Dr. Phil's Home

## Lectures in PHYS-1070 (29)

### CURRENT MID-TERM GRADES FOR PHYS-1070 CAN BE FOUND HERE

Updated: 13 November 2015 Friday.

### Week of 9-13 November 2015.

Monday 11/9: 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.

• Bernoulli's Equation, with six terms, is the longest equation of the semester. But like the Conservation of TME, upon which it is based, often we don't need all six terms and Bernoulli often simplifies to quite managable equations.
• Note that the solution to the water tower problem is the same equation as if I had just dropped the water from rest at the top of the water tower. (grin)

Tuesday 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.

• Video: Standing waves and resonance can occur when you don't want them to, due to Bernoulli, sometimes with disasterous results. See The Tacoma-Narrows Bridge Disaster. NOTE: The video in this article is shown in real time -- it is NOT speeded up.
• Mackinac Bridge with open green metal grates of inside lanes. These spoil the lift so Big Mac cannot become a wing. (Click on image for larger.)

Wednesday 11/11: Old wooden water towers and farm silos are wrapped in steel bands which are not evenly spaced. They are closer together at the bottom, farther away at the top. This is due to the increased pressure on the bottom. When these towers fail, it's usually on the bottom where the pressure is greatest. Q10 in-class.

Thursday 11/12: Dr. Phil out sick -- no subsitute available in time -- class cancelled.

Friday 11/13: Dr. Phil out sick -- substitute. Expected material available:

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.

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).

### Week of 7-11 September 2015.

Monday 9/7: Labor Day <No Classes>

Tuesday 9/8: Class begins. The nature of studying Physics. Science education in the United States. The Circle of Physics. Intro Handout. (Click here for a copy if you didn't make it to the first class.)

• Physics Help Room opens today -- 3302 Rood.
• NOTE: PHYS-1080 Lab begins this week. If you missed your first lab, don't panic. You will be responsible, however, to prove to your Lab T.A. that you have read and understood the Introduction to your PHYS-1080 Lab Manual.
• Reminder: PHYS-1080 is the lab course and is separate from PHYS-1070. I've been asked to remind you to buy the lab manual using the directions emailed to you from Chris Hoffman, the lab supervisor -- he arranged for a special low price for you. *** Read the emails -- the Lab Manuals may not be ready yet for PHYS-1080 ***

Wednesday 9/9: 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 . Rewrite as: d = v t.

Thursday 9/10: Distribute Syllabus. v = d / t or d = v t. So d = distance. Position also has units of length, is x, y or z. Displacement is final position minus initial position, or d = xfinal - xinitial = xf - xi. xi = xt=0 = x0 (x-sub-zero). Physicists love our subscripts -- they're like name tags. Finally d = x - x0 = v t or x = x0 + v t. All these equations are rewrites of the same thing, but these rewrites will become useful soon. Q1 (Attendance -- Q1A coming if you weren't in class.)

• No Panic Quiz 1½ on Friday, simple problem "to keep us honest".

Friday 9/11: Topic 1 assigned. (Updated Searchable booklist available online NOT UP YET -- use last years for now .) Q1½ In-Class worksheet -- "No Stress Quiz".

### Week of 14-18 September 2015.

Monday 9/14: PTPBIP - Putting The Physics Back Into The Problem. Go over Q1½. The P-O-R (Press-On-Regardless) road rally problem. "You can't average averages." Note that Q1½ part (c) is just like the P-O-R problem. 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.

Tuesday 9/15: English system of measurement. SI Metric System. Prefixes. What do we mean by Measurements? "Units will save your life." What is "1 m/s"? We need a few benchmark values to compare English and SI Metric quantities. NOTE: English-to-Metric conversions will NOT, with two exceptions, be tested on in this course. 60 m.p.h. = 26.8 m/s. 1.00 m/s = slow walking speed. 10.0 m/s = World Class sprint speed (The 100 meter dash -- Usain Bolt is the current Olympic (9.683 seconds) and World (9.58 seconds) record holder.) 26.8 m/s = 60 m.p.h.. 344 m/s = Speed of sound at room temperature. 8000 m/s = low Earth orbital speed. 11,300 m/s = Earth escape velocity. 300,000,000 m/s = speed of light in vacuum (maximum possible speed).

