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Physics 218, Lecture II1 Dr. David Toback Physics 218 Lecture 2

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Physics 218, Lecture II2 Announcements Having trouble getting started on WebCT? Try: –ITS Help sessions –Open access lab/student computing. –Instructions on faculty.physics.tamu.edu/toback/WebCT – to Check your neo account for announcements. Two of you had your bounce Any Volume 1 of the 11 th edition of Young & Freedman will be fine. You will need Volume 2 for Phys208 and Volume 3 for beyond that. The maroon “University Edition” is also fine.

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Physics 218, Lecture II3 Procedure for Each Week Week 1 (This week): –Lecture: Chapter 1 (Reading, but nothing due) –Recitation: Calculus and Lab Techniques –Homework due: None Week 2 (Next week): –Homework due (Monday): Math quizzes –Lecture: Chapter 2 (Reading and Lecture Assignment due) –Recitation: Chapter 1 (and Lab 1) Week 3 (The week after that): –Homework due (Monday): Chapter 1 –Lecture: Chapter 3 (Reading and Lecture Assignment due) –Recitation: Chapter 2 (no lab, but lab 1 is due) Etc..

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Physics 218, Lecture II4 Chapter 1: Math n’ Stuff Won’t cover the entire chapter: Problem Solving –Tricks –Methods Vectors –Components (Unit vectors) –Addition –Multiplication (dot and cross products)

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Physics 218, Lecture II5

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6 Problem Solving Overview There are good general problem solving TRICKS –Units checking –Special case checking –Etc. There are good METHODS of problem solving that prepare you for the exams We’ll use both to solve problems in lecture

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Physics 218, Lecture II7 First Things First! What’s the first thing you should do when you’re given a a problem? Draw a diagram!!! –Usually good for some partial credit List givens and wants as variables –Also a good bet for partial credit Then use reasonable equations and solve with your variables Trick #1

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Physics 218, Lecture II8 Trick #2: Units The speed of your car isn’t measured in seconds, its measured in meters/second (or miles/hour etc.) Paying attention to the units will help you catch LOTS of mistakes on exams, quizzes and homework!! –If we ask what the mass of your car is, make sure your answer is in kg (or lbs etc.) Trick #2: Every time you finish a problem ALWAYS check the units of your answer!!

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Physics 218, Lecture II9 Tricks #3 and #4 Check Reasonableness: Can you find another way to do the same problem that gives the same answer? Simple numbers give expected numerical answers? Example: Zero, or infinity Trick #3 Trick #4

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Physics 218, Lecture II10 How to use the Tricks and Methods Next we’ll do an example problem like one of the homework problems in the text book Solve this problem using the right method –Draw a diagram –Convert the numbers to variables –Solve to get a formula –Plug in the numbers at the end –Check Reasonable numbers? Silly numbers? Another way to do the same problem?

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Physics 218, Lecture II11 16 m Example Problem You want to measure the height of a building. You stand 2m away from a 3m pole and see that it’s “in line” with the top of the building. You measure 16 m from the pole to the building. What is the height of the building?

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Physics 218, Lecture II12 Vectors Vectors: –Why we care about them –Addition & Subtraction –Unit Vectors –Multiplication

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Physics 218, Lecture II13 Why do we care about Vectors? As you may have noticed, the world is not one-dimensional Three dimensions: X, Y and Z. Example: 1.Up from us 2.Straight in front of us 3.To the side from us –All at 90 degrees from each other. Three dimensional axis. Need a way of saying how much in each direction For this we use VECTORS

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Physics 218, Lecture II14 Vector and Scalar Vectors have a magnitude AND a direction –I’m driving 70 miles/hr SouthEast to Houston Scalars are just a number –My speedometer says 70 m/hr

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Physics 218, Lecture II15 Where am I? My single vector in some funny direction, can be thought of as two vectors in nice simple directions (like X and Y). This can make things much easier Let’s say I’m here You’re here (origin) I call you on the cell phone. How do I tell you how to get to me? 2 equivalent ways: 1)Travel 11.2 km at an angle of 26.5 degrees 2)Travel 10 km East then 5 km North

