Dr. Phil's Home
Updated: 1 July 2008 Tuesday.
Monday 6/23: (NOTE: With Bernoulli's and Continuity, we close the book on the Final Exam.) Demo: 2-liter bottle with holes in it -- water comes out in a parabolic arc, the cap can act as a "valve" and stop the water flow out of one hole, but not two, due to the drop in pressure as the water level drops in the sealed up bottle. Bernoulli's Equation and the Continuity Equation. When speed goes up, pressure goes down. 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 -- generating Lift.) The spoiler is a vent door in a wing designed to allow air to flow from bottom to top and thus "spoiling" the pressure difference and "spoiling" the lift. The Mackinac Bridge -- inside lanes are open metal grates and cannot support a pressure difference. 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. 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. Artilleryman's ear -- mid-range hearing loss. Q22 in-class attendance. Q23 will be a Check-Out form filled out when you turn in your Final Exam.
Tuesday 6/24: FINAL EXAM (2 HOURS)
Wednesday 6/25: Make-up exam at Noon.
Thursday 6/26: No office hours.
Friday 6/27: Office hours.
Monday 6/30: Office hours.
Tuesday 7/1: Grades will be done by Noon.
Monday 5/5: Class begins. The nature of studying Physics. Science education in the United States. Natural Philosophy. The Circle of Physics. Aristotle and the Greek Philosophers. Observation vs. Experiment - Dropping the book and the piece of paper (2 views). Distribute syllabus.
Tuesday 5/6: Observation vs. Experiment - Zeno's Paradoxes. "Speed Limit 70" First Equation: Speed = Distance / Time. Development of Speed equation for Constant or Average Speed. 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. Topic 1 assigned. (Click here for a copy of the handout.)
Wednesday 5/7: No class.
Thursday 5/8: The S-Shaped Curve continued. Acceleration. Integrating to find the set of Kinematic Equations for constant acceleration. Kinematic Equations for Constant Acceleration. The Equation Without Time -- Avoiding the Quadradic Formula. Discussion of Formula Cards. SI Metric System. What do we mean by Measurements? 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. (5/13/06 Sa: new World Record in 100m dash -- 9.76 seconds) Q1 and your PID number. (If you missed class on this day, check with Dr. Phil sometime soon.)
Friday 5/9: There are six kinematic variables for constant acceleration in 1-D: x0, x, v0, v, a and t. Example: car accelerating from rest. But what does the answer mean? PTPBIP -- Put The Physics Back Into the Problem. What do we mean by a = 1 meter/sec² ? You cannot accelerate at 1 m/s² for very long. Types of Motion: No Motion (v=0, a=0), Uniform Motion (v=constant, a=0), Constant Acceleration (a=constant). We generally cannot accelerate for very long. Free fall, ignoring air resistance -- all objects near the surface of the Earth will fall at an acceleration g = 9.81 m/s². Example: acceleration and time for a bullet fired from a rifle. 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). Dr. Phil's Reasonable Significant Figures. (Click here for a copy of the handout.) Q2 in-class.
Monday 5/12: Demo: Our class webpages and what you can find on them. 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." Re-visit the Simplified Trip to the Store. Can't actually move that way -- Nature does not like sharp edged changes in the speed. Real life has rounded edges. The fundamental equations of motion are based on the calculus: x, v and a are related by derivatives (slopes) and integrals (areas under the curve). v = dx/dt, a = dv/dt = d²x/dt². There are higher derivatives. For example, jerk is j = da/dt = d²v/dt² = d³x/dt³. Motion in Two-Dimensions: x and y directions are perpendicular to each other. You may be able to break it down into two one-dimensional problems, connected by time, which you can already solve. (The guy with the fedora and the cigar.) First Sample Exam 1 (Click here for a copy.) Quiz 3 Take-Home, due Tuesday 13 May 2008 in class or by 5pm.
Tuesday 5/13: Solution to The guy with the fedora and the cigar problem. 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. Another problem with two motions linked by time: 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. Types of Motion: No Motion (v=0, a=0), Uniform Motion (v=constant, a=0), Constant Acceleration (a=constant) -- These first three can all be included in the Kinematic Equations for Constant Acceleration -- and Higher Order Derivatives (jerk=constant, etc.) which require calculus. 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. Second Sample Exam 1 (Click here, here and here for a copy.) Quiz 4 Take-Home quiz, due Thursday 15 May 2008 in class or by 5pm.
