Dr. Phil's Home

Lectures in PHYS-1130 (5)

Updated: 16 December 2007 Sunday.

Week of December 10-14, 2007.

Monday 12/10: Office Hours.

Tuesday 12/11: Office Hours.

Wednesday 12/12: Office Hours.

Thursday 12/13: FINAL EXAM 8:00-10:00am

Friday 12/14: Office Hours. There is a chance that Dr. Phil may work from home on Friday if there is no need to come in on Friday, so you might want to check first.

Monday 12/17: Office Hours CANCELLED. There is a good chance now that Dr. Phil will NOT be in on Monday 17 December 2007. The weather forecasts on Friday suggested strongly that I gather all remaining materials and take home. Not sure how much snow K-zoo has as of Sunday afternoon -- why chance things? If you REALLY need to talk to me on Monday, either send me e-mail OR call me at home OR call the Physics Dept. at 269-387-4940 and have them e-mail or call me at home. Thanks!

Tuesday 12/18: GRADING DAY. Grades are due at Noon.


Week of September 3-7, 2007.

Monday 9/3: LABOR DAY -- No Classes.

Tuesday 9/4: Class begins. The nature of studying Physics. Science education in the United States. Distribute syllabus.

Wednesday 9/5: Natural Philosophy. The Circle of Physics. Aristotle and the Greek Philosophers. Observation vs. Experiment - Dropping the book and the piece of paper (2 views).

Thursday 9/6: Observation vs. Experiment - Zeno's Paradoxes. "Speed Limit 70" First Equation: Speed = Distance / Time. v = d/t .Development of Speed equation for Constant or Average Speed. Q1 and your PID number. (If you missed class on this day, check with Dr. Phil sometime soon or send email.)

Friday 9/7: More about speed = distance / time. An Equation is a contract -- the left and right sides must be the same thing and all terms must have the same units. A simplified trip to the store -- The S-Shaped Curve. Acceleration.

Week of September 10-14, 2007.

Monday 9/10: 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 Monday 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). Finding the set of Kinematic Equations for constant acceleration. Kinematic Equations for Constant Acceleration. The Equation Without Time -- Avoiding the Quadradic Formula. Distribute Topic 1 Handout. (Searchable Web Page; Downloadable PDF File) Please note that the URL on the handout is not correct. It should read http://homepages.wmich.edu/~kaldon/classes/ph113-5-115-6-bl.pdf. The links on the web site are correct.

Remember: PHYS-1140 Lab Begins This Week

Tuesday 9/11: A Remembrance from this class at this time in this room six years ago. SI Metric System. What do we mean by Measurements? "Units will save your life." Q2 in-class quiz. Handout about SI metric system prefixes and Dr. Phil's Practical Significant Figures.

Wednesday 9/12: "Units will save your life." What is "1 m/s"? We need a few benchmark values to compare English and SI Metric quantities. 60 m.p.h. = 26.8 m/s. 1.00 m/s = slow walking speed. 10.0 m/s = World Class sprint speed. NEWS: Saturday 5/13/2006 new World Record in 100m dash -- 9.76 seconds. What do we mean by a = 1 meter/sec² ? You cannot accelerate at 1 m/s² for very long. Is 1 m/s² a large or small acceleration? Free fall (near Earth's surface, neglecting air resistance) acceleration is g = 9.81 m/s². Example: bullet fired down a rifle barrel, solve for "a" using the Equation Without Time. NOTE: The syllabus had a typo on p. 14 -- Q3 is a take-home to be handed out tomorrow, not today.

Thursday 9/13: Solve for "t" in the rifle barrel problem -- (1) Using 2nd kinematic equation, (2) using 1st kinematic equation, (3) using the average speed under constant acceleration then v = d /t -- all three methods yield the same answer. Strategies for solving problems. The importance of small study groups. Two stories: Speed. 60 m.p.h. = "A Mile A Minute". (1848: The Antelope) The P-O-R (Press-On-Regardless) road rally problem. "You can't average averages." Q3 Take-Home, due Tuesday 18 September 2007.

Friday 9/14: Quick Tour of the PHYS-1130 Class website. Types of Motion: No Motion (v=0, a=0), Uniform Motion (v=constant, a=0), Constant Acceleration (a=constant). The consequences of Falling Down... ...and Falling Up. The Turning Point ( v=0 but a = -g during whole flight). The illusion of "hanging up there in the air" at the turning point. Hand out 1st Sample Exam 1. (Click here for a copy.)

Week of September 17-21, 2007.

