PhySP18SS5.4.1 Time Stamp: Walkout Wednesday. Hope it doesn’t mess up the Test 5B too much.

PhySP18SS5.4.2 Time Stamp. Got to watch Big John in a lead role in the excellent Les Mis at the Sooner Theater.

PhySP18SS5.4.3 Typical day in my advisory. Cooper leads the boys in Folk Songs. They are getting really good with their harmonies.

PhySP18SS5.4.4 There is a whole big explanation of this in the Facebook Group. Search “Inertial” and “Gravitational” probably a good idea to print out that bit from the group and put it in your notebook. Might come in handy in college or the final.

PhySP18SS5.4.5 . . .

PhySP18SS5.4.6 . . .

PhySP18SS5.4.7 Some call this sort of thing a crutch. I call it just another tool for working through a fairly simple physics problem. Sometimes its the simple ones that get you.

PhySP18SS5.4.8 5.10.10a. You see that (as Arnold said), the rocket thrust has to overcome the the force caused by gravitational mass of the rocket (which we call its weight) and the inertial mass (resistance to velocity change) of the rocket represented by the “ma” part of F=ma.

PhySP18SS5.4.9 another slightly different version of 5.10.10a

PhySP18SS5.4.10 This problem is on the THT5B

PhySP18SS5.4.11 yes it IS legal for the d/dt to switch partners. That lil d is a sneaky little stinker.

PhySP18SS5.4.12 Simplified version of the Thrust Equation.

PhySP18SS5.4.13 kg/sec is a weird unit to me, but I guess it makes sense. It is how much mass is being spit out the back of a rocket per second. Usually we keep these units in kg/sec, but it could be any mass over any time.

PhySP18SS5.4.14 messing with the units,

PhySP18SS5.4.15 an example to show you the importance of realizing that the escape velocity (ve) is RELATIVE to the rocket, NOT relaive to the woman watch this whole thing from a reference point.

PhySP18SS5.4.16 All of these are example of Newton’s 2nd Law.

PhySP18SS5.4.17 Mr. Babb’s take on the development of the Thrust Equation from a rocket’s point of view. part 1

PhySP18SS5.4.18 Part 2: A little bit of mass spits out the back of the rocket (dm)

PhySP18SS5.4.19 Part 3: Here he uses Conservation of linear momentum to derive the Thrust Equation. BRILLIANT! Now I wish I had done it this way. So much cooler. I only wish he had replaced the ∆ in the the fourth line on with “lil d” to make all this instantaneous.

PhySP18SS5.4.20 Part 4: So we get the Thrust equation. I wrote about this in the Physics Facebook Group. Notice that there is a second part to the thrust equation. You will need to know this part when you work for Elon Musk at SpaceX. I envy you. He wouldn’t take me. I’m too old and I’m damaged goods. ; )

PhySP18SS5.4.21 All those mean the same thing

PhySP18SS5.4.22 How to attack 5.10.12

PhySP18SS5.4.23 Pretty straight forward 5.9.2

PhySP18SS5.4.24 How to work THT5.13

PhySP18SS5.4.25 Notice all the @s. most of those are on the equation sheets now. This is not true for every car of course. We just have to reach an agreement in the 807.

PhySP18SS5.4.26 Air drag.

PhySP18SS5.4.27 Mean old Robert Brown. Biologist whose mistake changed the world in 1820. He looked through a microscope and thought that the pollen grains were alive because they were randomly moving around. Turns out they figured out later that the pollen grains were not alive (no vis viva). They were simply being bounced around by the water molecules that surrounded them. Turns out the water molecules are ALWAYS moving and bouncing into each other in this chaotic manner. We call it, you guessed it . . . Brownian Motion.

PhySP18SS5.4.29 An illustration of Brownian Motion. High Entropy. meaning that I can not predict where the molecules will be a few seconds after this picture is taken. There is equal chance that they could be anywhere in a three dimensional sphere. This is, by definition, maximum entropy and therefore , the textbook version of Brownian Motion.

PhySP18SS5.4.28 So what does this have to do with the force of lift on a fast moving car? Okay, I’ll give you the simplified non mathematical version of this. This really requires a lot of statistics and Calculus. So I will give you the Reader’s Digest version: All this brownian motion of air molecules (O2 and N2 molecules) cause a standard air pressure (Force per unit area) of 14.7 psi (lbs per square in). This air pressure is at sea level on earth. It tells you that the air molecules have reached maximum entropy and they are bouncing all over the place in all different directions causing little tiny force vectors in all directions.