• Wikipedia today reports that: "The current men's world record is 9.58 seconds, set by Jamaica's Usain Bolt in 2009, while the women's world record of 10.49 seconds set by American Florence Griffith-Joyner in 1988 remains unbroken."
• NOTE: Here's what Q1½ looks like in SI metric.
• Quiz 2 will be on FRIDAY 18 September 2015.

Wednesday 9/16: 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.

• NOTE: Due to doctors' appointments, there are NO 2-4pm Office Hours on 9/16 Wed or 9/17 Thurs.
• The Real World: Go to the Library, the magazine section of a book or grocery store, or a personal collection. Look for automobile magazines like Road and Track, Car and Driver, etc. Perhaps about 1/3 of the way in, look for a performance review of a new car with a graph of v vs. t under maximum acceleration conditions on a track. Note how the graph looks, as opposed to our Time Regions I and II in our S-Shaped Curve simplified trip. Do you understand why the real graph looks like it does?

Thursday 9/17: Kinematic Equations for Constant Acceleration. 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. 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. Dr. Phil's Simplified Significant Figures for multiplication, division and trig functions. (Click here if you need a copy.)

• NOTE: The class webpage now features some Sample Exam 1s. These are from real PHYS-1070 Exam 1s. Some have solutions, some do not not. The ones without solutions you need to figure out by PTPBIP or comparing answers with others to see if you're right. After all, you don't have the answers in front of you when you take the exams for real. Actual exams may have more white space to work in. Some have more than one exam's worth of material. Obviously there are some problems you can't do yet, because we haven't covered that material yet. Each semester is different, so you wull be told when "the book is closed" on material for your actual Exam 1.
• FORMAT FOR EXAM 1: Problem 1 -- ten multiple guess questions very much like those you'll see in some of the Sample Exam 1s. The first group will use the handy little table for Number of Minutes per Mile at various speeds in mph. Problem 2 -- one problem with five parts, much like those in the Quizzes and like the problems in the Sample Exams 1s.
• Table of   a = 1.00 m/s² :
 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

• If you were to accelerate at 1.00m/s² using your feet, you would not be able to do so for more than a few seconds. Because by 10.0 seconds you would be running at 10.0 m/s! And at 25.0 seconds you would be running at over 50 mph, which you can't do. This is different from a constant speed of 1.00 m/s, which you can do for a very long time.
• Note that even though we generated some new equations, they should NOT be put on your formula card. We start from the definitions or the kinematic equations. We don't generate a bazillion equations, each one designed to solve just one problem, but develope a toolkit that will solve many problems.
• Note that if a variable is zero, anything multiplying it will also be zero -- the whole term goes away.
• PLEASE! Do algebra on the equations first. THEN put in the units. THEN check your units. Only then do you punch numbers into the calculator. PTPBIP! Doing algebra with numbers is a recipe for disaster.

Friday 9/18: 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.

• a = 1000 g for a millisecond: Discovery Channel and YouTube come through! I've been telling the story of North American Aviation company test pilot Scott Crossfield and the static test stand explosion of the X-15 for years, and just now discovered that there's video online of this! You can see more successful flights of the three X-15 aircraft in this video and the first segment of this newsreel video. For more detailed shots of training, flights, landing, and the damage from a white covered X-15 flight that reached Mach 6.7, one last video. The X-15 lands as a glider, like the Space Shuttle, but it's a lousy glider. The only way the F-104 chase planes can follow it easily to the dry lakebed runway is to drop flaps and landing gear, and the X-15 still falls out of the sky like a brick. (grin)

### Week of 21-25 September 2015.

Monday 9/21: 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.

• Don't overrun the boundaries of a problem! The question, How fast are you going when you fall 3.00 m to the ground is asking for vy at the instant you touch the ground. The answer of zero, answers a different question -- That of what happens when a speeding object hits the ground. The speed you hit the ground at was around -7.7 m/s. The acceleration in bring it to a stop was about +90 m/s², or nearly ten times g, assuming you bend your knees and come to a stop over a distance of a foot (0.305 m).

Tuesday 9/22: The consequences of Falling Down... ...and Falling Up. The Turning Point ( vy = 0, but ay = -g during whole flight). The illusion of "hanging up there in the air" at the turning point. 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.