Monday 9/17: 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. Now we need to start dealing with two-dimensional problems in general. Two kinds of numbers: Scalars (magnitude and units) and Vectors (magnitude, units and direction).

Tuesday 9/18: 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). 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) Q4 Take-Home, due Thursday 20 September 2007. Second Sample Exam 1 handed out. (Click here for a copy.)

Wednesday 9/19: Arrr! It be International Talk Like A Pirate Day, me mateys. Analytical method. (Check to make sure your calculator is set for Degrees mode. Try cos 45° = sin 45° = 0.7071) Why arctangent is a stupid function on your calculator. Finding the final vector velocity of The guy with the fedora and the cigar problem. Ballistic Motion: ax = 0 and ay = -g.

Thursday 9/20: 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. Q5 Take-Home due Tuesday 25 September 2007. Read this NOTE about Q5.

Friday 9/21: YES! WE HAVE CLASS TODAY! Example: Cannon shot at 100.m/s @ 30°. Same Range if launched at 60°. Example: Rifle fired horizontally and a bullet dropped from the same height as the muzzle -- both bullets will hit level ground at the same time, since both have the same y-problem. Classic Simple Pursuit (Cop and the Speeder). Same Place at the Same Time. Our algebra for car 1 and car 2, we cancelled a factor of t at one point -- this represents t = 0, which by definition is also a solution. But... because our problem is Simple Pursuit, when the car 2 reaches car 1, the cop is traveling at twice the speed of the speeder. Third Sample Exam 1 handed out. (Click here for a copy.)

Week of September 24-28, 2007.

Monday 9/24: Types of Motion studied so far: No motion, Uniform motion (v=constant, a=0), Constant Acceleration. Uniform Circular Motion (UCM): speed is constant, but vector velocity is not; magnitude of the acceleration is constant, but the vector acceleration is not. Velocity is tangent to circle, Centripetal Acceleration is perpendicular to velocity and points radial INWARD. Demo: Rodney Reindeer. For UCM, ac = v²/r. Space Shuttle in Low-Earth Orbit. (There's still gravity up there!) Read this NOTE about Q5.

Tuesday 9/25: Uniform Circular Motion (UCM) comments. Easy to get very large centripetal accelerations. Space Shuttle stories. Offer to Review some Exam 1 Sample Exam problems, but end class five minutes early when there were no more questions. Q6 Take-Home due Thursday 27 September 2007.

Wednesday 9/26: Recap: Our studies so far have described "How" things move, and allow to say "When" and "Where" things move, but not "Why" things move. For that we have to start talking about Forces -- and that means Newton. Some stories about Sir Isaac Newton. Newton's Three Laws of Motion: Zeroeth Law - There is such a thing as mass. 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.)

Thursday 9/27: Exam 1.

Friday 9/28: YES! WE HAVE CLASS TODAY! Newton's Three Laws of Motion: Zeroeth Law - There is such a thing as mass. First Law - An object in motion tends to stay in motion, or an object at rest tends to stay at rest, unless acted upon by a net external force. Second Law - F=ma. Third Law - For every action, there is an equal and opposite reaction, acting on the other body. (Forces come in pairs, not apples.) SI unit of mass = kilogram (kg). SI unit of force = Newton (N). English unit of force = pound (lb.). English unit of mass = slug (Divide pounds by 32.) Force is a vector. Free Body Diagrams. Normal Force (Normal = Perpendicular to plane of contact). Sum of forces in x or y equations. Example of 125 kg crate sitting there. Example of 125 kg crate being dragged/pushed around. Variations as we allow for an applied force that it at an angle. "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."

Week of October 1-5, 2007.

Monday 10/1: Yes, WMU will be open even if the State of Michigan shuts down. More Newton stories. Example of 125 kg crate being dragged/pushed around. Variations as we allow for an applied force that it at an angle. "You can't push on a rope." Since the force from a wire/string/rope/chain/thread/etc. can only be in one direction, Dr. Phil prefers to call such forces T for Tensions rather than F for Forces. If you are hanging from a wire and are not in contact with the ground, there is NO Normal Force.

Tuesday 10/2: 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. Atwood's Machine -- two masses connected by a single cable via a simple pulley. 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. Q7 Take-Home, due Thursday 4 October 2007.