PhySP18SS5.4.30 Okay . . . so now when there is a breeze (either caused by wind blowing past an object or the object moving through “calm” air, more of the air molecules are flowing in one direction (this is called LAMINAR FLOW). When you are in a laminar flow situation, more air molecules (you can also, of course, do this with water molecules) are flowing in the same direction and the amount of Brownian Motion is reduced. There are less air molecules (or water molecules) to bounce off the sides of a tube they are in so the amount of molecules hitting the side are reduced and therefore the pressure (F/A) is reduced.

PhySP18SS5.4.31 . . .more visuals . .

PhySP18SS5.4.32 . . . more visual info about Laminar flow vs. Brownian motion.

PhySP18SS5.4.33 . . . so what does this have to do with the force of lift on a fast moving car? the faster the laminar flow there is over the top of car (becasue the air molecules have further to go) the less Brownian Motion there is on the top of the car and therefore, the less pressure. basically how an airplane wing works which is great for the airplane, but not good for a car.

PhySP18SS5.4.34 This can be demonstrated with a Venturi Tube.

PhySP18SS5.4.35 it is called the venture effect.

PhySP18SS5.4.36 an example of a venturi tube. Wish I still had mine.

PhySP18SS5.4.37 the same concept is used in perfume bottles.

PhySP18SS5.4.38 The venturi effect is used to increase the speed of escape gases in an F-15 or whatever jet this is.

PhySP18SS5.4.39 We demonstrated it with the old paper hanging from the bottom lip trick.

PhySP18SS5.4.40 Spoilers and Air Dams are how cars deal with lift.

PhySP18SS5.4.41 Cigarette Boats have a real problem with lift.

PhySP18SS5.4.42 So do dragsters

PhySP18SS5.4.43 Modifying the FBD for a car accelerating up to 120mph with the snapshot taken at 80mph

PhySP18SS5.4.44 the same car in neutral slowing down with the snap shot taken at 80mph.

PhySP18SS5.4.45 now slamming on the brakes skidding to a stop with the snapshot taken at 20mph.

PhySP18SS5.4.46 A rocket in the earths lower atmosphere traveling at 75° ALH. Notice there are three forces and a ∑F (because the rocket is Thrusting and accelerating in the DOM.

PhySP18SS5.4.47 An example of the Thrust force being a greater angle than the DOM. It HAS to be because it has to compensate for the weight of the rocket (the downward mg vector)

PhySP18SS5.4.48 another example

PhySP18SS5.4.49 From the Thursday night talk about Neutron stars being used to help us detect gravity waves.

PhySP18SS5.4.50 Most of the crew that went to the talk.

Here are the screenshots and captions (sorry I’m late) . . .

PhySP18SS5.3.1 Tiem Stamp: West Virginia teachers are out on strike for the 8th day in a row asking for a 5% raise. West Virginia is 48th in the nation in it’s teachers pay. Wow. No wonder they are going on strike. hmmm . . . Oklahoma is 50th in teacher pay and dropping fast. sad.

PhySP18SS5.3.2 This will help on one of the questions on THT5.

PhySP18SS5.3.3 zThis will help you with another of the problems on THT5A.

PhySP18SS5.3.4 Data from the Duck Walk Lab

PhySP18SS5.3.5 We compared possible relationships of the variables involved in the Duck Walk Lab.

PhySP18SS5.3.6 From the Duck Walk lab. We came up with the best relationship from the data which turns out to be Newton’s original 2nd law.

PhySP18SS5.3.7 Newton’s original 2nd Law.

PhySP18SS5.3.8 Using Newton’s Original 2nd to solve a problem. Probably a good screenshot for your notebook.

PhySP18SS5.3.9 The force suitcase.

PhySP18SS5.3.10 Here is the orange equation we used to determine the acceleration in the Duck Walk lab.

PhySP18SS5.3.11 Filling in the table of 5.6.7

PhySP18SS5.3.12 1st hour plotted data from Duck Walk

PhySP18SS5.3.13 2nd hour graph

PhySP18SS5.3.13 3rd hour data

PhySP18SS5.3.15 6th hour data (winner)

PhySP18SS5.3.14 7th hour data. Something went wrong.