Wednesday 5/14: No class.
Thursday 5/15: 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. Finding the final vector velocity of The guy with the fedora and the cigar problem. Third Sample Exam 1 (Click here for a copy.) Quiz 5 Take-Home quiz, due Friday 16 May 2008 in class or by 5pm.
Friday 5/16: Ballistic (or Projectile) Motion -- applies equally to a thrown football and a cannonball. Still working with ax = 0 and ay = -g. History of early cannons. 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. Fourth Sample Exam 1 (Click here for a copy.) Quiz 6 Take-Home, due Monday 19 May 2008 in class of by 5pm.
Monday 5/19: Unit Vectors: i-hat, j-hat, k-hat (point in x, y, z directions, respectively), have unitary length (length of 1). Allow you to describe a vector with x- and y-components times the i- and j-hat unit vectors. A final note on ballistic motion: You have to have some positive v0y if you want to jump a gap, because otherwise you start falling immediately once you are no longer supported. 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. For UCM, ac = v²/r. Space Shuttle in Low-Earth Orbit. (There's still gravity up there!).
Tuesday 5/20: Exam 1.
Wednesday 5/21: No class.
Thursday 5/22: Uniform Circular Motion (UCM) continued: Example of a 14" and a 2" hard disk drive spinning at 3600 rpm. Frequency (Hz) f = 1 / T. With spinning objects is very easy to come up with enormous centripetal accelerations. Recap: Our studies so far have described "How" things move, and allow to say "When" and "Where" things move, but not "Why" things move. For that we have to start talking about Forces -- and that means Newton. Some stories about Sir Isaac Newton. Zeroeth Law - There is such a thing as mass. Mass is a measure of how much "stuff" an object made of matter contains. SI unit of mass = kilogram (kg). 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. The Normal Force is a contact force perpendicular to a contact surface. 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.) "If I were to punch the wall, then the wall punches back." The Normal Force and the weight may be equal-and-opposite forces, but if they both apply to the same object, this is First Law, not Third Law. Force is a vector. Free Body Diagrams. Normal Force (Normal = Perpendicular to plane of contact). Sum of forces in x or y equations. SI unit of mass = kilogram (kg). SI unit of force = Newton (N). Pushing a 125 kg crate around. (Near the surface of the Earth, you can use the relationship that 1 kg of mass corresponds [not "equals"] to 2.2 lbs. of weight. So multiple 125 by 2 and add 10%... 250 + 25 = 275... so a 125 kg crate has a weight of mg = 1226 N or 275 lbs.). "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." Q7 in-class.
Friday 5/23: Some stories about Sir Isaac Newton. Continue with the 125 kg crate. 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." 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. Q8 in-class. Reminder: No class on Monday 26 May 2008 for Memorial Day holiday.
Monday 5/26: Memorial Day (Observed). No classes.
Tuesday 5/27: 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.). Atwood's Machine: Two blocks whose motion is link via a common cable and a pulley. Note that though they have a common magnitude of both speed and acceleration, the velocity vector has no bearing on either the F.B.D. or the solution to the Tension and acceleration. Elevator Problems. The Normal Force represents the "apparent weight" of the person in the elevator. For the elevator at rest or moving at constant speed, the Normal Force = weight, and the tension of the cable = weight of loaded elevator. But if there is an acceleration vector pointing up, the apparent weight and the tension of the cable increase; if the vector points down, the apparent weight and the cable tension decrease. In true Free Fall, without any air resistance, the Normal Force = 0 and you are floating. Hanging a sign with angled wires -- still the same procedure: Sketch of the problem, Free Body Diagram, Sum of Forces equations in the x- and y-directions, solve for unknowns. Need to deal with Friction -- two kinds (static and kinetic) -- but will next deal with inclined planes. Change the co-ordinate system, change the rules. In the tilted x'-y' coordinates, this is a one-dimensional problem, not two-dimensional. First Sample Exam 2. (Click here for a copy.) Quiz 9 Take-Home, due Thursday 29 May 2008 (may be extended if people are having trouble). Quiz 10 Take-Home, due Thursday 29 May 2008.
Wednesday 5/28: No class.
Thursday 5/29: Return X1. Two kinds of Friction: Static (stationary) and Kinetic (sliding). For any given contact surface, there are two coefficients of friction, µ, one for static and one for kinetic. Static is always greater than kinetic. Static Friction is "magic", varying between zero and its maximum value of µ times the Normal Force. Kinetic Friction is always µ times the Normal Force. Demonstration of block sliding down inclined plane with 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. 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. Second Sample Exam 2 (Click here and here for a copy.) Quiz 11 Take-Home, due Monday 2 June 2008.