• To fall from the ceiling is t = 1.059 sec. Final speed is vy = -10.39 m/s. Since for the whole trip y = y0, then t = 2(1.059 sec) = 2.118 sec. And the Initial speed is v0y = +10.39 m/s.
• If you have to take a square root to get an answer, remember that there are two possible answers, plus or minus, to a square root.
• If you divide both sides of an equation by t , then algebra says that t=0 is one of your solutions.
• Don't forget to update your Formula Card!

Wednesday 9/23: Q3 in-class on Free Fall motion.

Thursday 9/24: Return Q2. 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. 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°. Examples: vector C = vector A + vector B, vector D = vector A - vector B.

• If you are using the Testing Center for Exam 1, you must (a) make an appointment at the Testing Center AND (b) send me an e-mail saying that you are taking your Exam 1 at the Testing Center at such-and-such a time, so that I know to send an exam over there.
• If you run across a problem in the Sample Exam 1s that you don't know what it means, it might be something we haven't covered yet! (grin) The actual Exam 1 will only be on material we've covered.
• For the guy with the fedora and the cigar. x0 = 0, x = 8.00 m, v0x= vx = ?, ax = 0, t = ?, y0 = 20.0 m, y = 0, v0y = 0, vy=?, ay = - g,
• Last semester I made audio files of part of this lecture. These are not compact files. Do let me know if they are usable. Note that I pause a lot so you can keep up with your notes.

Friday 9/25: 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 is a Take-Home on Vector Addition, due on Tuesday 29 September 2015 at the beginning of class (or by 12:45pm). (Click here for a copy.)

• For Lecture Example: A-vector = 5.00m @ 30°, B-vector = 7.00m @ 120°. Ax = +4.330 m and Ay = +2.500 m.
• Another Vector Problem: Ax = -3.17 m and Ay = -4.55 m.
• Another set of audio files.

### Week of 28 September-2 October 2015.

Monday 9/28: 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 θ Ay = A sin θ 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°. 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.

• NOTE: Q4 Take-Home due Tuesday 29 September 2015 at class. Solution will be posted in afternoon.
• Exam 1 material ends with Vector Addition.
• For the Cop and the Speeder. x10 = 0, x = ?, v10= v1 = 40.0 m/s, a1 = 0, t = ?, x20 = 0, x2 = ?, v20 = 0, v2=?, a2 = +4.00 m/s².

Tuesday 9/29: Types of Motion: No Motion (v=0, a=0), Uniform Motion (v=constant, a=0), Constant Acceleration (a=constant). 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.

Wednesday 9/30: Exam 1.

Thursday 10/1: 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.

• The material on Ballistic/Projectile motion is based on the kinematic equations for constant acceleration and vectors, things that we have covered. However, the specialty equations we are developing are fair game for use, unless otherwise stated. As with any special equations, there are restrictions. Use with care.
• If you missed Exam 1, you need to contact Dr. Phil and arrange to make Exam 1 up.
• NOTE: Just found a typo in my Office Hours. A "2" was missing for 12:50pm -- can't have office hours AND a 1pm class at the same time. Fixed.

Friday 10/2: 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.

### Week of 5-9 October 2015.

Monday 10/5: Recap: Our studies so far have described "How" things move, and allow to say "When" and "Where" things move, but not "Why" things move. For that we have to start talking about Forces -- and that means Newton. Some stories about Sir Isaac Newton. (Reeding on the edge of the silver shilling or a U.S. dime/quarter.) (Mad as a hatter -- from mercury poisioning.) 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.

• The problem with the First Law is that all too often, "an object in motion tends to come to a stop." But friction, as we shall see later, is an external force, which therefore makes that Second Law, not First. In the 1970s, NASA used some of the surplus Saturn V equipment to fashion a space station, Skylab. Videos: (drifting through Skylab), (Skylab launch, damage and repairs)

Tuesday 10/6: 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. 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.). 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.