PhySP18SS5.3.17 The graphs showed us that F = ma, but we can also use Algebra to show it. Here is a derivation for Test 5.

PhySP18SS5.3.18 5.6.13a

PhySP18SS5.3.19 5.6.13b

PhySP18SS5.3.20 We stretched the spring to get 2N, 4N, 6N, 8N, and 10N of force. UT TENSIO SIC VIS!

PhySP18SS5.3.21 From sheet 5.7.4

PhySP18SS5.3.22 From 5.7 a graph of Hooke’s Law.

PhySP18SS5.3.23 Hooke’s Law showing the Spring Force (Fs) which is a restoring force. Restoring forces try to restore the situation back to equilibrium.

PhySP18SS5.3.24 From sheet 5.7.4

PhySP18SS5.3.25 5.8.2b

PhySP18SS5.3.26 5.8.2b

PhySP18SS5.3.27 5.8.4 Although each object only has one mass, there are sometimes two different interpretations of that mass. One is the resistance the object has to a change in the velocity of the object in any direction.

PhySP18SS5.3.28 Whereas “gravitational mass” is the measure of how much the object is affected by the gravitational field it finds itself in.

PhySP18SS5.3.29 The best way to describe the subtle differences between inertial mass and gravitational mass is the weird fact that objects with different masses still fall to the earth with the same acceleration (g=9.81m/s/s). Why is this? It’s cray cray. Gravitational mass goes into the weight formula (weight=mg) It is the force that causes the object to accelerate towards the earth. So the basketball dropping from the stadium experiences TEN TIMES the force from the earth to fall to the earth than a tennis ball that is falling beside it. So why doesn’t it fall 10x faster than the tennis ball. They hit at the same time with the same speed. WHAT? It’s because the basketball has TEN TIMES the RESISTANCE to fall (as represented by its inertial mass). So there is a perfect balance of attraction of the two balls to the earth and resistance of the two balls to be pulled to the earth. The tennis ball doesn’t have a lot of weight (mg) so not much of an attractive force, but it only has 1/10 the resistance to the pull of the earth. So they are attracted at the same 9.81m/s/s or 32.2ft/s/s. Wow, this is the longest caption I have ever wrote.

PhySP18SS5.3.30 Gotta give it up to Newton.

PhySP18SS5.3.31 Basil

PhySP18SS5.3.32 Print off this screenshot because it will come in handy the rest of the semester.

PhySP18SS5.3.33 Same as the last screenshot with some slightly different information.

PhySP18SS5.3.34 from 5.8.7

PhySP18SS5.3.35 From 5.8.7

PhySP18SS5.3.36 Another one from 5.8.7 Jeez, I guess that is an important problem.

PhySP18SS5.3.37 5.9.1 The fine art of FBDs. You must become an expert at these so you can help all your fellow college classmates.

PhySP18SS5.3.38 Another one from 5.9.1

PhySP18SS5.3.39 Three types of motion.

PhySP18SS5.3.40 Here is the reason why there is no movement at the tire-road contact for a rolling tire.

PhySP18SS5.3.41 The making of a cycloid pattern

PhySP18SS5.3.42 Cycloid patterns just touch the ground. There is no tire-road sliding going on. That only happens if you do a burnout or if you slam on your brakes.

PhySP18SS5.3.43 Cycloid pattern

PhySP18SS5.3.44 cycloid

PhySP18SS5.3.45 cycloid

PhySP18SS5.3.46 typical college physics professor. That is actually a very smooth ride. just switched role

PhySP18SS5.3.47 IF you look close at this flower, you will recognize the cycloid pattern

PhySP18SS5.3.48 Cycloid pattern front loads acceleration so that all these balls get to the end at the same time.

PhySP18SS5.3.49 The Brachistochrone.

PhySP18SS5.3.50 5.9.2

PhySP18SS5.3.51 Weight equal gravitational mass times the acceleration due to the mass of the earth. Basically, just a more specific version of F =ma.

PhySP18SS5.3.52 Deriving the thrust equation which is just another specific version of newton’s 2nd.

PhyS5.10.10aP18SS 5.3.53

PhySP18SS5.3.54 5.10.10b

PhySP18SS5.3.55 With that escaping mass, it’s all about the escape velocity.

Here are the screenshots and captions from last week . . .

