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Physics 231

Physics 231. Topic 1: Introduction, Units, Significant Figures. Alex Brown August 27, 2014. Today's Lecture: Key Concepts. Syllabus SI Units Mass: kilograms (kg) Length: meters (m) Time: seconds (s) Units and conversions Dimensional Analysis

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Physics 231

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  1. Physics 231 Topic 1: Introduction, Units, Significant Figures Alex Brown August 27, 2014

  2. Today's Lecture: Key Concepts • Syllabus • SI Units • Mass: kilograms (kg) • Length: meters (m) • Time: seconds (s) • Units and conversions • Dimensional Analysis • Scientific Notation (e.g., 4.3x1012 and 2.3E4) • Significant Figures Covers chapter 1 in Rex & Wolfson

  3. Textbook & Reading Essential College Physics, Volume 1 • The syllabus lists the relevant chapters for each lecture and homework • Read the material before class • All material in the assigned reading can be on homework/exams and not everything can be covered in class • Lectures are not a replacement for the textbook

  4. Homework Homework is to be done online using LON-CAPA http://msu.lon-capa.org Homework assignments are due Tuesdays at 10 PM • The deadline is strict. Being away from a network connection is no excuse. • Do not wait until the last minute! • Assignments are somewhat unique to each student • Discussion board • You are encouraged to use the discussion board inside LON-CAPA. If you don't understand a problem, or you need help, just click on the "Post Discussion" link and post your question. If you know the answer to somebody else's question, just don't be afraid to post you answer. Don't forget: The best way to learn is to teach. • But – to do well in the exams you should try the problem on your own first, and if you use the discussion board be sure you understand the concepts and the reasoning behind the solution.

  5. Extra Credit Quizzes • We will be doing in-class quizzes using i>Clickers • Quizzes will be given randomly throughout the semester • You must have in i>Clicker to participate • Start Wednesday September 4th • Be on time, quizzes are sometimes at the beginning of class. • There are NO make-ups for quizzes all of the points are for extra credit • You must take quizzes in this section. No credit for quizzes in other sections. • Quiz points: 3 for correct answers, 1 for incorrect answers • Scores will be posted on my website occasionally – check to ensure you're registered You must register your i<Clicker on lon-capa • Even if you have registered before, you need to re-register for this course! • You MUST enter the preceding “A” before your student ID

  6. Extra Credit Quizzes • You must use your own and ONLY your own i>Clicker in class • If you are found to be using another person's i>Clicker, all clickers will be confiscated • This will be considered a violation of the rules governing academic dishonesty

  7. Physics Learning Center (PLC) • The Strosacker Physics Learning Center is located in BPS 1248 • Details and schedule TBA • The PLC is a cooperative learning center, not a help room. TAs will encourage group work and will help groups who get stuck. • Group work • A very effective learning tool for both strong and weak students • You must do your own assignments and must learn how to do problems on your own • Do as much as you can of the assignments before group work – PREPARE!

  8. How to Suceed in PHY231 • Read the book before coming to class. Some quizzes will be on the reading material, even material that has not been covered in class. • Go to the Physics Learning Center frequently! The TAs are there to help you learn. • Always attend the lectures. • Recognize that learning physics is different than many other subjects • Physics is about understanding concepts and connecting your knowledge with these concepts. Physics is not just about memorizing facts. • Some physics concepts will be contrary to your instincts, but not contrary to your intellect. Be willing to think things through! • Keep working continuously – do the reading assignments, think about what you learned in lecture, keep thinking AS WE GO. Memorizing facts is not sufficient, so cramming before an exam is not effective. • Understanding the concepts helps you set up solutions to problems. Equation hunting is not a good strategy. • Little is learned by copying or memorizing the solution of another student.

  9. DOs and DON'Ts DON'T... • ...use LON-CAPA postings from others before you have given a problem a genuine attempt yourself. If you have to frequently look at how others solved the problem, it means you aren't understanding the material well. • ...try to memorize LON-CAPA problems; it is unlikely that you will get many problems in exams that are exactly like the homework • ...base your entire study routine on LON-CAPA. Bring variation in your studies and practice questions that are not phrased like LON-CAPA (eg, questions in the book) • ...wait until the last weeks of the semester to ask for help if you need it (ie, if you're working hard but still are not doing well) • ...cheat on exams, quizzes, homework

  10. DOs and DON'Ts DON'T... • …use your cell phone in class.

  11. Why Learn Physics? Example: Tacoma Narrows Bridge

  12. Why Learn Physics? Example: Mechanics of the Skeleton Key concept for: • Human medicine • Veterinary medicine • Sports training • Ergonomic engineering In other classes, you learn the names of bones, how to treat broken bones, where to drill to replace things. Physics teaches you HOW and WHY it works (and how to understand the system as a whole)  Combination is the key to innovation!

