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Lectures in PHYS-1070 (28)

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Updated: 16 December 2014 Tuesday.

PRE-FINAL GRADES FOR PHYS-1070 CAN BE FOUND HERE.

POST FINAL EXAM GRADING FOR PHYS-1070 CAN BE FOUND HERE.

FINAL COURSE GRADES AND BREAKDOWN BY CATEGORY FOR PHYS-1070 Fall 2014

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  • Week of 8-12 December 2014.

    Monday 12/8:Office Hours.

    Tuesday 12/9: FINAL EXAM (10:15am-12:15pm)

    Wednesday 12/10: Not on cammpus today. See Office Hours.

    Thursday 12/11: Office Hours.

    Friday 12/12: LAST DAY TO MAKE UP EXAMS.

    Monday 12/15: Office Hours.

    Tuesday 12/16: Grades due at Noon.

    Come here and I haven't updated the page yet? You can also check out the lecture notes from Spring 2014 here...


    Week of 1-5 September 2014.

    Monday 9/1: Labor Day <No Classes>

    Tuesday 9/2: Class begins. The nature of studying Physics. Science education in the United States. The Circle of Physics.

    Wednesday 9/3: Aristotle and the Greek Philosophers. Observation vs. Experiment - Dropping the book and the piece of paper (2 views). Mechanics is the study of motion. So what is motion? (Xeno) Zeno of Elea -- Zeno's Paradoxes. Speed Limit 70: What does it mean? First Equation: Speed = Distance / Time. v = d/t .

    Thursday 9/4: To understand the underlying concepts we need to Simplify The Universe. "Speed Limit 70" -- what does it really mean? First Equation: Speed = Distance / Time. v = d/t . Development of Speed equation for Constant or Average Speed. delta-x = xf - xi . Q1 (Attendance -- Q1A coming if you weren't in class.)

    Friday 9/5: Distribute Syllabus. Q1½ in-class.

    Week of 8-12 September 2014.

    Monday 9/8: PTPBIP - Putting The Physics Back Into The Problem. Go over Q1½. 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."

  • About a hundred years after the Antelope, in 1947, Chuck Yeager piloted the Bell X-1 and "broke the sound barrier" by design for the first time.
  • I've been telling the story of the Antelope for years, having learned about it in a kid's book on trains. Finally found a comment in Wikipedia, which says it wasn't five miles, but "First authenticated 60 mph, 26 miles in 26 minutes."
  • Tuesday 9/9: 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). Dr. Phil's Simplified Significant Figures for multiplication, division and trig functions. (Click here if you need a copy.)

    Wednesday 9/10: Return Q1½. Delta (&Delta;): &Delta;x = xf - xi = x - x0 = "the change in x". So our first equation becomes v = &Delta;x / &Delta;t . 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 Wednesday 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.

    Thursday 9/11: 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. Revisit: 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 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 (negativˆ). Example: A car goes from rest to 60.0 mph (26.8 m/s) with an acceleration a = 2.00m/s². Find the distance traveled and the time. Strategy: 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. In this case: The problem tells you v0 = 0, v = 26.8 m/s, a = 2.00 m/s². Choose x0 = 0. That's 4 out of 6 of the kinematic variables. Try to find t using one of the kinematic equations. (Hint: I'd use the 2nd equation.) Then either 1st or 4th equation to find x. Both work. Topic 1 assigned. (Updated Searchable booklist available online here .) Q2 Take-Home quiz on Kinematic Equations for Constant Acceleration, due Monday 15 September 2014. (Click here for a copy.)

     t (seconds)  v = a t (m/sec)  x = ½ a t² (meters)
     0 0 0
     1.00  1.00  0.500
     2.00  2.00  2.00
     3.00  3.00  4.50
     4.00  4.00  8.00
     5.00  5.00  12.5
     10.0  10.0  50.0
     25.0  25.0  312.5

    Friday 9/12: The 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. Problem: A rifle bullet is fired from rest to faster than the speed of sound, 425 m/s, in a distance of 1.00 m. Find a. Answer, a = 90,310 m/s². This is huge, which is why we don't fire people out of rifle barrels. Find t = 0.004706sec. 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.

    Week of 15-19 September 2014.

    Monday 9/15: 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.