Wednesday 10/3: The importance of Putting The Physics Back Into The Problem (PTPBIP): Example problem with suspended sign -- solutions must meet requirements of Newton's 1st Law in x- or y-directions, and while the tensions T1 and T2 are both less than w=mg, they are both more than ½mg because they are pulling against each other. Discussion of Safety Factors in choosing cables for real tension problems. 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. Friction is both a pain and a curse. Attempt by state to "repeal the law of friction" was an April Fool's joke. (Unlike the legislation making pi = 3 during the Homesteading era, which had practical value in squaring the circle.) Two kinds of Friction: Static (stationary) and Kinetic (sliding). For any given contact surface, there are two coefficients of friction, µ, one for static and one for kinetic. Static is always greater than kinetic for any given pair of materials in contact with each other.

Thursday 10/4: Two kinds of Friction: Static (stationary) and Kinetic (sliding). For any given contact surface, there are two coefficients of friction, µ, one for static and one for kinetic. Static is always greater than kinetic for any given pair of materials in contact with each other. Static & Kinetic Friction. Finding the coefficient of static friction by tilting µs = tan(thetamax). Similar for kinetic friction, except one has to tap the board to "break the static friction barrier". 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. If object is at rest, need to "test" to see if an applied external force exceeds the maximum static friction force ("breaks the static friction barrier"). Q8 In-Class quiz.

Friday 10/5: YES! WE HAVE CLASS TODAY! Static & Kinetic Friction continued: Examples using our 125 kg crate sliding on the floor. If object is at rest, need to "test" to see if an applied external force exceeds the maximum static friction force ("breaks the static friction barrier"). Static Friction can vary from zero to its max value in either direction. Friction while driving. Rubber on dry concrete, coefficients are 1.00 and 0.800 . 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. First Sample Exam 2 handed out. (Click here for a copy.)

Week of October 8-12, 2007.

Monday 10/8: Columbus Day (Observerd) -- not a WMU Holiday. Air Resistance. Low speed (Fdrag = - bv) and high speed (Fdrag = - cv2)air resistance. If allowed to drop from rest, then a real object may not free fall continuously, but may reach a Terminal Velocity (Force of gravity down canceled by Drag force up) and doesn't accelerate any more. Ping-pong balls versus turkeys or pennies. Tied up in the coefficients for drag are things like shape, air, cross-section area, surface type, etc. Terminal velocity of a person depends on clothes and orientation (which way they are pointing and whether they are stretched out or trying to be compact). Objects in Free-Fall with air resistance may reach a Terminal Velocity (Force of gravity down canceled by Drag force up) and doesn't accelerate any more. World's Record Free-Fall. Work: A Physics Definition (Work = Force times distance in the same direction). You can do no work, but that doesn't mean you aren't exherting an effort -- only that you aren't applying a force in the direction of a motion.

Tuesday 10/9: X1 Handed back. (Click here for a solution.) Work: A Physics Definition (Work = Force times distance in the same direction). You can do no work, but that doesn't mean you aren't exherting an effort -- only that you aren't applying a force in the direction of a motion. SI unit for Work & Energy is the Joule (J). Though technically (N·m) = (kg·m²/s²) = (J), Dr. Phil reserves (N·m) for torque (a rotational force). Lose angle and directional information because energy is a scalar, not a vector. Q9 Take-Home due Thursday 11 October 2007. NOTE: Read each part carefully to get the right F.B.D. for that particular problem. Additional NOTE: Part (b) is a little different that we are used to doing -- you are essentially trying to prove that using static friction doesn't work in this case.

Wednesday 10/10: 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 or to find a stopping distance. 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. Lose angle and directional information because energy is a scalar, not a vector.

Thursday 10/11: Conservation of Total Mechanical Energy (T.M.E. = K.E. + P.E.). 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.) Continue with Conservation of T.M.E. (P.E. + K.E.). Total energy limits maximum height. Lose angle and directional information because energy is a scalar, not a vector. Example: Roller-Coaster. If speed at top of the first hill is about zero, then this P.E. is all we have. Cannot get higher, but we can change height for speed. Q10 Take-Home due Tuesday 16 October 2007.

Friday 10/12: YES! WE HAVE CLASS TODAY! Hooke's Law (Spring force) is a second conservative force, which we can also write as a P.E. Using Conservation of Energy (P.E. + K.E.) with a spring. Linear Momentum ( p = mv ) is a vector quantity. Newton's form of the 2nd Law. Second Sample Exam 2 handed out. (Click here for a copy.)

Week of October 15-19, 2007.

Monday 10/15: Linear Momentum ( p = mv ) is a vector quantity. Newton's form of the 2nd Law. Two extremes in collisions: Totally Elastic Collision (perfect rebound, no damage) and Totally Inelastic Collision (stick together, take damage). The forces in collisions are complicated and always changing. Linear momentum is conserved in all types of collisions . Totally Inelastic Collisions. Example: The Yugo and the Cement Truck. Three example collisions: head-on, rear-end, and... to be continued tomorrow.

