1. Monday, June 6, 2011PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 1 PHYS 1443 – Section 001 Lecture #1 Monday, June 6, 2011 Dr. Jaehoon Yu Class Introduction Standard and units Dimensional Analysis Fundamentals One Dimensional Motion: Average Velocity; Acceleration; Motion under constant acceleration; Free Fall Today’s homework is homework #1, due 10pm, Wednesday, June 8!!

2. Monday, June 6, 2011PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 2 Announcements Reading assignment #1: Read and follow through all sections in appendices A and B by Wednesday, June 8 –There will be a quiz this Wednesday, June 8, on this reading assignment

3. Monday, June 6, 2011PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 3 Special Problems for Extra Credit Derive the quadratic equation for Bx 2 -Cx+A=0  5 points Derive the kinematic equation from first principles and the known kinematic equations  10 points You must show your work in detail to obtain full credit Due at the start of the class, Thursday, June 9

4. Monday, June 6, 2011PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 4 Who am I? Name: Dr. Jaehoon Yu (You can call me Dr. Yu ) Office: Rm 342, Chemistry and Physics Building –Office Hours: 2:30 – 3:30pm Mondays and Wednesdays or by appointment Extension: x22814, E-mail: jaehoonyu@uta.edu My profession: High Energy Particle Physics (HEP) –Collide particles (protons on anti-protons or electrons on anti-electrons, positrons) at the energies equivalent to 10,000 Trillion degrees –To understand Fundamental constituents of matter Interactions or forces between the constituents Origin of Mass Creation of Universe ( Big Bang Theory) –A pure scientific research activity Direct use of the fundamental laws we find may take longer than we want but Indirect product of research contribute to every day lives; eg. WWW

5. Monday, June 6, 2011 We always wonder… What is the universe made of? How does the universe work? What are the things that holds the universe together? What are the governing principles of the universe? How can we live in the universe well? Where do we all come from? HEP looks into the smallest possible things to find the answers to these deep questions PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 5

6. Monday, June 6, 2011 The Standard Model of Particle Physics Prescribes the following fundamental structure: Three families of leptons and quarks together with 12 force mediators  Simple and elegant!!! Tested to a precision of 1 part per million! ~0.01m p Family Discovered in 1995, ~170m p Directly observed in 2000 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 6

7. Monday, June 6, 2011 Good, but still lots we don’t know… Why are there three families of quarks and leptons? Why is the mass range so large (0.01m p – 175 m p )? How do matters acquire mass? –Higgs mechanism but where is the Higgs, the God particle? Why is the matter in the universe made only of particles? –What happened to anti-particles? Or anti-matters? Why are there only three apparent forces? Is the picture we present the real thing? –What makes up the 96% of the universe? –How about extra-dimensions? How is the universe created? Are there any other theories that describe the universe better? –Does the super-symmetry exist? PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 7

8. Monday, June 6, 2011PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 8 Accelerators are Powerful Microscopes. They make high energy particle beams that allow us to see small things. seen by high energy beam (better resolution) seen by low energy beam (poorer resolution)

9. Monday, June 6, 2011PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 9 Accelerators are also Time Machines. E = mc 2 They make particles last seen in the earliest moments of the universe. Energy Particle and anti-particle annihilate. particle beam energy anti-particle beam energy

10. Monday, June 6, 2011 Fermilab Tevatron and LHC at CERN World’s Highest Energy proton-anti-proton collider –6km circumference –E cm =1.96 TeV (=6.3x10 -7 J/p  13M Joules on 10 - 4 m 2 ) –Equivalent to the kinetic energy of a 20t truck at the speed 81mi/hr  130km/hr ~100,000 times the energy density at ground 0 of the atom bomb dropped on Hiroshima – To be shut down Sept. 30, 2011 Chicago Tevatron p p CDF DØ World’s Highest Energy p-p collider –27km circumference, 100m underground –Design E cm =14 TeV (=44x10 -7 J/p  362M Joules on the area less than 10 -4 m 2 )  Equivalent to the kinetic energy of a B727 (80tons) at the speed 193mi/hr  312km/hr  ~3M times the energy density at ground 0 of atom bomb dropped on Hiroshima First 7TeV collisions on 3/30/10  The highest energy humans ever achieved!! First collisions in 2011 in mid March, 2011 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 10

