth rotates once a day under these tides, so we see the water come up the beach at high tide, then retreat during low tides.
Wednesday 2/29: Exam 2.
Friday 3/2: WMU SPIRIT DAY -- No Classes.
SPRING BREAK -- NO CLASSES.
Monday 3/12: Reset. Demo: The Cartesian Diver -- we need to understand the Physics to know why I can make the "diver" in the bottle sink or rise at my command. (We'll come back to this later.) Or Balloons: You can buy a helium filled balloon and it will want to rise up in the air, but a balloon filled with air from your breath will want to sink to the floor. Three Classical States of Matter: Solid, Liquid, Gas. Gas molecules are free to move around, having totally elastic collisions with other atoms and molecules. When they bounce off the walls of a container or a balloon, they are applying a force. All those forces are extended over the area. And Pressure = Force ÷ Area, so the gas applies a pressure outward. Meanwhile the outside air and the elastic material of the balloon apply an equal pressure inward. Heating the air inside the balloon makes the gas molecules move faster and expands the balloon. 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. It's not what the object is made out of, it's the mass and volume of the whole object. A ship made be made of steel, but a ship is also mainly just air, like our lecture hall -- otherwise you couldn't get inside the ship. 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. Or for a balloon to rise, the Mass-to-Volume Ratio of the balloon < Mass-to-Volume Ratio of the air (typically 1.29 kg/m³). So using helium, instead of air, inside the balloon lowers the Mass-to-Volume Ratio of the whole balloon (less mass). Or heating air inside the balloon expands the balloon and increases the volume. From a question is class -- the pressure of the air is lower at higher altitudes and the air gets thinner. That's because the air pressure is based on supporting the weight of the air above you. Less atmosphere above you the higher you go, so lower pressure. A balloon will rise at first, but eventually it will reach an Equilibrium -- a balance -- where the Mass-to-Volume Ratio of the balloon equals the density of the air at that altitude. To go up further you have to either lower the mass or heat the balloon and expand it.
Wednesday 3/14: (Happy Pi Day! 3.14...) 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). 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. (The book rounds this off to 100,000 Pa.) Buoyant Force = Weight of the Boat = Weight of the Water Displaced by the Submerged Part of the Boat. (Similar for a Balloon in Air.) Because the Mass of the Boat = Mass of the Water Displaced, we can use the equation for Mass-to-Volume Ratio(rho) and explain why for a boat to float that rhoBoat < rhoWater. Archimedes and Eureka! (I found it!) Absolute (total) Pressure vs. Gauge Pressure (difference between two readings).
Friday 3/16: Return X2. (Lecture notes coming...) 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).
Monday 3/19: Recall (1) Pressure = Force ÷ Area, (2) Conservation of Energy (PE+KE), (3) mass-to-volume ratio = mass ÷ Volume. 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. Using a column of liquid to make a barometer to measure air pressure. Switch from water to mercury (Liquid mercury (Hg) mass-to-volume ratio = 13,600 kg/m³) changes h at 1 atm. from 10.33 m to 0.759m. The aneroid barometer. Water Tower and the Faucet Problem. Why the water tower needs a vent. Want Smooth Continuous Flow, not Turbulent Flow or Viscous Flow. Flow rate = Volume / time = Cross-sectional Area × Speed.
Wednesday 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. The Cartesian Diver Revisited: The diver is open at the bottom, closed on top, and has a bubble of air in it. Squeezing the sealed bottle increases the pressure inside the bottle, driving more water into the diver, raising its mass-to-volume ratio (density) and causing it to sink.