Tuesday 10/16: Three example collisions: head-on, rear-end, 2-D. (The Non-Collision -- if the car following is going slower, it isn't going to run into the car ahead. PTPBIP.) What happens in a wreck. Seat belts, shoulder belts, steel beams in doors and crumple zones. How airbags work. Q11 Take-Home due Thursday 18 October 2007.

Wednesday 10/17: "Best airbag story." What happens in a wreck. The myth of "better to be thrown from the wreck." 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. 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 to T.E.C.: The Executive Time Waster, the Physics of pool shots. Third Sample Exam 2 handed out. (Click here for a copy.)

Thursday 10/18: Why you want inelastics collisions in a wreck. 5 mph versus 3 mph impact bumpers. "Adobe: The Little Car Made of Clay". What's the opposite of a collision? An explosion. Or recoil. Example: A pitcher on ice skates at rest -- when he hurls a fastball to the right, he goes to the left. Total momentum of the system remains constant (in this case, zero). The Ballistic Pendulum -- We can find the speed of a projectile through an Inelastic Collision followed by Conservation of TME.

Friday 10/19: YES! WE HAVE CLASS TODAY! UCM Revisited. Centripetal Force. No such thing as Centrifugal Force. Only the Centrepital Force, which points radial inward, just like the centripetal acceleration. Note that the Centripetal Force is an ANSWER to the sum of forces equation -- it does not show up in the F.B.D. directly -- something has to CAUSE the Centripetal Force, such as a tension, normal force or a combination of forces. Although a loop-the-loop is not a proper UCM problem, we can apply UCM at the top of the loop and determine the minimum safe speed for going around the loop without falling off. At the minimum speed, the Normal Force between the wheels and rail goes to zero (the wheels just "kiss" the track), so the centripetal force is just equal to the weight, w = mg. Making "artificial gravity" for long-duration space flight by living in a rotating object.

Week of October 22-26, 2007.

Monday 10/22: The story of the 50,000 rpm Ultra-Centrifuge and the Fresh Rat's Liver. The formula w=mg gives us the gravitational force near the surface of the Earth. Newton had to work out gravity for anywhere, hence "Universal Gravity." Specifically Newton was working on trying to solve the problem of the motion of Mars in the night sky. 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. The Shuttle in Low Earth Orbit (Revisited). This closes the book on Exam 2 material. Q12 Take-Home, due Wednesday 24 October 2007 by Noon at the latest.

Tuesday 10/23: The problem of determining G and the mass of the Earth. g(r). Translating Linear physics to Rotational physics (as "easy" as changing Roman/English variables to Greek), because we already know the Physics of the first six chapters. The radian is a "quasi-unit" -- it's not really a unit, but represents a fraction of a circle. (We can "wish" it away when we need to.) We are building a table with three columns: Linear Physics on the left, Rotational Physics on the right and the conversion between linear and rotational variables in the center. Angular position, angular velocity, angular acceleration, angular kinematic equations for constant angular acceleration, angular force = torque. Newton's 3 Laws of Motion applied to rotations.

Wednesday 10/24: DVD movie clips: (1) 2001: A Space Odyssey (What would it look like to have use centripetal force for artificial gravity? Stanley Kubrick's 1968 movie showed us a large rotating space station and a smaller rotating carousel on a ship to Jupiter.). (2) Speed (You have to have some positive v0y if you want to jump a gap -- even with a speeding bus.) Review of some Sample Exam 2 problems.

Thursday 10/25: Exam 2.

Friday 10/26: YES! WE HAVE CLASS TODAY! Translating Linear physics to Rotational physics (con't.). Examples using the rotational kinematic equations. For wheels which do not slip, there is a direction connection between the linear and rotational kinematic variables. Rotational Work, rotational K.E., angular momentum. Rotational collisions. Q13 Take-Home, due Thursday 1 November 2007. Note: We haven't completely covered the Moment of Inertia, I, so unless you go to the book, you'll only be able to work on the top section and determine the six rotational kinematic variables. NOTE: If you've done Q13 correctly, then (d) = (c) and (e) = (b).

NOTE: The Physics Help Room moves temporarily to 2242 Rood Hall - Oct. 26-Nov. 2, 2007

Week of October 29-November 2, 2007.

NOTE: The Physics Help Room moves temporarily to 2242 Rood Hall - Oct. 26-Nov. 2, 2007.