    Tuesday 9/16: .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. Example: It is 5.50 meters to the ceiling in 1104 Rood. Consider tossing a ball up to the ceiling. If we ignore air reistance, then the time to rise is the same as the time to fall -- the latter is easier to calculate because if you start a problem at the turning point, then v0y = 0. 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. 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). Note that (1) if you take a suqare root of t , you get two answers, +/- , (2) if you divide both sides of an equation by t then t = 0 is also a solution. In both cases, these other solutions may not be useful to our problem, because they occur at the beginning or before the problem starts -- the equations go on forever in the past or the future, but the problem is defined only over a narrow range.

    Wednesday 9/17: Q3 in-class.

    Thursday 9/18: Abject apologies, PHYS-1070. One can prepare for many contingencies except "I thought this was Friday." Class cancelled. No computer, no documents to project, no person.

    Friday 9/19: 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). Note that (1) if you take a suqare root of t , you get two answers, +/- , (2) if you divide both sides of an equation by t then t = 0 is also a solution. In both cases, these other solutions may not be useful to our problem, because they occur at the beginning or before the problem starts -- the equations go on forever in the past or the future, but the problem is defined only over a narrow range. 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. Sig.Figs for angles doesn't quite make sense -- both 359° and 1.00° look like 3 sig. fig. But how can we know one angle to 0.01° and the other only to a whole degree, when they are just 2° apart? 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 vectors, and now due Tuesday 23 September 2014. (Click here for a copy.)

    Week of 22-26 September 2014.

    Monday 9/22: 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. Example: A-vector = 2.00 m @ 17° and B-vector 6.00 m @ 173°.

     Vector  Ax = A cos &theta;  Ay = A sin &theta;
     A  1.913 m  0.585 m
     B  -5.955 m  0.731 m
     A+B  -4.042 m  1.316 m

    C = 4.595 m , Arctan gives us -18.0°, which is a small angle, so given that Cx points in the -x and Cy in the +y, if you make a sketch you should find that &theta; = 162.0° or C-vector = 4.595 m @ 162.0°.

    Tuesday 9/23: Exam 1 Review.

    Wednesday 9/24: Exam 1.

    Thursday 9/25: Return Q2. 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 &theta;) term in the Range Equation means that (1) 45° gives the maximum range for a given initial velocity and (2) that all other angles have a complementary angle (90° - &theta;) that gives the same range (but a different time and height). High and low trajectories for Range Equation. 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°?

    Friday 9/26: 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°? Or 45°, which should give the maximum range? Compare h, time t to max height and range R. To Jump A Gap, you MUST have a positive v0y, because you are immediately in freefall. Demo: A bullet fired horizontally has the same y-motion as a bullet dropped from the muzzle height. Use two pieces of chalk, one tossed, one dropped. They hit the table at the same time.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. 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.

    Week of 29 September-3 October 2014.

    Monday 9/29: 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 9/30: U.C.M. 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.

    Wednedsday 10/1: Return X1. 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.) Newton's Three Laws of Motion: Zeroeth Law - There is such a thing as mass. 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.

    Thursday 10/2: 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.) 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.). Q5 Take-Home on U.C.M. and Newton's Laws, handed out Thursday 2 October 2014 and due on Monday 6 October 2014. (Click here for a copy.)

    Friday 10/3: No class on Friday, as there is no in-class quiz.

    Week of 6-10 October 2014.

    Monday 10/6: 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. Simple pulleys (Massless, frictionless, dimensionless, only redirect the forces). "There is no free lunch." The bracket for the pulley will have to support a force greater than the weight of the hanging object. Mechanical advantage: multiple pulleys allow us to distribute the net force across multiple cables or the same cable loop around multiple times. Tension in the cable is reduced, but you have to pull more cable to move the crate.

    Tuesday 10/7: 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. The Centripetal Force, Fc = mv²/r , is from the tension force of his string -- let him go and he literally goes ballistic. 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 10/8: 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. 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.

    Thursday 10/9: Q6 in-class.

    Friday 10/10: 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). Coefficients of friction have no units, so they are the same for SI metric and English. They are generally less than 1. Static is always greater than kinetic. Kinetic friction opposes motion and is always Ff,k = µk Fn. Static friction opposes impending motion and can be zero to a maximum of Ff,s,max = µsFn. 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.

    Week of 13-17 October 2014.