Friday 3/23: Heat Energy (Q) and Temperature Change & Phase Change. Heat energy can move by Conduction (contact), Convection (transport of material, typcially gas or liquid, in a heating/cooling, rising/falling cycle) and Radiation (light). When you feel the warmth of the Sun, you're really detecting the invisible Infrared (IR) light from sunlight. Block the IR light and the remaining visible light does not feel warm. 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. Add/remove Heat Energy Q will change its phase between solid-liquid-gas using the Latent Heat of Fusion, Lf, between solids and liquids, or the Latent Heat of Vaporization Lv, between liquids and gasses. Example: Take a 1.00 kg block of ice from the freezer (T = -20°C, about 0°F) and heat it in a pan until it is all boiled away. (1) Heat ice from -20°C to ice at 0°C; (2) melt ice to water at 0°C; (3) heat water from 0°C to 100°C, (4) boil water into steam at 100°C. Using Power = Work/time, we can apply heat at the rate of 1000 W = 1000 J/sec, 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.)
Monday 3/26: Latent Heat of Fusion versus Latent Heat of Vaporization in water. "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. Those bubbles in boiling water are in some ways similar to the bubbles in carbonated water -- they require a nucleation site (seed) to form on . If you have a really smooth glass container and heat water in a microwave, you may get superheated water -- any disturbance will cause the water to suddenly and violently erupt and change phase. The Whistling Tea Kettle: The white cloud is condensing water vapor as the steam expands and is cooled in the air. The actual steam (gaseous water) is invisible, like air, and is in a small jet coming out of the hole -- it will give you a severe burn injury! Thermal Conductivity -- depends on the material. Heat Flow = (Thermal Conductivity × delta-T × Area) ÷ (gap distance) = (k)(delta-T)(A) / d . Heat flow is in J/sec = Watts, the same as power. Some materials, like gold, conduct heat very well -- gold "feels" nice on the skin because it quickly gets warm to the touch. Some materials don't conduct heat well -- some of these insulators may use air to bulk up the volume and decrease the amount of material that can conduct heat. For example, warm thermal blankets and quilts, or down or fiberfill winter coats. 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.
Wednesday 3/28: 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. Sample Exam 3 page. (Click here for a copy.) Q7 Take-Home quiz on Heat Engines, due on Monday 2 April 2012.
Friday 3/30: Final thoughts about Heat Engines and Refrigerators: When an engine is cold, TH = TC, and the Carnot efficiency is zero. You have to establish a temperature difference between the hot and cold reservoirs in order to extract useful work, W. Especially with the larger blocks of truck diesels -- have to warm up the engine to get anything out of them. Glow plugs -- heating elements used to prewarm the cylinders in diesel engines and soon to preheat catalytic converters in your anti-pollution system to reduce the pollution from the first 60 seconds of engine running. End of Exam 3 material. Waves: Single Pulse vs. Repeating Waves. The motion of the material vs. the apparent motion of the wave. For Repeating Waves, we have a Repeat Length (wavelength) and a Repeat Time (Period). Frequency = 1/Period. Wave speed = frequency × wavelength. 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.
Monday 4/2: DEMO DAY: Waves: Single Pulse vs. Repeating Waves. The motion of the material vs. the apparent motion of the wave. For Repeating Waves, we have a Repeat Length (wavelength) and a Repeat Time (Period). Frequency = 1/Period. Wave speed = frequency x wavelength. Demonstration: the Slinky shows both longintudinal (string type) and transverse waves (sound type). 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. 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. Demo: Tuning forks require both tines to work -- the "sound of a tuning fork with one tine" is that of silence. Musical instruments: Accoustic string instruments have a resonance box. Brass instruments start from the "natural trumpet", which can only play the fundamental and overtones for the pipe. Woodwind instruments get more complicated. Beat frequencies occur when two sounds have almost the same frequency -- get a distinctive wah-wah-wah sound, whose beat frequency = | f1 - f2 | .
Wednesday 4/4: Exam 3.
Friday 4/6: The speed of sound in air. Sonic Booms and other
shockwaves. Bullwhip stories. Waves take
time to travel. Sound takes time to travel. The speed of sound in helium is
greater than the speed of sound in air. When you talk, you make sounds using
the vocal cords which are based on wavelength. But your hearing is based on
frequency. So when you talk in helium, it sounds high pitched and squeaky. The
perils of SCUBA diving. 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
Demo: Static electricity. 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. 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. Protons repel
protons, neutrons ignore neutrons -- but protons WILL stick to neutrons with
the Strong Nuclear Force. 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.