Monday 10/29: Translating Linear physics to Rotational physics (con't.). Torque = r F, when applying a linear force perpendicular to a radius line to the axis of rotation. (Most torques we apply are done this way.) A "breaker bar" is a pipe used to extend the handle of a wrench -- this increases the torque for a given applied force, but the use of a breaker bar may damage the thing you are trying to torque. Using Right Hand Rule to assign directions to x,y,z coordinates and the sense of rotations for theta, omega (angular velocity), alpha (angular acceleration) and tau (torque). The Moment of Inertia, I, goes as m r² . Page 241 - Table 8-1: Some Moments of Inertia of Standard Shapes. A rod or stick of length l rotated about its center has I = (1/12)ml², whereas rotating the same rod about its end raises its moment of inertia to I = (1/3)ml². A thin ring of mass m and radius r rotated about its center has I = mr², but a solid disk has I = ½mr². Why we need a "rotational mass": Applications to angular momentum, L An ice skater spinning, bringing her arms closer to her axis of rotation -- this in an internal motion which means Newton's First Law. But Newton's version of the law looks at L, the change in the angular momentum. So L is constant, but her moment of inertia decreases (mass closer to body/axis), so therefore her angular velocity increases. Story of the large physicists and the merry-go-round.

Tuesday 10/30: Hand back (FINALLY!) some quizzes. Table 8-1: Some Moments of Inertia of Standard Shapes. Moment of Inertia of Ring, Solid Disk. Moment of Inertia of Solid Cylinder, Hollow Sphere, Solid Sphere. Rotational K.E., Rolling objects down an incline (rolling without slipping). mgh = ½ mv² + ½ Iw², the energy available from the P.E. is split between linear K.E. and rotational K.E. Depending on the moment of inertia of the rolling object, the final speed at the bottom of the incline varies, but does not depend on the mass m or the radius R. Demo: A "race" between aluminum rings of different sizes (R and L do not show up in the final solution, so don't matter, but one of the rings had a thicker wall so wasn't really a thin ring -- it had a lower I, so a faster speed), between two steel balls (again, radius R is not a factor), and finally between a metal ring, a solid disk, a hollow ball and a solid ball (here the finish order depends on the I used).

Wednesday 10/31: Statics: objects not translating in any direction and objects not rotating in any direction. Free Body Diagrams, Free Rotation Diagrams (sum of forces, sum of torques). Simple bridges, unloaded and loaded. Helpful hint: You can choose to put your pivot point (axis of rotation) anywhere you like, because if an object is not rotating, it is not rotating around any axis. So put the pivot point where one of your unknown forces is attached, and the algebra is easier.

Thursday 11/1: Free Body Diagrams, Free Rotation Diagrams (sum of forces, sum of torques). The Diver and the Springboard. Note that even though we had the direction of F1 wrong, it just came out negative, which means other way. Recall Atwood's Machine: Two masses suspended by a cable looped over a simple pulley. Two F.B.D.'s give us 2 equations in 2 unknowns: the common tension T1 and the common acceleration a. In the Real Pulley case, we have to also rotate the physical pulley, which has a mass, radius and a moment of inertia I. For a solid disk of mass M and radius R, the moment of inertia is Isolid-disk = ½MR². Now we have two F.B.D.'s and an F.R.D. (Free Rotation Diagram), giving us 3 equations in 3 unknowns: the two separate tensions T1 and T2 and the common acceleration a, after we use the conversion between linear and rotational acceleration. Finish this problem at home. m1 = 5.00 kg, m2 = 10.0 kg, M = 3.00 kg, R = 10.0 cm, and find T1, T2, and a. Q14 in-class quiz.

Friday 11/2: YES! WE HAVE CLASS TODAY! Extended Objects: We have been treating our objects really as dimensional dots, that have been allowed to have mass. Now we want to start considering how that mass is distributed. An airplane with mass unevenly concentrated in front, back or to one side, may not be flyable. Center of mass and Center of gravity are usually the same thing. Both are a "weighted average", meaning it combines a position with how much mass (weight) is involved. Center of mass in the x-direction: discrete case (Example: A meter stick balances at the 50 cm mark.) We have been calculating the motion of the center of mass all this time. Demo: Suspending real objects from different points to find the center of mass -- hung from the center of mass, the object is perfectly balanced. Include: irregular plate, rectangular plate, triangular plate, Michigan (Lower Pennisula), Florida. The center of mass does NOT have to be located ON the object -- the obvious example is a ring or hoop, where the center is empty. Demo: The toy that "rolls uphill" -- actually, whether with the cylinder or the double-cone, the center of mass is going downhill.