    Monday 10/13: 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. Kinetic friction opposes motion and is always Ff,k = µk Fn. Static friction opposes impending motion and can be zero to a maximum of Ff,s,max = µsFn. Example: Using our 125 kg. crate, applied force with F1 = 100.N and coefficients 0.600 and 0.400. (1) If at rest, F1 < Ff,s,max, therefore Ff,s = 100.N and the crate does not move. (2) If moving with v0 = 4.00 m/s, then Ff,k > F1 , so the crate will be slowing down. (3) If at rest and apply force F2 = 1000. N > Ff,s,max then break the staic friction barrier and switch to kinetic friction, so will move, and accelerate around 4 m/s². (4) To move crate at constant speed, get it started then apply force F3 = Ff,k .Friction Problems: (1) A car moving at 70 mph (31.3 m/s) on dry concrete (coefficients of friction 1.00 and 0.800) -- find the shortest stopping distance. To find the distance, we need the acceleration. To find the acceleration we need to find the net force (F = ma). To find the forces, we need the sum of forces equations in x and y, which we get from the Free Body Diagram. Shortet stopping distance requires maximum static friction -- if the car is moving to the right, friction must point to the left to stop. (2) Repeat for the car on sheer ice -- divide the coefficients of friction by 10 (0.100 and 0.0800) -- where in a panic the cars slides to a stop. (3) At 70 mph, what is the minimum radius r for a circular turn with a flat road -- in control on dry concrete? -- skidding on ice? For UCM we need the centripetal acceleration, which we get from the Centriptal Force: Fc = mac = mv²/r .

    Tuesday 10/14: 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(&theta;max). 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 &theta;max greater than 45° -- rare, but yes. Banked Turns: The angled normal force FN has a horizontal component which provides the centripeta; force FC. Remember -- something has to CAUSE the centripetal force.

    Wednesday 10/15: RESET. Q6 turned out to be a disaster, so "Q6 didn't happen". Review material for Q6 and Q7. New Schedule: Q7 postponed to Thursday, in class. Q8 take-home, handed out Thursday, due Monday. Q6R (rerun) Monday, in class. X2 still on Wednesday -- have no choice with mid-term grades due...

    Thursday 10/16: Q7 in-class.

    Friday 10/17: Return Q5. 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 = &Delta;p / &Delta;t = change in momentum / change in time instead of F=ma, but really the same thing. Impulse Equation: &Delta;p = F &Delta;t .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. 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.

    Week of 20-24 October 2014.

    Monday 10/20: Linear Momentum ( p = mv ) is a vector quantity. Newton's form of the 2nd Law: F = &Delta;p / &Delta;t = change in momentum / change in time instead of F=ma, but really the same thing. Impulse Equation: &Delta;p = F &Delta;t .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. More on automobile safety systems and how they work to save your life. Q6R in class.

    Tuesday 10/21: Return Q7. Exam 2 Review.

    Wednesday 10/22: Exam 2.

    Thursday 10/23: 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. 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).

    Friday 10/24: UCM Revisited -- A Problem to do this weekend: 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 a few weeks ago. Working backwards, 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.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.).

    Week of 27-31 October 2014.

    Monday 10/27: Return X2. 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.).

    Tuesday 10/28: X2 solutions. 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.

    Example: Consider: a 1.00 kg mass undergoing a net force of 1.00 N for an acceleration of 1.00 m/s². (Please note I chose simple numbers for this illustration. The mass isn't usually 1.00 kg, so the actual numbers aren't going to be the same between columns, but the ratios mentioned below still work..)

     t  v = at  p = mv  d = ½at² KE = ½mv² 
     0  0  0  0  0
     1.00 sec  1.00 m/s  1.00 kg·m/s  0.500 m  0.500 J
     2.00 sec  2.00 m/s 2.00 kg·m/s  2.00 m  2.00 J
     3.00 sec  3.00 m/s  3.00 kg·m/s  4.50 m  4.50 J
     4.00 sec  4.00 m/s  4.00 kg·m/s 8.00 m  8.00 J

    Wednsday 10/29: 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 = 50.0 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 = 31.32 m/s, v3 = 27.30 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 )

    Thursday 10/30: 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? 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. 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. 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. Q9 Take-Home on Work, Energy and Conservation of TME, due Monday 3 November 2014. (Click here for a copy.)