A NOTE ON HISTORY BEING MADE THIS WEEK: Click here to see one of the most important photographs in human history. Be sure to click on the link Full Resolution to see the picture in detail. Not sure why this is so important? Click here for one scientist's view. -- You're welcome, Dr. Phil.
Friday 5/30: 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. Work: A Physics Definition (Work = Force times distance in the same direction). Work = Energy. Pay particular attention to Units. Dot products: one of two methods of multiplying two vectors -- this method generates a scalar, which is a good thing because Work happens to be a scalar, which is Work's virtue (i.e. why we care). Dot products: run through two 3-dimensional vector case. Kinetic Energy -- an energy of motion, always positive, scalar, no direction information. Work-Energy Theorem (net Work = Change in K.E.). Lose angle and directional information because energy is a scalar, not a vector. Potential Energy: Storing energy from applied work for later. Gravitational P.E. = mgh. Conservation Laws are very important in Physics. Conservation of Total Mechanical Energy (T.M.E. = K.E. + P.E.). Lose angle and directional information because energy is a scalar, not a vector. Example: Roller-Coaster. If speed at top of the first hill is about zero, then this P.E. is all we have. Cannot get higher, but we can change height for speed. 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.) Quiz 12 Take-Home, due Monday 2 June 2008.
NOTE: Our Exam 2 this semester will NOT include momentum (p = mv) and collisions, power (P = Work/time) and won't include Newton's Law of Universal Gravity.
Monday 6/2: Work through some examples of Work, the Work-Energy Theorem, Conservation of Energy. New material for class on Thursday: We need another Physics quantity, one which describes the "relentless quality" of motion, one that includes mass. Inertial or Linear momentum: p = m v. This is a vector. More Conservation Laws in Physics. Two extremes in collisions: Totally Elastic Collision (perfect rebound, no damage) and Totally Inelastic Collision (stick together, take damage). Linear momentum is conserved in all types of collisions. Example: The Yugo and the Cement Truck. Head-on Collisions. Fourth Sample Exam 2 (Click here for a copy.)
Tuesday 6/3: Exam 2.
Wednesday 6/4: No class.
Thursday 6/5: Linear momentum is conserved in all types of collisions. Example: The Yugo and the Cement Truck. 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.) Seat belts, shoulder belts, steel beams in doors and crumple zones. What happens in a wreck. The myth of "better to be thrown from the wreck." How airbags work. 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: The Executive Time Waster. Why you want inelastics collisions in a wreck. 5 mph versus 3 mph impact bumpers. Quiz 13 Take-Home, due on Friday 6 June 2008.
Friday 6/6: Why you want inelastics collisions in a wreck. "Adobe: The Little Car Made of Clay". Newton's Form of the Second Law (differential form). Impulse (integral form). NOTE: The difference between Work and Impulse, is that one integrates the Force over distance, the other Force over time. What's the opposite of a collision? An explosion. Or recoil. Example: A pitcher on ice skates at rest -- when he hurls a fastball to the right, he goes to the left. Total momentum of the system remains constant (in this case, zero). The Rocket Equation -- use conservation of momentum. Resistive Forces: Air Resistance. Low speed and high speed air resistance. If allowed to drop from rest, then a real object may not free fall continuously, but may reach a Terminal Velocity (Force of gravity down canceled by Drag force up) and doesn't accelerate any more. Ping-pong balls versus turkeys or pennies. World's Record Free-Fall. And 27 May 2008 Failed Attempt. Quiz 14 Take-Home, due on Monday 9 June 2008.
Monday 6/9: Translating Linear physics to Rotational physics (as "easy" as changing Roman/English variables to Greek). The radian is a "quasi-unit" -- it's not really a unit, but represents a fraction of a circle. (We can "wish" it away when we need to.) Angular position, angular velocity, angular acceleration, angular force = torque. Newton's 3 Laws of Motion applied to rotations. Angular momentum. Rotational Work, rotational K.E., angular momentum. Extended Objects: We have been treating our objects really as dimensional dots, that have been allowed to have mass. Now we want to start considering how that mass is distributed. An airplane with mass unevenly concentrated in front, back or to one side, may not be flyable. Center of mass is a "weighted average", meaning it combines a position with how much mass is involved. Center of mass in the x-direction: discrete case and 1-D uniformly distributed mass (Example: A meter stick balances at the 50 cm mark.) We have been calculating the motion of the center of mass all this time. Quiz 15 Take-Home, due on Thursday 12 June 2008. NOTE: That the quiz has two pages. If done correctly, (b) = (e) and (c) = (d).