STILL Need to do this at home. Recall Atwood's Machine: Two masses suspended by a cable looped over a simple pulley. Two F.B.D.'s give us 2 equations in 2 unknowns: the common tension T1 and the common acceleration a. In the Real Pulley case, we have to also rotate the physical pulley, which has a mass, radius and a moment of inertia I. For a solid disk of mass M and radius R, the moment of inertia is Isolid-disk = ½MR². Now we have two F.B.D.'s and an F.R.D. (Free Rotation Diagram), giving us 3 equations in 3 unknowns: the two separate tensions T1 and T2 and the common acceleration a, after we use the conversion between linear and rotational acceleration. Finish this problem at home. m1 = 5.00 kg, m2 = 10.0 kg, M = 3.00 kg, R = 10.0 cm, and find T1, T2, and a.

Week of November 5-9, 2007.

NOTE: The Physics Help Room returns to 0077 Rood Hall - Nov. 5, 2007

Monday 11/5: Another classic statics problem: The ladder leaning on the wall. Choose pivot point at floor to eliminate two of the three unknown forces from the sum of torques equation. Homework: Figure out whether the perpendicular components of the weight and the wall (normal) force use sin or cos of theta, the angle the ladder makes with the floor. Is there enough static friction to hold it? (theta = 62°, m = 15.0 kg, L = 4.00 m, mu's of 0.600 and 0.800 for floor only, no friction with wall -- answer is YES.) Stability of objects -- demo with heavy steel plate. Falls over when center-of-mass is unsupported. Tall & skinny objects much easier to tip over, than low & wide.

Tuesday 11/6: Stability of objects -- not tipping over. Rollovers, "J-Turns" (a U-turn with a rollover), Jeep CJ vs. Jeep YJ. Ground clearance and the HUMVEE. Newton's Law of Universal Gravity. Tides (high/low, spring/neap).

Wednesday 11/7: Planetary Orbits. Ptolemy to Copernicus to Johannes Kepler. Epicycles, elliptical orbits and Occam's Razor. Tycho Brahe's observatory and his data. Q15 Take-Home, due Tuesday 13 November 2007.

STILL Need to do this at home:

Recall Atwood's Machine: Two masses suspended by a cable looped over a simple pulley. Two F.B.D.'s give us 2 equations in 2 unknowns: the common tension T1 and the common acceleration a. In the Real Pulley case, we have to also rotate the physical pulley, which has a mass, radius and a moment of inertia I. For a solid disk of mass M and radius R, the moment of inertia is Isolid-disk = ½MR². Now we have two F.B.D.'s and an F.R.D. (Free Rotation Diagram), giving us 3 equations in 3 unknowns: the two separate tensions T1 and T2 and the common acceleration a, after we use the conversion between linear and rotational acceleration. Finish this problem at home. m1 = 5.00 kg, m2 = 10.0 kg, M = 3.00 kg, R = 10.0 cm, and find T1, T2, and a. NOTE: This was assigned as homework on Thursday, zero had it done on Friday, 3(?) had it done on Monday, 9 on Tuesday and STILL ONLY 10 on Wednesday. (sigh)

Thursday 11/8: Kepler's First Law -- All orbits are ellipses, with the larger mass at one focus. Circular orbits are a special case where the semi-major axis is the same as the semi-minor asix: a = b = R. Kepler's Second Law -- The Equal Area Law is equivalent to a statement of Conservation of Angular Momentum. Kepler's Third Law -- T² = C R³, where R is the radius of a circular orbit, or the average distance in an elliptical orbit. There is one value for the constant C for every orbital system, i.e. one C for objects orbiting the Earth, another C for objects orbiting the Sun. Example: Using our data from the Space Shuttle's Low Earth Orbit, we can calculate C for Earth. Then plug in the R for the Moon's orbit and get an orbital period of 27.4 days, which is essentially correct. NOTE: There are several definitions of the lunar month -- the one normally used is the time to return to the same place in the sky, which because the Earth is going around the Sun, is slightly MORE than one orbit and is about 28 days. Extended Objects: Mass occupies a volume and shape. Three Classical States of Matter: Solid, Liquid, Gas. Combinations: Condensed Matter (covers both Solids and Liquids) and Fluids (covers both Liquids and Gasses). Two Extreme States of Matter: Plasma (electrons stripped off, high temperature), Cryogenics (extreme cold, odd behavior).