11. Monday, June 6, 2011PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 11 LHC @ CERN Aerial View Geneva Airport ATLAS CMS France Swizerland

12. Monday, June 6, 2011 A Future Linear Collider An electron-positron collider on a straight line for precision measurements CMS Energy: 0.5 – 1 TeV 10~15 years from now Takes 10 years to build the accelerator and the detector L~31km PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 12 Circumference ~6.6km ~310 soccer fields

13. Monday, June 6, 2011PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 13 DØ Detector 30’ 50’ ATLAS Detector Weighs 5000 tons and 5 story tall Can inspect 3,000,000 collisions/second Record 100 collisions/second Records approximately 10,000,000 bytes/second Records 0.5x10 15 (500,000,000,000,000) bytes per year (0.5 PetaBytes). Weighs 7000 tons and 10 story tall Can inspect 1,000,000,000 collisions/second Records 200 – 400 collisions/second Records approximately 350,000,000 bytes/second Will record 2x10 15 (2,000,000,000,000,000) bytes each year (2 PetaByte).

14. Monday, June 6, 2011PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 14 DØ Central Calorimeter 1990

15. Monday, June 6, 2011PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 15 Computers put together a picture Digital data Data Reconstruction pp p

16. Monday, June 6, 2011PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 16 Time “parton jet” “particle jet” “calorimeter jet” hadrons  CH FH EM Highest E T dijet event at DØ How does an Event Look in a Collider Detector?

17. Monday, June 6, 2011PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 17 GEM Application Potential FAST X-RAY IMAGING Using the lower GEM signal, the readout can be self-triggered with energy discrimination: A. Bressan et al, Nucl. Instr. and Meth. A 425(1999)254 F. Sauli, Nucl. Instr. and Meth.A 461(2001)47 9 keV absorption radiography of a small mammal (image size ~ 60 x 30 mm 2 )

18. And in not too distant future, we could do … 18

19. Monday, June 6, 2011PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 19 Information & Communication Source My web page: http://www-hep.uta.edu/~yu/http://www-hep.uta.edu/~yu/ –Contact information & Class Schedule –Syllabus –Homework –Holidays and Exam days –Evaluation Policy –Class Style & Communication –Other information Office Hours: 10:00 – 11:00am, Mondays through Thursdays or by appointments

20. Monday, June 6, 2011PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 20 Evaluation Policy Homework: 30% Exams –Midterm and Final Comprehensive Exams (6/21 and 7/11): 22.5% each –Missing an exam is not permissible unless pre-approved No makeup test!! You will get an F if you miss any of the exams without a prior approval Lab score: 15% Pop-quizzes: 10% Extra credits: 10% of the total –Random attendances –Strong participation in the class discussions –Special projects –Planetarium shows and Other many opportunities Grading will be done on a sliding scale 100%

21. Monday, June 6, 2011PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 21 Homework Solving homework problems is the only way to comprehend class material An electronic homework system has been setup for you –Details are in the material distributed today and on the web –https://quest.cns.utexas.edu/student/courses/listhttps://quest.cns.utexas.edu/student/courses/list –Choose the course PHYS1443-001-SUMMER2011, unique number 43111 –Download homework #1, solve the one problem and submit them online –Multiple unsuccessful tries will deduct points –Roster will close at midnight Wednesday, June 8 –You need a UT e-ID: Go and apply at the URL https://idmanager.its.utexas.edu/eid_self_help/?createEID&qwicap-page- id=EA027EFF7E2DA39E if you don’t have one. Each homework carries the same weight ALL homework grades will be used for the final grade Home work will constitute 30% of the total  A good way of keeping your grades high Strongly encouraged to collaborate  Does not mean you can copy

22. Monday, June 6, 2011PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 22 Attendances and Class Style Attendances: –Will be taken randomly –Will be used for extra credits Class style: –Lectures will be on electronic media The lecture notes will be posted on the web AFTER each class –Will be mixed with traditional methods –Active participation through questions and discussions are STRONGLY STRONGLY encouraged  Extra credit…. –Communication between you and me is extremely important If you have problems, please do not hesitate talking to me