Tuesday 6/10: Center of Mass (con't.): 2-D uniformly distributed mass -- Center of mass in x-direction and in y-direction. Rectangular plate. Note that the center of mass value depends on the coordinate system, but the center of mass point remains in the same place. Triangular plate -- parameterizing y = y(x) (y as a function of x). Mass per unit length (lamda), mass per unit area (sigma). Demo: Suspending real objects from different points to find the center of mass -- hung from the center of mass, the object is perfectly balanced. Include: irregular plate, rectangular plate, triangular plate, Michigan (Lower Pennisula), Florida. The center of mass does NOT have to be located ON the object -- the obvious example is a ring or hoop, where the center is empty. Demo: The toy that "rolls uphill" -- actually, whether with the cylinder or the double-cone, the center of mass is going downhill. Start discussion of Moment of Inertia. We will be reproducing the results from Table 10-2 in your textbook, but you can use these results on your Formula Card and on this next quiz. Moment of Inertia, discrete case. Parallel Axis Theorem. Moment of Inertia by Integration, Double- and Triple-Integrals in Rectangular, Polar, Cylindrical and Spherical Co-ords. An aside on Polar Coordinates and the integration of dL to get C = 2 pi R and dA to get A = pi R². Moment of Inertia of Ring, I = MR² by inspection, by integration. Moment of Inertia by Integration, Double- and Triple-Integrals in Spherical Co-ords. Moment of Inertia of Ring, Solid Disk. Moment of Inertia of Solid Cylinder, Hollow Sphere, Solid Sphere. Rotational K.E., Rolling objects down an incline. First Sample Exam 3. (Click here for a copy.) Quiz 16 Take-Home, due on Friday 13 June 2008. *** Note that for Summer 2008, Dr. Phil is not taking the time to cover the items in gray text -- you're welcome. (grin) We will simply use the results from Table 10-2 of your textbook.
Wednesday 6/11: No class.
Thursday 6/12: The Cross Product and Right-Hand Rule (R.H.R.). 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 vectors for these variables ends up pointing up or down the axis of rotation. 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. Angular momentum L = r p, when the linear momentum vector is perpendicular to the radius vector. The Cross Product (or Vector Product) is the exact opposite of the Dot Product (or Scalar Product). Multiplying two vectors together by a cross product gives us another vector (instead of a scalar). And the cross product is not commutative, vector-A × vector-B = - (vector-B × vector-A), so the order is paramount. How we solve force problems: (1) Free Body Diagram, (2) Sum of Forces equations, (3) Newton's Laws. How we solve torque problems: (1) Free Rotation Diagram, (2) Sum of Torques equations, (3) Newton's Laws. Real pulleys vs. Perfect Massless Pulleys. The acceleration of the Atwood's Machine with a real pulley is less than the acceleration with a simple pulley, because it takes work and energy to rotate the real pulley. The "Free Rotation Diagram". Statics: objects not translating in any direction and objects not rotating in any direction. Free Body Diagrams, Free Rotation Diagrams (sum of forces, sum of torques). Loaded bridge. Diving board. Second Sample Exam 3. (Click here, here and here for a copy.) Quiz 17 Take-Home, due on Monday 16 June 2008. If you're keeping score at home, Statics is in Chapter 12 of your book, and teeter-totters and the leaning ladder are both examples in the book.
Friday 6/13: FRIDAY THE THIRTEENTH -- not a WMU Holiday. Return X2. Statics problems (no translation, no rotation about any axis) con't. 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 = 70°, m = 15.0 kg, L = 3.00 m, mu's of 0.600 and 0.700 for floor only, no friction with wall.) If you're keeping score at home, Statics is in Chapter 12 of your book, and teeter-totters and the leaning ladder are both examples in the book. Stability of objects -- demo with heavy lead brick. (Additional demo of inertia -- volunteer doesn't feel hammer blow when hand is under lead brick.) Falls over when center-of-mass is unsupported. Tall & skinny objects much easier to tip over, than low & wide. 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 Normal Force (or component), friction, etc. For a car on a flat road making a turn, the maximum safe speed for a turn comes from the maximum static friction. For a car on a banked (angled) curve, there is a "natural" design speed where you can go around a curve with that radius without friction. Stability around a curve also connected with previous discussion of stability and center-of-mass. Rollovers, "J-Turns" (a U-turn with a rollover), Jeep CJ vs. Jeep YJ. Ground clearance and the HUMVEE. NOTE: All three current take-home quizzes, Q15, Q16 and Q17, extended to Monday 16 June 2008. Would like to get them all turned in by 3pm on Monday, so that I can post the solutions on Monday afternoon.
