New Phenomena: Recent Results and Prospects from the Fermilab Tevatron

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Physics 218Lecture 2
Dr. David Toback
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In Class Quiz

• Write down the most important student case
  study from the Frequently Asked Questions handout

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Announcements WebCT

• Having trouble getting started? Try
• ITS Help sessions
• Open access lab/student computing
• Instructions on faculty.physics.tamu.edu/toback/We
  bCT
• email to webct_at_physics.tamu.edu
• Check your neo email account for announcements
• Still working on Math Quiz figures sorry about
  that..
• Finish your Preliminary Course Materials

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Due dates coming up

• Week 1 (This week)
• Lecture Chapter 1 (Reading, but nothing due)
• Recitation Lab Lab 1 (AB)
• Homework due None
• Week 2 (Next week)
• Homework (Monday) Math quizzes
• Lecture Chapter 2
• Recitation Lab Chapter 1 and Lab 2
• Week 3 (The week after that)
• Homework due (Monday) Chapter 1
• Lecture Chapter 3 4
• Recitation Chapter 2 and Lab 3
• Etc..

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(No Transcript)
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Chapter 1 Calculus

• Wont cover the chapter in detail
• This is a chapter that is best learned by DOING
• Well cover it quickly
• Lots more examples in Chapter 2
• Lots of practice in Math Quizzes on WebCT (when
  theyre fixed)

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Where are we going?

• We want Equations that describe
• Where am I as a function of time?
• How fast am I moving as a function of time?
• What direction am I moving as a function of time?
• Is my speed changing? Etc.

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• Use calculus to solve problems!

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Motion in One Dimension

• Where is the car?
• X0 feet at t00 sec
• X22 feet at t11 sec
• X44 feet at t22 sec
• Since the cars position is changing (i.e.,
  moving) we say this car has speed or velocity
• Plot position vs. time
• How do we get the speed from the graph?

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Speed

• Questions
• How fast is my position changing?
• What would my speedometer read?

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How do we Calculate the speed?

• Define speed Change in position during a
  certain amount of time
• Math Calculate from the Slope The Change in
  position as a function of time
• Change in Vertical divided by the Change in
  Horizontal
• Speed DX/Dt

Change D
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Constant Speed

• Equation of Motion for this example is a straight
  line
• Write this as
• X bt
• Slope is constant
• Velocity is constant
• Easy to calculate
• Same everywhere

time
Position
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Moving Car

• A harder example
• X ct2
• Whats the speed at t1 sec?
• Want to calculate the Slope here
• What would the speedometer say?

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Derivatives

• To find the slope at time t, just take the
  derivative
• For Xct2 , Slope V dx/dt 2ct
• Gerbil derivative method
• If X atn ?Vdx/dtnatn-1
• Derivative of X with respect to t
• More examples
• X qt2 ?Vdx/dt2qt
• X ht3 ?Vdx/dt3ht2

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Common Mistakes

• The trick is to remember what you are taking the
  derivative with respect to
• More Examples (with aconstant)
• What if X 2a3tn?
• Why not dx/dt 3(2a2tn)?
• Why not dx/dt 3n(2a2tn-1)?
• What if X 2a3?
• What is dx/dt?
• There are no ts!!! dx/dt 0!!!
• If X22 feet, what is the velocity? 0!!!

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Going the other way Integrals

• What if you know how fast youve been going and
  how long youve been driving
• How can you figure out how far youve gone?
• What would your cars odometer read?

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Getting the Displacement from Velocity

• If you are given the speed vs. time graph you can
  find the total distance traveled from the area
  under the curve
• ?XV0t ½at2
• Can also find this from integrating

Slope is constant Constant acceleration
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Definite and Indefinite Integrals
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Some Integrals
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Our Example
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For Next Week

• Before Lecture
• Read Chapter 2
• Math Quizzes due Monday
• In Lecture
• Cover Chapter 2
• Recitation, Lab and Homework
• Start Chapter 1 problems and exercises before
  recitation
• Read your lab materials before lab

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End of Lecture Notes
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Simple Multiplication

• Multiplication of a vector by a scalar
• Lets 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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Subtraction

• Subtraction is easy
• Its 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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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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Problem Solving Diagrams

• This class is mostly problem solving (well you
  need to understand the concepts first in order to
  solve the problems, but well 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 2Draw a diagram!

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Announcement Free Tutoring

• Four foreign graduate students are available to
  tutor Physics 218 Students without charge.
  Students desiring help are to e-mail the tutor
  and arrange a time to meet in Heldenfels 211 on
  weekdays. The tutors are
• Sunnam Min, smin_at_physics.tamu.edu
• Xi Wang, xwang_at_phyiscs.tamu.edu
• Rongguang Xu, rxu_at_physics.tamu.edu
• Hong Lu, hlu_at_physics.tamu.edu

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Components

• Lets 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 A2 B2 C2

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Chapter 1 Introduction

• This chapter is fairly well written. I wont
  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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Models, theories and Laws

• Models, theories and Laws
• Prescriptive vs. Descriptive
• What should happen vs. What does happen when you
  do an experiment
• US law doesnt allow killing
• Physics law shows clearly that it does happen.

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Estimating

• Order of Magnitude
• This is a useful thing to be able to do at home
• Lets say you are at a grocery store and its
  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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Number of Significant Figures

• 15 1 feet (1 digit in uncertainty, same 10s
  as last digit)
• 15.052 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 dont use them correctly.

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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!)
• Example1 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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Significant Figures

• Good test Write the primary number as 1.5x101
  feet (get rid of zeros on either end) which is
  the powers of 10 notation or what we call
  scientific notation
• 17526.423 1.7526423 x 104
• Then deal with the uncertainty
• Usually only one digit in the uncertainty
• Example Fix 15.052 1 feet
• ? (1.5052 0.1) x 101 feet
• ? (1.5 0.1) x 101 feet

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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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First the Math Vector Notation

• Vector notation
• In the book, variables which are vectors are in
  bold
• On the overheads, Ill use an arrow over it
• Vectors are REALLY important
• Kinda like calculus These are the tools!

Some motion represented by vectors. What do these
vectors represent physically?
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Adding vectors in funny directions

• Lets 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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Example

• We have two known displacements D1 and D2. What
  is the magnitude and angle of the net
  displacement in this example?

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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
  Q) 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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Examples without an axis
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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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Addition using Components cont

• Next add separately in the X and Y directions

Magnitudes of VF
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Drawing the components
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Vector Cross Product Cont

• Calculating the cross product is the same as
  taking the determinant of a Matrix