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Physics 218, Lecture II16 Vector Addition To specify where I am, often doing the two vector version is easier Represent Graphically: Lay down first vector Lay down second vector –Put the tail at the head of the first vector The “Sum” is where I am Adding vectors is a skill Use this in far more than just physics More on this later…

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Physics 218, Lecture II17 Re-write my location Describe my location in terms of the sum of two vectors Careful when using the sin and cos

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Physics 218, Lecture II18 Specifying a Vector Two equivalent ways: –Components V x and V y –Magnitude V and angle Switch back and forth –Magnitude of V |V| = (v x 2 + v y 2 ) ½ Pythagorean Theorem –Tan = v y /v x Either method is fine, but you should pick which is easiest, and be able to use both

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Physics 218, Lecture II19 Unit Vectors This is how the pros write things!

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Physics 218, Lecture II20 Unit Vectors The pros also use:

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Physics 218, Lecture II21 Vector in Unit Vector Notation

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Physics 218, Lecture II22 General Addition Example Add two vectors using the i-hats, j-hats and k-hats

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Physics 218, Lecture II23 How do we Multiply Vectors? First way: Scalar Product or Dot Product –Why Scalar Product? Because the result is a scalar (just a number) –Why a Dot Product? Because we use the notation A. B A. B = |A||B|Cos

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Physics 218, Lecture II24 A. B = |A||B|Cos First Question:

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Physics 218, Lecture II25 Harder Example

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Physics 218, Lecture II26 Vector Cross Product This is the last way of multiplying vectors we will see Direction from the “right-hand rule” Swing from A into B!

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Physics 218, Lecture II27 Vector Cross Product Cont… Multiply out, but use the Sin to give the magnitude, and RHR to give the direction

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Physics 218, Lecture II28 Cross Product Example

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Physics 218, Lecture II29 Results of Math Quizzes The average of all Math Quizzes taken so far (not the Math Assessment) is about an 8.1 with a standard deviation of just above 1.1. How to evaluate where you stand. If the average of the scores of all the quizzes you have taken is: 95% or above: Well prepared 85% - 90%: Good, but needs to be better 80% – 85%: Ok, but really needs some work 75% - 80%: Hmmmm…maybe get some help 75% or below: Careful…Definitely get help! Maybe drop…

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Physics 218, Lecture II30 For Next Week Before Lecture: –Read Chapter 2 –Math Quizzes due Monday –Lecture Assignment: Q2.8 and Q2.20 (These are the “Discussion Questions”) In Lecture –Cover Chapter 2 –Turn in Lecture Assignment at the beginning Recitation, Lab and Homework: –Start HW1 on WebCT before recitation –All Ch. 1 problems due Monday after recitation –Read your lab materials before lab

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Physics 218, Lecture II31

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Physics 218, Lecture II32 Simple Multiplication Multiplication of a vector by a scalar –Let’s say I travel 1 km east. What if I had gone 4 times as far in the same direction? →Just stretch it out, multiply the magnitudes Negatives: –Multiplying by a negative number turns the vector around

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Physics 218, Lecture II33 Subtraction Subtraction is easy: It’s the same as addition but turning around one of the vectors. I.e., making a negative vector is the equivalent of making the head the tail and vice versa. Then add:

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Physics 218, Lecture II34 Where am I? Traveling East then North is the same as traveling NorthEast Can think of this the other way: If I had gone NorthEast, the displacement is equivalent to having gone both North and East My single vector in some funny direction, can be thought of as two vectors in nice simple directions (like X and Y). This can make things much easier

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Physics 218, Lecture II35 Problem Solving & Diagrams This class is mostly problem solving (well… you need to understand the concepts first in order to solve the problems, but we’ll do both). In order to solve almost any problem you need a model Physicists/engineers are famous for coming up with silly models for complicated problems The first step is always: Trick #2:“Draw a diagram!”