Monday 6/16: Remember, X3 material begins with Totally Inelastic Collisions. 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 Normal Force (or component), friction, etc. For a car on a flat road making a turn, the maximum safe speed for a turn comes from the maximum static friction. For a car on a banked (angled) curve, there is a "natural" design speed where you can go around a curve with that radius without friction. Extended Objects -- Allowing for Deformation. Young's Modulus. Tension, Compression. Bulk Modulus. Decided not to give a Q18 in-class quiz today -- ended class early so people could work on their Take-Home quizzes, print out their papers, ask questions about Exam 3, etc.
Tuesday 6/17: Exam 3.
Wednesday 6/18: No class.
Thursday 6/19: Power = Work / time. Since W=Fd, then P=W/t = Fd/t = Fv for constant Force and constant speed. Newton's Universal Law of Gravity (or Newton's Law of Universal Gravity). Gravity is attractive between any two masses. Same magnitude, opposite direction by Newton's Third Law. Use Universal Gravity to check "g". The value we calculate is close, 9.83m/s², which turns out to be only off by 0.2%. Why is it off? Because using Univeral Gravity in this manner makes the assumption that the entire Earth is uniform and homogenous from the surface to the core -- which it is not. We would need to integrate over layers to get the observed value of 9.81m/s². The problem of determining G and the mass of the Earth. The four fundamental forces in nature, from weakest to strongest: Gravity, Electromagnetism, Weak Nuclear Force, Strong Nuclear Force. Gravity may be the weakest, but it holds us onto this planet and "binds the galaxies together". Story of researchers thinking they'd discovered a "fifth" force -- turned out to be Moon's attraction. Tides (high/low, spring/neap). 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). Mass-to-Volume Ratio (Density). NOTE: Do not confuse the Density of the Materials with the Mass-to-Volume Ratio of the OBJECT. Density of Water built into the SI metric system (1 gram/cm³ = 1000 kg/m³). Floating on the Surface: Mass-to-Volume Ratio of the boat < Mass-to-Volume Ratio of the Liquid. Why Boats Float. Example: Front lab table as a 250 kg boat with 4.00 m³ volume. Buoyant Force = Weight of the Boat = Weight of the Water Displaced by the Submerged Part of the Boat. Finding how much of a rectangular boat is submerged. First Sample Final Exam. (Click here and here for a copy.) Double-Quiz 18 & 19 Take-Home, due FRIDAY 20 June 2008. NOTE: The mass and radius of the Moon are available in tables in your textbook.
Friday 6/20: Mass-to-volume Ratio -- Archimede's and the Crown. Water is an unusual material, as the mass-to-volume ratio of ice (solid) is less than water (liquid). Thus ice floats and lakes freeze from the top down, rather than the bottom up. Floating ice, when melted, does not change the water level. But grounded ice, especially inland glaciers will add volume (and depth) to the sea when melted. If the seas were raised by 60-125 feet, how much of Florida would be left? Hooke's Law (Spring force) is a second conservative force, which we can also write as a P.E. Pressure = Force / Area. SI unit: Pascal (Pa). Example: Squeezing a thumbtack between thumb and forefinger. One Atmosphere standard air pressure = 1 atm. = 14.7 psi = 101,300 Pa. Pressure at a depth due to supporting the column of liquid above. 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). 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. 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. Water Tower and the Faucet Problem. Why the water tower needs a vent. The Continuity Equation. When speed goes up, pressure goes down. Second Sample Final Exam. (Click here and here for a copy.) Double-Quiz 20 & 21 Take-Home due Monday 23 June 2008 by 3pm. NOTE: Both Double-Quizzes 18-21 must be turned in by 3pm Monday 23 June 2008, so I can post the solutions!
A cartoon for your amusement: http://dr-phil-physics.livejournal.com/164829.html. (I've been arguing that Physics is the Senior Science for years...)