TIme Stamp: Nathan Chen does SIX QUADS in the 2018 olympics in his redemption skate. First time in history. Li = Lf

PhySP18SS5.2.1 From Sheet 5.2.3

PhySP18SS5.2.2 Also from Sheet 5.2.3

PhySP18SS5.2.3 DANGER!! but useful

PhySP18SS5.2.4 Sheet 5.3.2

PhySP18SS5.2.5 Sheet 5.3.3 One of the most tedious problems of the year.

PhySP18SS5.2.6 Sheet 5.3.5

PhySP18SS5.2.7 Sheet 5.3.5

PhySP18SS5.2.8 Sheet 5.3.5 The hard part was using the ratios to help you unpack the Final momentum suitcase.

PhySP18SS5.2.9 Sheet 5.3.6 Just head-to-tail

PhySP18SS5.2.10 The return of the Gold Standard!! Sheet 5.4.5

PhySP18SS5.2.11 Glance Ball! The most points earned were 14 bonus. We are working on GLANCE BALL SQUARED. GB^2 for the hipsters.

PhySP18SS5.2.12 GLANCE BALL from the past.

PhySP18SS5.2.13 A true genius.

PhySP18SS5.2.14 Newton’s version of what Hooke looked like. FAKE NEWS!

PhySP18SS5.2.15 This COULD be Hooke.

PhySP18SS5.2.16 Two hours Division time given for reading this book. Have the NHS Library order it.

PhySP18SS5.2.17 Hooke’s microscope.

PhySP18SS5.2.18 A fold out from Hooke’s best seller Micrographia. Fleas were a real problem (Black Plague and all) The second pandemic of bubonic plague was active in Europe from AD 1347, the beginning of the Black Death, until 1750.

PhySP18SS5.2.19 Another major problem was head lice. Here he finally settles the mystery of how those infernal bugs hang on to hair follicles.

PhySP18SS5.2.20 We did an impromptu lab/demo with a hanging spring and came up with this graph.

PhySP18SS5.2.21 This is NOT Hooke’s Law.

PhySP18SS5.2.22 This IS Hooke’s Law

PhySP18SS5.2.23 Hooke’s Anagram. He didn’t want Newton taking credit for his discovery of a property of these new found springs made of the new alloy of “steel”.

PhySP18SS5.2.24 Another interpretation of Hooke’s Law.

PhySP18SS5.2.25 I asked Mrs. Davis to weigh in on the controversy.

PhySP18SS5.2.26 How Hooke made the springs.

PhySP18SS5.2.27 Hooke’s Apparatus

PhySP18SS5.2.28 . . .

PhySP18SS5.2.29 . . .

PhySP18SS5.2.30 One of the most important graphs in Mechanics.

PhySP18SS5.2.31 The +, – areas of those right triangles are VERY important for AP Physics.

PhySP18SS5.2.32 Compression on the left and stretch on the right.

PhySP18SS5.2.33 Another version of Hooke’s Law. Showing the Spring Force (Fs). It is ALWAYS trying to restore equilibrium and get back to it’s happy place. Isn’t that we are all trying to do?

PhySP18SS5.1.1 Time Stamp — Those Intel Drones were very impressive at the Opening Ceremonies.

PhySP18SS5.1.2 You all wrote the four questions. Now I just have to pick out the ones I want to use.

PhySP18SS5.1.3 This is the big picture of Physics. We only study the Mechanics part.

PhySP18SS5.1.4 Here are the two branches of Physics

PhySP18SS5.1.5 Here are the big three conservation laws that run mechanics

PhySP18SS5.1.6 We are going to study lil p for a bit. It’s actually a lil suitcase. with even a smaller suitcase inside it.

PhySP18SS5.1.7: Inertia and momentum

PhySP18SS5.1.8 It’s not really lil p that we are so interested in . . . it is CONSERVATION of a systems lil p that is so awesome. It’s one of the big three laws that runs pretty much the whole show.

PhySP18SS5.1.9 Con of Mom can be broken down into four equations, but they are really

PhySP18SS5.1.10 Conservation of energy gets more complicated to more you look at it. Especially when that old dog PacMan gets involved.

PhySP18SS5.1.11 That equation on the bottom is the beginning of the Ultimate Fighting Tool. We will barely get to it this year, but you will use the heck out of it next year in AP Physics . . . and in college.

PhySP18SS5.1.12 Conservation of Angular Momentum is another one that gets more and more complicated the more you dive into it.