23. Monday, June 6, 2011PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 23 Lab and Physics Clinic Physics Labs: –Starts, Wed. June 8, 2011 –Important to understand physical principles through experiments –15% of the grade –Lab syllabus is available in your assigned lab rooms. Go by the lab room between 8am - 6pm M – F and pick up the syllabus Physics Clinic: –Room SH007, 12 – 6pm Mon – Thur and 1 – 6pm Sat. –Free of charge –They provide general help on physics, including help solving homework problems Do not expect solutions of the problem from them! Do not expect them to tell you whether your answers are correct! It is your responsibility to make sure that you have done everything correctly! –Will let you know via e-mail when the service begins

24. Extra credit 10% addition to the total –Could boost a B to A, C to B or D to C What constitute for extra credit? –Random attendances –Physics department colloquium participation Some will be double or triple credit ( –Strong participation in the class discussions –Special projects –Watch the valid planetarium shows –Many other opportunities Monday, June 6, 2011PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 24

25. Valid Planetarium Shows Regular running shows –Magnificent Sun –Violent Universe –Wonders of the Universe Shows that need special arrangements –Stars of the Pharaohs –Black Holes –Two small pieces of glass –SOPHIA How to submit for extra credit? –Obtain the ticket stub that is signed and dated by the planetarium star lecturer of the day –Collect the ticket stubs –Tape all of them on a sheet of paper with your name and ID written on it –Submit the sheet at the end of the semester when asked Monday, June 6, 2011PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 25

26. Monday, June 6, 2011PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 26 What can you expect from this class? All A’s? –This would be really nice, wouldn’t it? –But if it is too easy it is not fulfilling or meaningful…. This class is not going to be a stroll in the park!! (Very fast pace!!) You will earn your grade in this class. –You will need to put in sufficient time and sincere efforts –Exams and quizzes will be tough!! Sometimes problems might not look exactly like what you learned in the class Just putting the right answer in free response problems does not work! But you have a great control of your grade in your hands –Homework is 30% of the total grade!! Means you will have many homework problems –Sometimes much more than any other classes –Sometimes homework problems will be something that you have yet to learn in class –Lab 15% –Extra credit 10% I will work with you so that your efforts are properly awarded

27. Monday, June 6, 2011PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 27 What do we want to learn in this class? Physics is everywhere around you. Understand the fundamental principles that surrounds you in everyday lives… Identify what laws of physics applies to what phenomena and use them appropriately Understand the impact of such physical laws Learn how to research and analyze what you observe. Learn how to express observations and measurements in mathematical language Learn how to express your research in systematic manner in writing I don’t want you to be scared of PHYSICS!!! Most importantly, let us have a lot of FUN!!

28. Monday, June 6, 2011 28 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 28 Why do Physics? To understand nature through experimental observations and measurements ( Research ) Establish limited number of fundamental laws, usually with mathematical expressions Predict the nature’s course ⇒ Theory and Experiment work hand-in-hand ⇒ Theory works generally under restricted conditions ⇒ Discrepancies between experimental measurements and theory are good for improvements ⇒ Improves our everyday lives, even though some laws can take a while till we see them amongst us Exp. { Theory {

29. Monday, June 6, 2011 29 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 29 Brief History of Physics AD 18 th century: –Newton’s Classical Mechanics: A theory of mechanics based on observations and measurements AD 19 th Century: –Electricity, Magnetism, and Thermodynamics Late AD 19 th and early 20 th century ( Modern Physics Era ) –Einstein’s theory of relativity: Generalized theory of space, time, and energy (mechanics) –Quantum Mechanics: Theory of atomic phenomena Physics has come very far, very fast, and is still progressing, yet we’ve got a long way to go –What is matter made of? –How do matters get mass? –How and why do matters interact with each other? –How is universe created?