Friday 11/9: YES! WE HAVE CLASS TODAY! Return X2. Extended Objects -- Allowing for Deformation. Stress = Force / Cross-sectional Area. Pressure also is Force = F/A. (SI units = N/m² = Pascal = Pa) Strain = Delta-L / L0 , the amount of deformation divided by the original length. First Sample Exam 3 handed out. (Click here for a copy.)

Week of November 12-16, 2007.

Monday 11/12: Extended Objects -- Allowing for Deformation. Stress versus Strain graph. Linear region (no damage), elastic limit, plastic deformation, brittle and ductile failures. Tensile Strength, necking, voids, failure. Young's Modulus. Tension, Compression, Shear. Pre-Stressed Concrete. Bulk Modulus, for compression of bulk material due to applied Pressure (also equals Force/Area). LAST DAY TO TURN IN DRAFT PAPERS TO DR. PHIL.

Tuesday 11/13: 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). Pressure = Force / Area. SI unit: Pascal (Pa). Example: Squeezing a thumbtack between thumb and forefinger. The difference between Gauge Pressure (pressure difference inside and out, can be positive, negative or zero) and Absolute Pressure (total pressure, always positive or zero only for vacuum). One Atmosphere standard air pressure = 1 atm. = 14.7 psi = 101,300 Pa. Pressure at a depth due to supporting the column of liquid above. Water pressure = 101,300 Pa at depth h = 10.33 m. Second Sample Exam 3 handed out. (Click here for a copy.) Q16 Take-Home, due Thursday 15 November 2007.

Wednesday 11/14: Pressure at a depth due to supporting the column of liquid above. Water pressure = 101,300 Pa at depth h = 10.33 m. Why you need a qualified SCUBA instructor. 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. Floating on the Surface: Mass-to-Volume Ratio of the boat < Mass-to-Volume Ratio of the Liquid.

Thursday 11/15: Floating on the Surface: Mass-to-Volume Ratio of the boat < Mass-to-Volume Ratio of the Liquid. Why Boats Float. Example: Front lab table as a 250 kg boat with 4.00 m³ volume. Buoyant Force = Weight of the Boat = Weight of the Water Displaced by the Submerged Part of the Boat. NOTE: Do not confuse the Density of the Materials with the Mass-to-Volume Ratio of the OBJECT. First day to turn in Topic 1 Papers -- continues through Monday 19 November 2007 at 5pm. (Draft papers get extended deadline.) Third Sample Exam 3 handed out. (Click here for a copy.) Q17 in-class quiz. Q18 Take-Home, due Tuesday 20 November 2007.

Friday 11/16: YES! WE HAVE CLASS TODAY! Pressure from a column of liquid looks like P.E. Create a Kinetic Pressure term which looks like K.E. to create Bernoulli's Equation and the Continuity Equation. Water Tower and the Faucet Problem. Why the water tower needs a vent. When speed goes up, pressure goes down. Air flow around a wing. (Faster air over top means lower pressure on top, so net force is up -- Lift.) Why the Mackinac Bridge has grates on the inside north- and soundbound lanes. This should close the book on Exam 3 topics. Topic 2 Worksheets (Click here for Worksheets and Directions)

Week of November 19-23, 2007.

Monday 11/19: Review for X3. Bernoulli's Equation and the Continuity Equation. When speed goes up, pressure goes down. The aspirator, a vacuum pump with no moving parts.

Tuesday 11/20: Exam 3.

Wednesday 11/21: Class cancelled.

Thursday 11/22: <Thanksgiving Day> No classes.

Friday 11/23: No classes.

Week of November 26-30, 2007.

Monday 11/26: Temperature & Heat. Heat = Energy. Two objects in thermal contact, exchange heat energy, Q. If net heat exchange is zero, the two objects are at the same temperature. Temperature Scales: °F, °C and K (Kelvins).

Tuesday 11/27: 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 (0°C) to summer (40°C), but that's about a meter for every mile of railroad track. Bimetalic strip uses two coefficients of linear expansion to curve one way or the other when heated or cooled. Can be used in a thermostat. Bridge expansion joints. Why "Bridge Freezes Before Roadway" signs. Q19 Take-Home, due Thursday 29 November 2007. NOTE: On 11/27 you can do part (a), you can do part (b) "the hard way" by finding the new lengths in all three directions, otherwise parts (b) and (c) will be covered on 11/28.