• For a pair of equal and opposite forces -- it's First Law if they both act on the SAME object and Third Law if they both act on DIFFERENT objects.
• For our 125 kg crate, w = mg = 1226 N. At rest or moving horizontally at a constant speed, our only forces are FN going up and w=mg going down. FN = w = 1226 N. If apply a horizontal force F1 = 100. N, the sum of forces in the y-direction is the same, and now we get F1 = max. ax = 0.8000 m/s². The F.B.D. screams NET FORCE IN THE +X DIRECTION! When F1 is angled up, F1x = F1 cos 30°. ax = 0.6928 m/s².

Wednesday 10/7: 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. Q5 in-class.

Thursday 10/8: Return X1. "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.

• First Sample Exam 2s posted on class web page.

Friday 10/9: 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.

• You should use both equations from the Atwood's Machine problem to find the tension T1 and check that they give you the same answer. (m1 = 5.00 kg ; m2 = 7.00 kg ; we found that the common acceleration was a = g/6 )

### Week of 12-16 October 2015.

Monday 10/12: 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. 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.

• For the sign problem, the equations are
• T2 = T1 (cos30°/cos45°)
• T1 = mg / [sin30° + (cos30°)(sin45°)/(cos45°)]

Tuesday 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). 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. Example: Using our 125 kg. crate, applied force with F1 = 100.N and coefficients 0.800 and 0.600. (1) If at rest, F1 < Ff,s,max, therefore Ff,s = 100.N and the crate does not move. (2) If moving with v0 = 5.00 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 5 m/s². (4) To move crate at constant speed, get it started then apply force F3 = Ff,k. 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.

• It is static friction in play when we are driving and have our vehicle under control, because the tread of our tire is lowered onto the pavement, does not slide, and then is lifted off. We often don't notice that the coefficients of friction have dropped greatly when it is slippery outside, until we need to steer or brake, and then we start skidding. Slow down! (grin)
• Since it is hard to get a coefficient of static friction µs > 1, real car accelerations will generally be much less than 9.81 m/s².
• Another round of audio lectures from another semester
• Anti-lock Braking and Traction Control (MP3)

Wednesday 10/14: 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. Q6 in-class.

• (1) ax = -9.81m/s², x = 49.93 m (half a football field + 1 endzone), t = 3.191 sec. (2) ax = -0.7848m/s², x = 624.2 m (over six footnall fields including endzones, about 3/8th of a mile), t = 39.88 sec.

Thursday 10/15: 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. Driving up and down mountains. Truck Escape Ramps.

Friday 10/16: 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. 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)

• Those low and high speed drag constants, b and c , contain a lot of Physics -- based on shape of object, roughness of surface, composition od atmosphere its passing through, etc. Which equation do we use? Well, low speed drag is traveling slow and high speed if traveling fast... see tomorrow's lecture!
• The Discovery Channel's show Mythbusters has, of course, done some episodes on things like the terminal velocities of pennies -- or falling bullets from guns fired straight up. The real world, as usual, is much more complicated than the simplified Physics we introduce here, but the concepts remain the same.
• Pointed straight up and down, the terminal velocity of a person is > 200 mph. Falling flat, clothing spread out, can get terminal velocity below 60 mph.

### Week of 19-23 October 2015.

Monday 10/19: 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.)

• ABC News video of a U.K. tanker truck with a car stuck on its front bumper. (Presumably NOT a head-on collision.)
• For Yugo and Cement Truck: m1 = 1000 kg, v1 = 25.0m/s (to right), m2 = 20,000 kg, v2 = 25.0 m/s (to left). V = -22.62 m/s. ( V = (m1v1-m2v2)/(m1+m2) =(25,000 kgm/s - 500,000 kgm/s)/(21,000 kg) = -22.62m/s. So it's correct...)
• For the wrecks today, assuming I remember the numbers correctly, Car 1 had m1 = 1850 kg, v1 = 22.5 m/s, so p1 = m1v1 = 41,600 kg·m/s ; Car 2 had m2 = 2350 kg, v2 = 19.7 m/s, so p2 = m2v2 = 46,300 kg·m/s. Total mass of both cars, M = m1 + m2 = 4200 kg. The head-on collision left the wreck with speed V = -1.12 m/s ; the rear-end collision had V = 20.93 m/s.

Tuesday 10/20: 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.