30. Monday, June 6, 2011 30 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 30 Models, Theories and Laws Models: An analogy or a mental image of a phenomena in terms of something we are familiar with –Thinking light as waves, behaving just like water waves –Often provide insights for new experiments and ideas Theories: More systematically improved version of models –Can provide quantitative predictions that are testable and more precise Laws: Certain concise but general statements about how nature behaves –Energy conservation –The statement must be found experimentally valid to become a law Principles: Less general statements of how nature behaves –Has some level of arbitrariness

31. Monday, June 6, 2011 31 Uncertainties Physical measurements have limited precision, however good they are, due to: –Number of measurements –Quality of instruments (meter stick vs micro-meter) –Experience of the person doing measurements –Etc In many cases, uncertainties are more important and difficult to estimate than the central (or mean) values Stat.{ { Syst. PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu

32. Monday, June 6, 2011 32 Significant Figures Denote the precision of the measured values –The number 80 implies precision of +/- 1, between 79 and 81 If you are sure to +/-0.1, the number should be written 80.0 –Significant figures: non-zero numbers or zeros that are not place- holders 34, 34.2, 0.001, 34.100 –34 has two significant digits –34.2 has 3 –0.001 has one because the 0’s before 1 are place holders to position “.” –34.100 has 5, because the 0’s after 1 indicates that the numbers in these digits are indeed 0’s. When there are many 0’s, use scientific notation for simplicity: –31400000=3.14x10 7 –0.00012=1.2x10 -4 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu

33. Monday, June 6, 2011 33 Significant Figures Operational rules: –Addition or subtraction: Keep the smallest number of decimal place in the result, independent of the number of significant digits: 12.001+ 3.1= –Multiplication or Division: Keep the smallest number of significant difits in the result: 12.001 x 3.1 =, because the smallest significant figures is ?. 15.1 37 What does this mean? The worst precision determines the precision the overall operation!! PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu Can’t get any better than the worst measurement! In English?

34. Monday, June 6, 2011 34 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 34 Needs for Standards and Units Seven basic quantities for physical measurements –Length, Mass, Time, Electric Current, Temperature, the Amount of substance and Luminous intensity Need a language that everyone can understand each other –Consistency is crucial for physical measurements –The same quantity measured by one must be comprehendible and reproducible by others –Practical matters contribute A system of unit called SI SI ( System Internationale ) was established in 1960 – Length – Length in meters (m)(m) – Mass – Mass in kilo-grams ( kg ) – Time – Time in seconds (s)(s)

35. Monday, June 6, 2011 35 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 35 Definition of Three Relevant Base Units One second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the Cesium 133 (C 133 ) atom. 1 s (Time) It is equal to the mass of the international prototype of the kilogram, made of platinum-iridium in International Bureau of Weights and Measure in France. 1 kg (Mass) = 1000 g One meter is the length of the path traveled by light in vacuum during the time interval of 1/299,792,458 of a second. 1 m (Length) = 100 cm DefinitionsSI Units There are total of seven base quantities (see table 1-5 on page 7) There are prefixes that scales the units larger or smaller for convenience (see pg. 7) Units for other quantities, such as Newtons for force and Joule for energy, for ease of use

36. Monday, June 6, 2011 36 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 36 Prefixes, expressions and their meanings deci (d): 10 -1 centi (c): 10 -2 milli (m): 10 -3 micro (μ): 10 -6 nano (n): 10 -9 pico (p): 10 -12 femto (f): 10 -15 atto (a): 10 -18 zepto (z): 10 -21 yocto (y): 10 -24 deca (da): 10 1 hecto (h): 10 2 kilo (k): 10 3 mega (M): 10 6 giga (G): 10 9 tera (T): 10 12 peta (P): 10 15 exa (E): 10 18 zetta (Z): 10 21 yotta (Y): 10 24 LargerSmaller

37. Monday, June 6, 2011 37 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 37 International Standard Institutes International Bureau of Weights and Measure http://www.bipm.fr/ –Base unit definitions: http://www.bipm.fr/enus/3_SI/base_units.html –Unit Conversions: http://www.bipm.fr/enus/3_SI/ US National Institute of Standards and Technology (NIST) http://www.nist.gov/

38. Monday, June 6, 2011 38 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 38 How do we convert quantities from one unit to another? Unit 1 =Unit 2Conversion factor X 1 inch2.54cm 1 inch0.0254m 1 inch2.54x10 -5 km 1 ft30.3cm 1 ft0.303m 1 ft3.03x10 -4 km 1 hr60minutes 1 hr3600seconds And manyMoreHere….