Wednesday 11/28: Expansion joints. I-57 in Chicago and the expanding asphault. 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). Heat Energy (Q) and Temperature Change & Phase Change. Add/remove Heat Energy Q will raise/lower the temperature of a material using the Specific Heat (J/kg·°C) for objects of mass m, or the Heat Capacity (J/mole·K) for objects with n moles of atoms or molecules. Add/remove Heat Energy Q will change its phase between solid-liquid-gas using the Latent Heat of Fusion, Lf, between solids and liquids, or the Latent Heat of Vaporization Lv, between liquids and gasses.

Thursday 11/29: Heat Energy (Q) and Temperature Change & Phase Change. 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. "A watched pot never boils". Water will boil in a pan for a long time. Indeed, the latent heat of vaporization of water, 2,260,000 J/kg is huge and important for cooking and putting out many fires. Water doesn't drown the fire, it removes heat from the fire, lowering its temperature eventually below the ignition point. Can't use water on all fires. Class D (magnesium) fires, electrical fires. Halon gas fire supression systems protect computer hardware in a big data center, but displace the breathable air -- get out when alarm sounds! NOTE: Dry Ice (solid CO2) at 1 atm air pressure, does not exist as a liquid, so it goes directly from solid to gas -- it would have a latent heat of sublimation. The change in the internal energy of system Uf - Ui = Q + W. The Laws of Thermodynamics. (Zeroeth Law -- There is such a thing as temperature.) Entropy examples -- It takes work to clean or restore things. Left to themselves, everything falls apart. The Heat Engine.Q20 Take-Home, due Tuesday 4 December 2007. (Click here for a copy.) NOTE: We will be covering the Physics for this quiz on Friday! NOTE: No afternoon office hours -- Dr. Phil has a dentist appointment.

Friday 11/30: 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. Smaller, lighter cars with smaller, lighter engines. To improve efficiency, can reduce TC or raise TH . First Sample Final Exam handed out. (Click here and here for a copy.)

Week of December 3-7, 2007.

Monday 12/3: Reverse the arrows in the Heat Engine and you get a Refrigerator. Cannot place an open refrigerator or a window air conditioner in the middle of a room and cool the room, because the exhaust heat to the hot side includes the heat pulled from the cold side plus the work done on the compressor. A Heat Pump is a reversible system which cools inside of the house in summer and heats the inside of the house in winter -- just because it is cold outside, doesn't mean there is not heat energy Q in the outside air. (There has to be, otherwise the air would be at 0 K.) Coming up -- Periodic Motion, Waves and Resonance. Revisit Mass on a spring. F = -kx = ma. Equations for x, v and a are sine & cosine solutions. NOTE: Due dates for Topic 2 Worksheets and Q20 Take-Home quiz both extended by one day, to accomodate those having weather problems.

Tuesday 12/4: Revisit Mass on a spring. F = -kx = ma. Equations for x, v and a are sine & cosine solutions. Angular frequency omega = 2pi f= sqrt(k/m). Any time you have a conservative linear restoring force that can act as periodic motion you have a Simple Harmonic Oscillator that undergoes Simple Harmonic Motion. S.H.O. & S.H.M. Simple Pendulum -- omega = sqrt(g/L). Grandfather clocks won't work right in space or on the Moon. (But a tortional pendulum mantlepiece clock will.) Q21 Take-Home, due Thursday 6 December 2007.

Wednesday 12/5: 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). If you exceed the wave speed in a material, you get a Shock Wave -- distinctive V-shaped pattern from front and back of moving object. Sonic booms in air (actually get a double-boom, because of the two V's.), wake from a boat in water. Resonance allows us to see the wave confined to the geometry of the problem. Standing Waves on a string. Fundamental, First Overtone, Second Overtone, etc. Demonstration: First and higher overtones on a string driven by a saber saw. Third Sample Final Exam -- the All-Titanic exam. (Click here for a copy.)

Thursday 12/6: Return X3. Standing Waves in a tube. Tuning forks, resonance tubes. 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. "Normal" human hearing is frequencies from 20 Hz to 20,000 Hz. Artilleryman's ear -- mid-range hearing loss. dB = decibel, a logarhythmic scale. Sound Meter results from a previous semester: ambient noise in 1110 Rood = 56 dB; Dr. Phil talking at ½ meter = 63 dB; Class shouting = 83 dB; Dr. Phil shouting at ¼ meter = 108 dB. Q22 points for attendance sign-in sheet.

Friday 12/7: LAST DAY OF CLASS. At this point, all outside work (Take-Home Quizzes and Worksheets, plus the Paper) has been assigned. Only outstanding item is the Final Exam, including Q23 as the Check-Out form. Course Review. Finish up the day with the course & teacher evaluations for the semester.