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Physics 218, Lecture II36 Announcement: Free Tutoring Four foreign graduate students are available to tutor Physics 218 Students without charge. Students desiring help are to the tutor and arrange a time to meet in Heldenfels 211 on weekdays. The tutors are: Sunnam Min, Xi Wang, Rongguang Xu, Hong Lu,

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Physics 218, Lecture II37 Components Let’s do this with the math: Break a vector into x and y components (I.e., a right triangle) THEN add them This is the sine and cosine game Can use the Pythagorean Theorem A 2 + B 2 = C 2

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Physics 218, Lecture II38 Chapter 1: Introduction This chapter is fairly well written. I won’t lecture on most of it except for the parts which I think are useful in helping you be a better problem solver in general or at least helping you look like a professional

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Physics 218, Lecture II39 Models, theories and Laws Prescriptive vs. Descriptive What should happen vs. What does happen when you do an experiment –US law doesn’t allow killing –Physics law shows clearly that it does happen.

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Physics 218, Lecture II40 Estimating Order of Magnitude This is a useful thing to be able to do at home Let’s say you are at a grocery store and it’s full. How much will it cost you to buy it all? –Estimate using round numbers –50 items (assuming not lots of little things) –A dollar an item $50

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Physics 218, Lecture II41 Number of Significant Figures 15 ± 1 feet (1 digit in uncertainty, same “10’s” as last digit) ± 1 feet (Makes you look like an amateur) 15 ± 1.05 feet (Same thing) 15.1 ± 0.1 feet (Ok) 15 ± 10 feet (Ok) An aside: Personally, I take significant digits seriously. It makes you look bad when you mess them up. Also, WebCT will do unpredectible things if you don’t use them correctly.

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Physics 218, Lecture II42 Converting Units Multiplying anything by 1 (no units!) is a GREAT trick! Use it often!! 1 meter x 1 = 1 meter 1 yard x 1 = 1 yard x (3 feet/yard) = 3 feet (simple! Units cancel out!) Example:1 football field in feet –1 football field x (1) x (1) = 1 football field –1 football field x (100 yards/1 football field) x (3 feet/yard) = 300 feet –Both are units of length!

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Physics 218, Lecture II43 Significant Figures Good test: Write the primary number as 1.5x10 1 feet (get rid of zeros on either end) which is the “powers of 10 notation” or what we call “scientific notation” – = x 10 4 Then deal with the uncertainty Usually only one digit in the uncertainty –Example: Fix ± 1 feet → ( ± 0.1) x 10 1 feet → (1.5 ± 0.1) x 10 1 feet

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Physics 218, Lecture II44 Reference Frames Frame of reference: Need to refer to some place as the origin Draw a coordinate axis –We define everything from here –Always draw a diagram!!!

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Physics 218, Lecture II45 Vector notation: –In the book, variables which are vectors are in bold –On the overheads, I’ll use an arrow over it Vectors are REALLY important Kinda like calculus: These are the tools! First the Math: Vector Notation Some motion represented by vectors. What do these vectors represent physically?

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Physics 218, Lecture II46 Adding vectors in funny directions Let’s say I walk in some random direction, then in another different direction. How do I find my total displacement? We can draw it It would be good to have a better way…

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Physics 218, Lecture II47 Example We have two known displacements D 1 and D 2. What is the magnitude and angle of the net displacement in this example?

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Physics 218, Lecture II48 Go home with a friend You are going home with a friend. You live in Houston and your friend lives in San Antonio. First you drive 100 miles SouthEast (known angle ) from Aggieland to Houston, then 300 miles West to San Antonio? Using unit vector notation, what is your displacement from the center of the universe?

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Physics 218, Lecture II49 Examples without an axis

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Physics 218, Lecture II50 Addition using Components To add two vectors, break both up into their X and Y components… First break each vector into its X and Y components

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Physics 218, Lecture II51 Addition using Components cont… Next: add separately in the X and Y directions Magnitudes of V F

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Physics 218, Lecture II52 Drawing the components

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Physics 218, Lecture II53 Vector Cross Product Cont… Calculating the cross product is the same as taking the determinant of a Matrix

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