39. Monday, June 6, 2011 39 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 39 Examples 1.3 and 1.4 for Unit Conversions Ex 1.3: An apartment has a floor area of 880 square feet (ft 2 ). Express this in square meters (m 2 ). Ex 1.4: Where the posted speed limit is 55 miles per hour (mi/h or mph), what is this speed (a) in meters per second (m/s) and (b) kilometers per hour ( km/h )? (a) What do we need to know? (b)

40. Monday, June 6, 2011 40 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 40 Estimates & Order-of-Magnitude Calculations Estimate = Approximation –Useful for rough calculations to determine the necessity of higher precision –Usually done under certain assumptions –Might require modification of assumptions, if higher precision is necessary Order of magnitude estimate: Estimates done to the precision of 10s or exponents of 10s; –Three orders of magnitude: 10 3 =1,000 –Round up for Order of magnitude estimate; 8x10 7 ~ 10 8 –Similar terms: “Ball-park-figures”, “guesstimates”, etc

41. Monday, June 6, 2011 41 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 41 Example 1.8 Estimate the radius of the Earth using triangulation as shown in the picture when d=4.4km and h=1.5m. R d=4.4km R+h Pythagorian theorem Solving for R

42. Monday, June 6, 2011 42 Dimension and Dimensional Analysis An extremely useful concept in solving physical problems Good to write physical laws in mathematical expressions No matter what units are used the base quantities are the same –Length (distance) is length whether meter or inch is used to express the size: Usually denoted as [L] –The same is true for Mass ([M]) and Time ([T]) –One can say “Dimension of Length, Mass or Time” –Dimensions are treated as algebraic quantities: Can perform two algebraic operations; multiplication or division PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu

43. Monday, June 6, 2011 43 Dimension and Dimensional Analysis One can use dimensions only to check the validity of one’s expression: Dimensional analysis –Eg: Speed [v] = [L]/[T]=[L][T -1 ] Distance (L) traveled by a car running at the speed V in time T –L = V*T = [L/T]*[T]=[L] More general expression of dimensional analysis is using exponents: eg. [v]=[L n T m ] =[L][T -1 ] where n = 1 and m = PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu

44. Monday, June 6, 2011 44 Examples Show that the expression [v] = [at] is dimensionally correct Speed: [v] =[L]/[T] Acceleration: [a] =[L]/[T] 2 Thus, [at] = (L/T 2 )xT=LT (-2+1) =LT -1 =[L]/[T]= [v] Dimensionless constant Length Speed rv a Suppose the acceleration a of a circularly moving particle with speed v and radius r is proportional to r n and v m. What are n and m ? PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu

45. Monday, June 6, 2011 45 Some Fundamentals Kinematics: Description of Motion without understanding the cause of the motion Dynamics: Description of motion accompanied with understanding the cause of the motion Vector and Scalar quantities: –Scalar: Physical quantities that require magnitude but no direction Speed, length, mass, height, volume, area, magnitude of a vector quantity, etc –Vector: Physical quantities that require both magnitude and direction Velocity, Acceleration, Force, Momentum It does not make sense to say “I ran with velocity of 10miles/hour.” Objects can be treated as point-like if their sizes are smaller than the scale in the problem –Earth can be treated as a point like object (or a particle)in celestial problems Simplification of the problem (The first step in setting up to solve a problem…) –Any other examples? PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu

46. Monday, June 6, 2011 46 Some More Fundamentals Motions:Can be described as long as the position is known at any given time (or position is expressed as a function of time) –Translation: Linear motion along a line –Rotation: Circular or elliptical motion –Vibration: Oscillation Dimensions –0 dimension: A point –1 dimension: Linear drag of a point, resulting in a line  Motion in one-dimension is a motion on a line –2 dimension: Linear drag of a line resulting in a surface –3 dimension: Perpendicular Linear drag of a surface, resulting in a stereo object PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu

47. Monday, June 6, 2011PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 47 Displacement, Velocity and Speed One dimensional displacement is defined as: The average velocity is defined as: The average speed is defined as: Displacement per unit time in the period throughout the motion Displacement is the difference between initial and final potions of the motion and is a vector quantity. How is this different than distance? Unit? m/s Unit? m m/s A vector quantity A scalar quantity A vector quantity

48. Monday, June 6, 2011PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 48 How much is the elapsed time? What is the displacement?