PhySP18SS5.1.13 For every equation in linear world there is a corresponding equation in Circular World.

PhySP18SS5.1.14 . . . I kept this slide because it has the definition of Moment of Inertia. We will discuss that later.

PhySP18SS5.1.15 Basic elastic collision

PhySP18SS5.1.16 Basic elastic collision with numbers

PhySP18SS5.1.17 . . .

PhySP18SS5.1.18 The first boxes on sheet 5.1

PhySP18SS5.1.19 $5000 wasted

PhySP18SS5.1.20 5.1.1

PhySP18SS5.1.21 5.1.2

PhySP18SS5.1.22 sheet 5.1.4

PhySP18SS5.1.23 Sheet 5.1.8 (Key is posted on Facebook)

PhySP18SS5.1.24 Sheet 5.2.1

PhySP18SS5.1.25 another one of 5.2.1

PhySP18SS5.1.26 Sheet 5.2.2

PhySP18SS5.1.27 Sheet 5.2.3

PhySP18SS5.1.28 Sheet 5.2.3

PhySP18SS5.1.29 Conservation of momentum in a “strike” in pool. The initial momentum of the cue ball is transferred to all those numbered pool balls. No momentum is lost. It is all just transferred. That blew me away in college at first until, one night I was laying in bed staring at the ceiling and it finally hit me. MOMENTUM IS A VECTOR. Which simply means the big initial arrow of the cue ball (containing its mass and velocity) gets transfomed into 16 different arrows. How can this happen? Because much of those arrows cancel each other. Check out this picture. If you assume the cue ball is originally moving ONLY in the y direction, all the x components are going to cancel each other. All the final momentum y components will add up to the original momentum of the cue ball. I was so excited by my epiphany that I got out of bed and did a naked glorious jig in my bedroom.

PhySP18SS5.1.30 Now take this idea of con of mom to a bigger level. Shoot a firework shell into the air. After the explosion, the 1000 momentums of all those colorful 3D scintillations when added up equal the original momentum of the sheel JUST BEFORE EXPLOSION. So . . . if you follow the combined vectors of all the scintillations, it will complete the parabolic type 2A projectile motion that the original shell had. Ha!! Good Grief . . . I love physics so much.

Here are the screen shots for this week . . . Will add more captions as I get time.

PhySPSS4.4.1a A clean room finally. Thanks to these brilliant young men.

PhySPSS4.4.1b They took all the chairs and tables to the hallway, then wiped them all down as well.

PhySP18SS4.4.1c Inertia is resistance. This screen shot gives a little history to inertia and momentum.

PhySP18SS4.4.2 Type 1. Basically, all projectile motion is free fall on a conveyor belt.

PhySP18SS4.4.3 How an object falls: 1-3-5-7-9-….

PhySP18SS4.4.4 All type 1 with different initial velocities

PhySP18SS4.4.5 This is the basic way that any type 1 Proj Mot set of graphs will look.

PhySP18SS4.4.6: A Land-Air type 1 Proj Mot. Remember, the final velocity of the object on land is the intial velocity of the object in the air.

PhySP18SS4.4.7 We call that a Bridge Equation because it links the two parts of the problems togather.

PhySP18SS4.4.8 Gravity acts only on the center of mass (also called center of gravity) of any object.

PhySP18SS4.4.9 The center of mass of the system makes a perfect parabola.

PhySP18SS4.4.10 . . .

PhySP18SS4.4.11 Type 2A

PhySP18SS4.4.12 Type 2A

PhySP18SS4.4.13 This is the basic shape of the Duet/Trio that goes with Type 2A Proj Mot.

PhySP18SS4.4.14: DANGER! DANGER! DANGER! The Range Equation is convenient when you don’t know time, but can ONLY be used in type 2A Proj. Mot. problems

PhySP18SS4.4.15 Finishing up the Range Equation

PhySP18SS4.4.17

PhySP18SS4.4.18 The three types of Proj Mot.

PhySP18SS4.4.20 Type 2B

PhySP18SS4.4.21 Type 2B

PhySP18SS4.4.22 Type 2B . . . also notice the center of mass OF THE SYSTEM is in a perfect parabola.

PhySP18SS4.4.19 This is what the five graphs look like for Type 2B

PhySP18SS4.4.23 Type 2B

PhySP18SS4.4.24

PhySP18SS4.4.25

PhySP18SS4.4.26 Sometimes you will find that you get two positive times from the Blue Quad. One of the times is on the way up and one of the times is on the way down.