    Friday 10/31: 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. 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.) The Ballistic Pendulum -- Old School Physics, in the days before all our modern electronics: We can find the speed of a projectile through an Inelastic Collision into a block of wood, followed by Conservation of TME, as the block+projectile swings up and comes to a stop.

    Week of 3-7 November 2014.

    Monday 11/3: Archimedes and Eureka! (I found it!) Using mass-to-volume ratio and water displacement to determine if gold crown was solid gold or not. 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, but the Total Volume of the Boat and Submerged Volume of the Boat ( = Volume of Displaced Water) are different. Large Ships sre described by how many tons of water (1 ton = 2000 lb.) they displaced. I believe that empty, RMS Titanic displaced 69,000 tons of water. It is importatant gto know the draft or how far down the keel or bottom of the boat is -- heavily laden ships always leave or arrive at high tide, when there is more water in the harbor and therefore more water under the keel. 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 11/4: 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. 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: P = &rho;gh. Pressure due to a column of water = 1 atm 101,300 Pa. at h = 10.33m = 33.86 feet. How to get liquid out of a cup using a straw -- or why Physics does not "suck", but pushes using a pressure difference. Absolute (total) Pressure vs. Gauge Pressure (difference between two readings).

    Wednesday 11/5: Q10 In-Class/Open Quiz.

    Thursday 11/6: Absolute (total) Pressure vs. Gauge Pressure (difference between two readings). 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. 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.

    Friday 11/7: Return Q6R. Bernoulli's Equation. The Water Tower and the Faucet Problem. Why the water tower needs a vent. 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. Topic 2 Worksheets (Click here for 1st Worksheet and Directions)

    Week of 10-14 November 2014.

    Monday 11/10: 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 (Fdrag = -bv ) and high speed (Fdrag = -cv²) air resistance. The minus sign is there to remind us that air resistance, like friction, opposes motion. 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.

    Tuesday 11/11: 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, &rho;seawater = 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.

    Wednesday 11/12: Q11 in-class / Open Quiz.

    Thursday 11/13: Temperature & Heat. Heat = Energy. Two objects in thermal contact, exchange heat energy, Q. If net heat exchange is zero, the two objects are at the same temperature. Temperature Scales: °F, °C and K (Kelvins). Linear Expansion: Most objects expand when heated, shrink when cooled. 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.

    Friday 11/14: Expansion joints. Linear Expansion: Why "Bridge Freezes Before Roadway" signs. Bridge expansion joints. 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, &beta; = 3&alpha;. 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.

    Exam 3 Topics:
    
    Leftover from Sample Exam 2:
    == Work, KE, PE, Conservation of Energy
    == Newton's Law of Universal Gravity
    
    Current topics:
    == Mass-to-volume ratio (density)
    == Floating and displacement
    == Pressure = Force / Area
    == Pressure due to a column of liquid
    == Bernoulli's Law
    == Continuity Equation
    == Length and Volume Expansion
    == Simplified Ideal Gas Law
    
    Next topics:
    >> Heat capacity and energy to change phases 
       (This material will NOT be covered in Fall 2014 and will NOT be on Exam 3.)
    == Heat engines and efficiencies 
       (This material WILL be covered on Monday and Tuesday and WILL be on Exam 3. 
        It will also be used on Worksheet 4 for Topic 2.)
    >> Sound, wavelengths, resonance and interference 
       (This material WILL be covered and WILL appear on the Final Exam. 
        It will NOT be on Exam 3.)

    Week of 17-21 November 2014.

    Monday 11/17: 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). 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 -- there is not much room between the actual efficiency and the Carnot efficiency to make an 8- to 10-fold increase in m.p.g. To use less fuel, do less work.

    Tuesday 11/18: Classes canceled by winter storm.

    Wednesday 11/19: Exam 3 Review. The Heat Engine and Three Efficiencies (Actual, Carnot and 2nd Law). Power is Work per time. We talk of Useful Work, Total Energy, Waste Energy -- we can substitute the rate work is done, power, for Useful Power, Total Power, Waste Power. Example: It takes 15 to 50 h.p. from your car's engine to maintain highway speed due to air resistance and friction. 15 h.p. × 746 W/h.p. = 11,190 W = 11,190 J/s . This is the useful power. Each second, the useful work is W = 11,190 J. What happens if we reverse the arrows in the Heat Engine diagram? We get a refrigerator. Air conditioners and Heat Pumps.