• For the wrecks today, assuming I remember the numbers correctly, Car 1 had m1 = 1850 kg, v1 = 22.5 m/s, so p1 = m1v1 = 41,600 kg·m/s ; Car 2 had m2 = 2350 kg, v2 = 19.7 m/s, so p2 = m2v2 = 46,300 kg·m/s. Total mass of both cars, M = m1 + m2 = 4200 kg. The head-on collision left the wreck with speed V = -1.12 m/s ; the rear-end collision had V = 20.93 m/s and the side-impact collision had V = 14.82 m/s and ¸ = 48.1°

Wednesday 10/21: Work: A Physics Definition (Work = Force times distance in the same direction). Work = Energy. Q7 in-class. Q8 Take-Home on Inclined Planes, due Tuesday 27 October 2015. (Click here for a copy.)

• Another round of audio lectures:
• If you are using the Testing Center for Exam 2, you must (a) make an appointment at the Testing Center AND (b) send me an e-mail saying that you are taking your Exam 2 at the Testing Center at such-and-such a time, so that I know to send an exam over there.

Thursday 10/22: 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
• From 1.00 sec to 2.00 sec, doubling the time gives double the speed, double the momentum, but 4x the distance and 4x the KE.
• From 1.00 sec to 4.00 sec, quadrupling (4x) the time gives 4x the speed, 4x the momentum, but 16x the distance and 16x the KE.

Friday 10/23: See chart problem above. This helps explain why it takes longer and longer to speed up -- because the Work needed to increase the K.E. keeps getting much bigger and bigger because of the v2. Work = Energy. Power = Work / time. You are limited in how much work you can do in a given time by the maximum power available. NOTE: for a car, the upper speed limit is generally where all the available work from the max power goes into opposing the work done by friction and air resistance -- leaving nothing for the Work-Energy Theorem to increase the speed. 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. 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 ) NOTE: We usually have covered Uniform Circular Motion by now, but that's our next topic...

• Another round of audio lectures:

### Week of 26-30 October 2015.

Monday 10/26: 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. The Centripetal Force, Fc = mv²/r = mac . The Centripetal Force is "the answer" on the right side of the Sum of Forces equation. Something has to cause the centripetal force -- it does not show up on the F.B.D. as Fc.

• Low Eath Orbit (LEO) is about 250. miles = 400. km = 400,000 m above the surface of the Earth. The radius of the Earth is RE = 6,370,000 m, so r = RE + h = 6,770,000 m. For a periodic or repeating motion, T = period, the time to go around once. v = d / t = C / T = 2&pi; r / T = 7877 m/s. With ac = v²/r = 9.165 m/s², which is 93% of the gravity on the surface of the Earth.
• My sketch of the Space Shuttle in orbit has 3 flaws. The first being no human has ever orbited the Earth in polar orbit (going strictly north and south), though the US Air Force planned to launch Space Shuttles into polar orbits from Vandenberg AFB before the Challenger disasater.
• Webcomic xkcd on Centrifugal vs. Centripetal Force. (I thought I remembered it being Goldfinger, but I guess Randal used his usual troublemaker with the hat.) (grin)

Tuesday 10/27: 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. ac = v²/r. You can generate very large centripetal acclerations very quickly. Demo: Rodney Reindeer does UCM. 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. Review for X2.

• For an early hard drive with platters 14" in diameter: D = 14", r = D/2 = 7.00" = 0.1778 m. 3600 rpm = 60 revs per second. T = 1/60 revs per sec = 0.01667 sec. v = d / t = C / T = (2&pi;r)/T = 67.03 m/s or about 150 mph. ac = v²/r = 25,270 m/s² or 2576 g. You can generate very large centripetal acclerations very quickly.

Wednesday 10/28: Exam 2.

Thursday 10/29: Return Q7. UCM Revisited: Centripetal Force, Fc = mac = mv²/r. 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), tension, friction, or a combination of forces, etc. Making "artificial gravity" for long-duration space flight by living in a rotating object. Test tube example. The story of the 50,000 rpm Ultra-Centrifuge and the Fresh Rat's Liver. 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%. (9.83/9.81 = 1.002) 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.