PhySP18SS4.4.27 See? the minus root gives you the time when the object is on the way up and the plus gives you the time when the object is on the way down.

PhySP18SS4.4.28 One of the top ten hardest problems of the year.

PhySP18SS4.4.29 . . .

PhySP18SS4.4.30 Be careful on angles in the 4th quadrant. They are negative reference angles.

PhySP18SS4.4.31

PhySP18SS4.4.32 My new rules for football.

PhySP18SS4.4.33 4.10

PhySP18SS4.4.34b Proj Launch!

PhySP18SS4.4.34c Proj Launch!

PhySP18SS4.4.34 4.10.4

PhySP18SS4.4.35

PhySP18SS4.4.36 When we were determining the V naught for the projectile motion launcher.

PhySP18SS4.4.37 The two types of launches we did.

PhySP18SS4.4.38 The crazy equation we used to determine our ∆x in our hallway activity.

PhySP18SS4.4.39 . . .

PhySP18SS4.4.40 . . .

PhySP18SS4.4.41 Graph from our hallway activity (4.11)

Here are the screenshots from last week. I will be working on the captions this weekend.

PhySP18SS4.3.1 Time stamp. It was shut down when I put this weeks screenshots together. DO YOUR JOB!! Government employees, like Air Traffic Controllers aren’t getting paid as of today (but are still expected to show up to work), but . . . Congress (whose fault it is), managed to put a provision in there where THEY still get paid. Run for office a few years and let’s boot these numbskulls out of there. Okay . . . back to Physics.

PhySP18SS4.3.2 remember, i rrroof goes with anything horizontal or east-west, j rrroof goes with anything vertical or north south.

PhySP18SS4.3.3 . . .

PhySP18SS4.3.4 . . .

PhySP18SS4.3.5 The equilibrant is the opposite of the resultant.

PhySP18SS4.3.6 When you construct the addition of vectors you need to use a ruler and a protractor. No freehand

PhySP18SS4.3.7 old shakey hands doesn’t work on head to tail method.

PhySP18SS4.3.8 . . .

PhySP18SS4.3.9 . . .

PhySP18SS4.3.10 Inertia is a property of matter!

PhySP18SS4.3.11 Basically, inertia is any objects resistance to a change in its velocity or lack of velocity. The more mass, the more the resistance.

PhySP18SS4.3.12

PhySP18SS4.3.13 lil p!

PhySP18SS4.3.14 Newton’s 1st. Notice that the force must be EXTERNAL and UNBALANCED.

PhySP18SS4.3.15 Newton’s first in 5 words.

PhySP18SS4.3.16 so when a ball is being thrown across the room the only force acting on it (assuming air drag is negligible) is the force of gravity. What keeps in moving through the air is moving inertia (momentum).

PhySP18SS4.3.17 Galileo and Faraday were thought to be fools by some. Field forces?? Turns they were right.

PhySP18SS4.3.18 This is a preview of Free Body Diagrams (FBDs) You won’t be tested on it yet.

PhySP18SS4.3.19 I don’t trust you Pee Boy.

PhySP18SS4.3.20 Type I Projectile Motion. The object starts off horizontal. We catch a big break here because Voy = 0.

PhySP18SS4.3.21 THe path of a ball in Type I Proj Mot.

PhySP18SS4.3.22 Three different balls in Type I Proj Mot each moving at a different Vx.

PhySP18SS4.3.23 THe equations we use to Type I Proj Mot.

PhySP18SS4.3.24 4.8.2

PhySP18SS4.3.25 4.8.5 hint. Key posted on the Facebook group.

PhySP18SS4.3.26 4.8.(front) A ball falling on Planet X. How big is it?

PhySP18SS4.3.27 We’ll discuss how I could do this in a few weeks.

PhySP18SS4.3.28 You can use a modified Newton’s IUNiversal Law of Gravity to determine the “g” on earth.

PhySP18SS4.3.29 The densities of rocky planets are pretty close. Usually around 5 g/cc

PhySP18SS4.3.30 A clever way to determine the radius of planet x once we know it’s “g”

PhySP18SS4.3.31 subbing and canceling

PhySP18SS4.3.32 A thought experiment. What is we drilled a hole through the earth and jumped in?

PhySP18SS4.3.33 Homework for this weekend. this gets you started.