Reminder that ICES Student Course Evaluations are available now online via GoWMU .
Monday 4/9: 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. 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. 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. Q8 Take-Home quiz on Standing Waves (Resonance), and due on Friday 13 April 2012.
Wednesday 4/11: Return X3. Update on remaining class time, discussion of format of the Final Exam. Black Box devices -- whether electronic or mechanical (iPad to new car) -- often make it difficult to see "How Things Work". Using Static Charges with Xerox copiers, laser printers, inkjet printers.
Friday 4/13: D.C. Electrical circuits. Ohm's Law. V=IR form. The Simplest Circuit: Battery, wires, load (resistor). Power dissipated by Joule heating in a resistor. P = I V . 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. Topic 3 is a worksheet on looking at Real World Data, due on Friday 20 April 2012. (Click here for a copy.) Q9 Take-Home quiz on Electrical Circuits, due on Wednesday 18 April 2012.
Monday 4/16: The Great 19th Century Debate: Is Light a Particle or a Wave? The answer is "YES" -- the "wavicle" is both a wave (with a frequency and wavelength) and a particle (the photon is a discrete bundle of energy, E = h f, where h = Planck's constant = 6.626 × 10 -34 J·sec and f = frequency in Hz.) Wave-Particle Duality did not seem obvious at the time. The Electromagnetic Wave travels at the speed of light. c = 300,000,000 m/s = 186,000 miles/sec. Electromagnetic Spectrum: Visible light (ROYGBIV=red orange yellow green blue indigo violet). Visible light is 400nm to 750nm (4000 angstroms to 7500 angstroms). Cannot "see" atoms with visable light, because the atom is about 1 angstrom across (1.00E-10 meters). The visible light wave is too large to see something that small. Frequences LOWER and wavelengths LONGER than visible light (IR infrared, Microwave, Radio waves, ELF extremely low frequency). Microwave ovens have metal screens in their windows -- the centimeter-range sized EM waves cannot see the "small" holes in the screen, so they bounce off the window as if it were just like the metal in the other five walls. Discussion of how microwave ovens "cook" food. Frequencies HIGHER and wavelengths SHORTER than visible light (UV ultraviolet, X-rays, Gamma rays). UV-A and UV-B, tanning and the problem of cheap sunglasses. Images inside object using X-rays passing through or scattering or being absorbed by the object. Why Superman's X-ray vision cannot work -- because everyday situations are "dark" in the X-ray band, thankfully!
Wednesday 4/18: Optics: When a straight light ray hits a boundary between one material and another, three things can happen: Reflection, Absorption, Transmission. The Law of Reflection. When light rays strike a rough surface, you get Scattering, which is reflections off many different angles. People tend to not like photographs of themselves, because they are used to seeing their mirror image -- their normal image, which the rest of us sees, looks "wrong". The Optical Lever -- move a mirror by 10° and the reflected ray moves by 20°. (Dr. Phil's theory on the origin of "seven years of bad luck for breaking a mirror".) The speed of light in vacuum is c = 300,000,000 m/s. The speed of light in a medium (air, water, glass, etc.) cm < c. The index of refraction of a medium is nm = c ÷ cm and is always greater than or equal to 1. nair is approximately 1. nwater = 1.33. For ordinary glass, nglass = 1.50. The Law of Refraction - Snell's Law. For our purposes, Snell's Law tells us that if light goes from a lower index of refraction to a higher index, then the angle must get smaller. Light bent at the interface between two media, because the speed of light changes in the media. (Analogy: If you are driving along the road and your right tires go off onto the soft shoulder, they can't go as fast and the car turns towards the shoulder until all four wheels are driving off the road.) If going from an high index of refraction media to a lower index media ONLY, have a chance for Total Internal Reflection (T.I.R.). This is a "perfect" reflection, better than a mirror. Used in high-end optical systems instead of mirrors. Also useful in fiber optics cables.
Friday 4/20: THE LAST CLASS.