49. Monday, June 6, 2011PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 49 Displacement, Velocity and Speed One dimensional displacement is defined as: The average velocity is defined as: The average speed is defined as: Can someone tell me what the difference between speed and velocity is? Displacement per unit time in the period throughout the motion Displacement is the difference between initial and final potions of the motion and is a vector quantity. How is this different than distance? Unit? m/s Unit? m m/s

50. Monday, June 6, 2011 50 Difference between Speed and Velocity Let’s take a simple one dimensional translation that has many steps: Let’s call this line as X-axis Let’s have a couple of motions in a total time interval of 20 sec. +10m +15m -15m-5m-10m +5m Total Displacement: Total Distance Traveled: Average Velocity: Average Speed: PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu

51. Monday, June 6, 2011 51 Example 2.1 Displacement: Average Velocity: Average Speed: The position of a runner as a function of time is plotted as moving along the x axis of a coordinate system. During a 3.00-s time interval, the runner’s position changes from x 1 =50.0m to x 2 =30.5 m, as shown in the figure. What was the runner’s average velocity? What was the average speed? PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu

52. Monday, June 6, 2011PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 52 Instantaneous Velocity and Speed Can average quantities tell you the detailed story of the whole motion? *Magnitude of Vectors are Expressed in absolute values Instantaneous speed is the size (magnitude) of the velocity vector: Instantaneous velocity is defined as: –What does this mean? Displacement in an infinitesimal time interval Average velocity over a very, very short amount of time NO!!

53. Monday, June 6, 2011PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 53 Instantaneous Velocity Time Average Velocity Instantaneous Velocity

54. Monday, June 6, 2011PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 54 Position vs Time Plot time t1t1 t2t2 t3t3 t=0 Position x=0 x1x1 1 23 1.Running at a constant velocity (go from x=0 to x=x 1 in t1,t1, Displacement is + x1 x1 in t1 t1 time interval) 2.Velocity is 0 (go from x1 x1 to x1 x1 no matter how much time changes) 3.Running at a constant velocity but in the reverse direction as 1. (go from x1 x1 to x=0 in t 3 -t 2 time interval, Displacement is - x1 x1 in t 3 -t 2 time interval) It is helpful to understand motions to draw them on position vs time plots. Does this motion physically make sense?

55. Monday, June 6, 2011PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 55

56. Monday, June 6, 2011PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 56 Example 2.3 (a) Determine the displacement of the engine during the interval from t 1 =3.00s to t 2 =5.00s. Displacement is, therefore: A jet engine moves along a track. Its position as a function of time is given by the equation x=At 2 +B where A=2.10m/s 2 and B=2.80m. (b) Determine the average velocity during this time interval.

57. Monday, June 6, 2011PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 57 Example 2.3 cont’d Calculus formula for derivative The derivative of the engine’s equation of motion is (c) Determine the instantaneous velocity at t=t 2 =5.00s. and The instantaneous velocity at t=5.00s is

58. Monday, June 6, 2011PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 58 Displacement, Velocity and Speed Displacement Average velocity Average speed Instantaneous velocity Instantaneous speed

59. Monday, June 6, 2011PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 59 Acceleration In calculus terms: The slope (derivative) of the velocity vector with respect to time or the change of slopes of position as a function of time analogous to analogous to Change of velocity in time (what kind of quantity is this?) Definition of the average acceleration: Definition of the instantaneous acceleration: Vector

60. Monday, June 6, 2011PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 60 Acceleration vs Time Plot What does this plot tell you? Yes, you are right!! The acceleration of this motion is a constant!!

61. Monday, June 6, 2011PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 61 Example 2.4 A car accelerates along a straight road from rest to 75km/h in 5.0s. What is the magnitude of its average acceleration?

62. Monday, June 6, 2011PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 62 Few Confusing Things on Acceleration When an object is moving in a constant velocity ( v=v 0 ), there is no acceleration ( a=0 ) –Is there any acceleration when an object is not moving? When an object is moving faster as time goes on, ( v=v(t) ), acceleration is positive ( a>0 ). –Incorrect, since the object might be moving in negative direction initially When an object is moving slower as time goes on, ( v=v(t) ), acceleration is negative ( a<0 ) –Incorrect, since the object might be moving in negative direction initially In all cases, velocity is positive, unless the direction of the movement changes. –Incorrect, since the object might be moving in negative direction initially Is there acceleration if an object moves in a constant speed but changes direction? The answer is YES!!