I will add all captions to these fresh shots as the weekend continues . . .

PhySP18SS4.2.1

PhySp18SS4.2.2 Proper way to describe a vector in “people speak”.

PhySp18SS4.2.3 Map View, like I am looking down on the problem from above.

PhySp18SS4.2.4 Profile view, like I am looking at the problem from the side.

PhySp18SS4.2.5 . . .

PhySp18SS4.2.6 Head-to-tail method or sometimes called “tip-to-tail” method. Best way to visualize the interactions of the vectors in your problem.

PhySp18SS4.2.7 . . .

PhySp18SS4.2.8 adding vectors is kind of weird

PhySp18SS4.2.9 Remember, the resultant always starts at the first tail (the beginning) and ends at the last head (the ending).

PhySp18SS4.2.10 . . .

PhySp18SS4.2.11 Line of Action is a virtual extension of the vector to infinity (or off your page, whichever one comes first ; ) It is useful when you are trying to redraw a vector and you want to keep the orientation the same (railroad track method). It also comes in REAL handy when you are doing torque problems.

PhySp18SS4.2.12 Using LOAs to help you construct a head to tail

PhySp18SS4.2.13 Instead of calling the resultant here, I should have labeled ∑F.

PhySp18SS4.2.14 . . .

PhySp18SS4.2.15 You can multiply a vector by a scalar. All that does is make it longer or shorter. It does NOT affect the orientation (angle).

PhySp18SS4.2.16 . . .

PhySp18SS4.2.17 Head to tail of adjustred lengths

PhySp18SS4.2.18 . . .

PhySp18SS4.2.19 Adding six force vectors together to produce a resultant (∑F). It is the tan colored arrow. If you end up with a resultant force vector then the object that the six forces are acting on will not only move, it will accelerate (speed up or slow down). If you were to add those six vectors together and the sixth arrows tip ended up touching the first arrows tail, then there would be NO resultant vector an therefore, no acceleration. This is called EQUILIBRIUM. If you go one step further and make the object stationary, the situation is called “static”.

PhySp18SS4.2.20 Here are those same vectors from the previous screen shot, but now they are arranged in a Free Body Diagram (FBD). If you look back and forth, you will see that all the vectors are the same, except that here, they all emanate from the center of mass of the object. This is how you have to draw the vectors if you are adding them using the component method.

PhySp18SS4.2.21 Head to tail vs. FBD method.

PhySp18SS4.2.22 Here is an example of a FBD. We will get good at these later.

PhySp18SS4.2.23: You should be at the “dog tilting head” stage of understanding right now for dot products and scalar products. They will slowly begin to dominate your thinking about the universe. I can’t believe I get the privilege of being the first to introduce them to you.

PhySp18SS4.2.24 . . .

PhySp18SS4.2.25 . . .

PhySp18SS4.2.26 . . .

PhySp18SS4.2.27 Well, this is way beyond where we are, but up until about mid April we can get away with calling everything a dot (center of mass) like in the figure on the left, but once we start talking about cross products we are going to have to start thinking about objects as “extended objects” because WHERE a force hits a body will matter since now the object can ROTATE. Anyway . . . forget I said anything. That’s acomin.

PhySp18SS4.2.28 Another example of cross product causing torque which causes rotation.

PhySp18SS4.2.29 cross products causing a water molecule to rotate inside your food inside your microwave oven.

PhySp18SS4.2.30 Kind of a cool puzzle for adding vectors. Various combos.

PhySp18SS4.2.31 .. .

PhySp18SS4.2.32 Adding and subtracting vectors sometimes have the same rules as you learned b ack in grade school

PhySp18SS4.2.33 You can add, subtract, multiply (dot or cross product), but you can NOT divide a vector by a vector.

PhySp18SS4.2.34 Ahhh . . . three dimensional vectors.

PhySp18SS4.2.35 3D dimensional vectors

PhySp18SS4.2.36 Unit vectors turn scalars into vectors by giving them up,down,left,right,out, in direction.

PhySp18SS4.2.37 turning a vector into its components.

PhySp18SS4.2.38

PhySp18SS4.2.39 The girl who made this poster went off to dominate West Point . . . just like she dominated vectors.

PhySp18SS4.2.40 . . .

PhySp18SS4.2.41 Component method

PhySp18SS4.2.42 All the rest of these are examples of component method.