    Thursday 11/20: Exam 3.

    Friday 11/21: 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 &lambda; (wavelength) and a Repeat Time T (Period). Frequency = 1/Period  or f = 1 / T . Wave speed = frequency × wavelength ; v = f &lambda; Demonstration: the Slinky shows both transverse waves (string type) and longintudinal (sound type). [Corrected 11-30-2014 Su] The speed of sound in air. 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. Sonic Booms and other shockwaves.

    Week of 24-28 November 2014.

    Monday 11/24: Q11 returned. 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 &lambda; (wavelength) and a Repeat Time T (Period). Frequency = 1/Period  or f = 1 / T . Wave speed = frequency × wavelength ; v = f &lambda;. Waves and Resonance. Standing Waves on a string. Fundamental, First Overtone, Second Overtone, etc. Demonstration: First and higher overtones on a string driven by a saber saw. We are varying the speed of the wave by changing the tension. With a fixed frequency from the saber saw, this changes the wavelength. (Can't see the Fundamental on the saber saw demo, because the tension required usually breaks the string.) Standing Waves in a tube. Demo: Variable length organ pipe -- Fundamental and First Overtone (overblowing), varying pitch (musical note) by changing length of tube open at only one end. Topic 2 Worksheets 2-4 handed out. (Click here for a copy.)

    Tuesday 11/25: Return X3. 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. 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 | . Constructive and Destructive Interference. Acoustics of concert halls. The range of "normal" human hearing: 20Hz-20,000Hz (10 octaves).

    Wednesday 11/26: WMU Classes end at Noon -- Class does not meet.

    Thursday 11/27: Thanksgiving Day. No classes.

    Friday 11/28: No classes.

    Week of 1-5 December 2014.

    Monday 12/1: dB = decibel, a logarhythmic scale. A change of 10dB is twice as loud, a change of 20dB is four times as loud. Ten sound sources is perceived as only twice as loud as one source. 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. 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. Q12 take-home, on Waves and Resonance, due Wednesday 3 December 2014. (Click here for a copy.)

    Tuesday 12/2: 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 (weakest), E & M, Weak Nuclear Force, Strong Nuclear Force (strongest). The Hydrogen Atom. One proton in the nucleus, one electron in orbit around the nucleus. The total net charge is qnet = +e-e=0. Ions have more or fewer electrons than protons, and therefore have a net charge. This allows molecules to hold together. But the total charge of an object is usually close to zero, so we don't use the Electric Force to hold you on the surface of the Earth or the Earth in orbit around the sun. 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 (due to the Weak 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. The Periodic Table of the Elements has rows and columns due to Quantum Mechanics -- a Modern Physics requirement that we don't need in the usual macro world. The electrons are allowed to have only certain values -- just like the Lecture Hall, where you can only put one person in a seat, they are all different, and the rows are at different heights, so you have different values of P.E.

    Wednesday 12/3: Q13 - THE LAST QUIZ - In-Class/Open Quiz.

    Thursday 12/4: IMPORTANT: In class today you filled out a new sheet with a PID Personal Identification Number -- this is so I can post grading info on the website. If you weren't in class, you need to email me a 5-digit PID number. Doesn't matter if you remember the one you filled out in September. A similar form is online for "Quiz 1A" here. Turn in on Friday or email me the PID number. 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.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. Short topics for beginning of Friday: (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"). 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.

    In case you suddenly realize you need data for Topic 2 (which will now be late):
    
    1996 T-10 Chevy 4WD Blazer
    4300 lbs., 185 hp
    0 to 45 mph in 12 seconds
    Trip and Gas Run Together:
    313,895.3 to 314179.6
    7:33am to 9:15am (stops of 10 min + 20 min)
    2:50pm to 4:30pm (stop of 7 min)
    7:34am to 9:30pm (stops of 7 min + 20 min)
    4:55pm to 6:30pm (stop of 7 min)
    gas at 2nd fill: 15.83 gallons
    
    Dr. Phil

    Friday 12/5: D.C. Electrical circuits. Ohm's Law. V=IR form. Short topics for beginning of Friday: (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"). 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. REVIEW.