• NOTE: No Thursday 2-4pm Office Hours due to doctor's visit.
• Finding the universal constant G was complicated by (1) the gravitational force between two ordinary objects is very small and (2) how do you figure out the mass of the Earth when you're standing on it?
• The problem of using UCM to create "artificial gravity" is not a trivial one for long-term space missions. Your internal organs "hang" suspended from your rib cage -- without gravity they not only float, but no longer require all the bone and muscle mass to support them and move around. Even dietary supplements and exercise do not stop the atrophy. See Spaceflight osteopenia.
• NASA and other operations can simulate the "weightless" or "zero G" environment by flying parabolas -- the original plane they used was a VC-135, which got nicknamed the "Vomit Comet". More recently NASA would like us to use the less fun term Weightless Wonder. Many of the zero G scenes in the film Apollo 13 were shot using this technique.

Friday 10/30: 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. 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).

• Orbital mechanics: Speed up and radius decreases, slow down and radius increases. For the Moon, the period is around 28 days at a quarter of a million miles away. Geosynchronous orbits occur when T = 1 day exactly, and for geosynchronous communications sattelites, the orbit must be directly over the equator -- hence all sattelite dishes in the U.S. face south.
• That our oceans are all connected together and that the Moon's influence creates tides is very important to life on Earth. In particular, the boundaries between fresh and salt waters include marshes and estuaries, which are some of the most productive breeding grounds for creatures on the planet, in part due to the twice daily flushing effect of the tides to wash away wastes and flood in nutrients.
• Your Weekend Moment of Pure Physics Zen: Article about the Video.
• Time Change on Sunday! 2am Eastern Dayling Time magically becomes 1am Eastern Standard Time. Adjust your clocks accordingly.
• Total Solar Eclipse of 21 August 2017.

### Week of 2-6 November 2015.

Monday 11/2: Four Fundamental Forces in Nature: Gravity (weakest), E & M, Weak Nuclear Force, Strong Nuclear Force (strongest). 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.

• For our front lab table boat, it's mass-to-volume ratio is 62.50 kg/m³ < 1000 kg/m³, so not only does it float, it is mostly out of the water!
• With a volume of 4.00 m³, at a total mass of 4000 kg, the loaded boat would have its top level with the water, so essentially it's about to sink. That translates into 3750 kg of cargo (coal, corn, iPods, passengers, etc.). Realistically, 2000 kg of cargo, 4400 lbs. on Earth, can be loaded with plaenty of boat out of the water. NOTE: We will not address how the cargo is loaded -- the boat needs to be reasonably balanced or it will swamp and sink.
• First Sample Exam 3s posted. Remember, Exam 3 is on TUESDAY 24 November 2015. No class the next day...

Tuesday 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. Water is unusual: (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.

• For our front lab table boat, it's mass-to-volume ratio is 62.50 kg/m³ < 1000 kg/m³, so not only does it float, it is mostly out of the water!
• With the mass of the water displaced by the boat equalling the mass of the boat, and the volume of the water displaced = the volume of the submerged part of the boat, we can use the mass-to-volume ratio of the water to find the volume, the length and width dimensions of the rectangular boat can be used to find h, the depth of the submerged part of the boat. For our lab desk in water, this is h = 0.06250 m = 6.250 cm.
• Mass-to-volume ratios of various materials: Lead (Pb) = 11,340 kg/m³; Gold (Au) = 19,300 kg/m³; Liquid mercury (Hg) = 13,600 kg/m³.

Wednesday 11/4: Newton's Law of Universal Gravity and Tides: We don't see tides in the Great Lakes (or your bathtub), because they are isolated and cannot draw water from a quarter of the way around the Earth. The oceans, however, are all connected, so we do get ocean tides. Q9 in-class.

Thursday 11/5: Return X2. 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.

• FYI: Remember, last day to withdraw from a class is Monday 9 November 2015. BUT... should you decide to, make sure you CAN withdraw before you do so -- sometimes it messes up scholarships or student visas if you drop below a certain number of credits.
• Full estimated course grades will be posted tomorrow. (There is still plenty of time to pull your grade up -- see Dr. Phil)

Friday 11/6: 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). Possible to have a "negative gauge pressure", but absolute pressure is always zero or positive.

• SCUBA = Self-Contained Underwater Breathing Apparatus -- invented by the famous Jacques Cousteau in WW II.