  13. Why Learn Physics? Example: Dark Matter & Dark Energy • Cosmological measurements have told us that our universe is not made the way we thought. • IE, what we see in telescopes corresponds to what we are all made out of: atoms (stars, gases, planets) Bullet Cluster

  14. Why Learn Physics? Example: Dark Matter & Dark Energy • Cosmological measurements have told us that our universe is not made the way we thought. • IE, what we see in telescopes corresponds to what we are all made out of: atoms (stars, gases, planets) • But this is only 4% of what’s out there! Bullet Cluster

  15. Système Internationale (SI) Units (ones used for this course) Unit Abbreviation Base unit for meter m length kilogram kg mass second s time Kelvin K temperature mole mol amount of substance (others) ampere A electric current candela cd luminous intensity • Also called the MKS unit system • Based on powers of 10 relative to base units • All other units derive from these (Area: m2, Speed: m/s, etc)

  16. Defining Standard Units Original definition of the meter: 1/10,000,000 of earth's arc length • Today: 1m = distance light travels in 1/299,272,458 s

  17. Defining Standard Units Platinum-Iridium Kilogram Prototype • The kilogram defined by a fixed “prototype” of matter • Standards are important: when you buy 1kg of gold, you want to get it right!

  18. Defining Standard Units Cesium Atomic Clock National Institute of Standards and Technology (NIST) Original definition of the second: 1/86,400 of a solar day • 1960: based on a tropical year • Since 1967: 9,192,631,770 periods of radiation corresponding to the transition between two hyperfine states of the ground state of 133Cesium

  19. Unit Conversion Example Treat conversions as algebraic equivalencies: Convert by multiplying your existing units by a numerical equivalent of 1.0 Jon has walked 3 miles in 1 hour, what is his average speed in m/s? Given: 1 mile = 1609.3 m ie, 1.0 = ( 1609.3 m/ 1 mile ) Velocity (speed) = distance / time = ( 3 miles ) / ( 1 hour ) Equal to 1.0 = ( 3 miles/hr ) x ( 1609.3 m / mile ) = 4827.9 m/hr = ( 4827.9 m/hr ) x (1 hr / 60 min) x (1 min / 60 sec) = ( 4827.9 m/hr ) x (1 hr / 3600 s) = ( 4827.9/3600 ) m/s = 1.341 m/s

  20. A Wide Range of Units

  21. Scientific Notation • For very large or very small numbers the scientific notation is advantageous. • Write number as mantissa x 10Exponent • Example: 0.000000001 = 1 × 10-9 34000000 = 3.4 × 107 • Alternative notation: 3.4E7 (CAPA, computers) 1 m = 1000 mm = 1E3 mm

  22. Very Large and Very Small Numbers 0.000000000000001 = 10-15 = 1E-15 femto (f) 0.000000000001 = 10-12 = 1E-12 pico (p) 0.000000001 = 10-9 = 1E-9 nano (n) 0.000001 = 10-6 = 1E-6 micro () 0.001 = 10-3 = 1E-3 milli (m) 0.01 = 10-2 = 1E-2 centi (c) 0.1 = 10-1 = 1E-1 deci (d) 1 = 100 = 1E+0 10 = 101 = 1E+1 deca (da) 100 = 102 = 1E+2 hecto (h)1000 = 103 = 1E+3 kilo (k) 1000000 = 106 = 1E+6 mega (M) 1000000000 = 109 = 1E+9 giga (G) 10000000000 = 1012 = 1E+12 tera (T)

  23. Significant Figures

  24. Significant Figures • Two statements: • The population of the USA is 294,109,799 • The population of the USA is 294,000,000=2.94×108 • First statement implies precision that is probably not warranted • Second statement claims that the population is somewhere between 293M and 295M. This is reasonable! • General Rules: • The number of digits we write down in a number specifies the precision with which we can claim to know the number • All non-zero figures are signficant (except exponent in scientific notation) • Zeros only count when They are between non-zero figures They are to the right of a non-zero figure and there is a decimal point

  25. Significant Figures Example • An athlete must bicycle around a circular track for a time trial. His coach tells him that the radius of the circular track is 40.2 m. How far does he ride? • Formulae: C = π D = 2 π R • D = diameter of the circle • R = radius of the circle • π = 3.14159265..... We know π to many decimal places, but we only know the radius is between 40.2 and 40.3 m (ie, 3 significant figures). • Thus we can only know the circumference to 3 significant figures! What is the answer? • C = 2 × 3.14159265... × 40.2 m = 253 m

  26. How to Solve Problems There are no general rules but here are some pointers: • READ the problem carefully! • Summarize (throw away unnecessary info) • Visualize (drawing can often help) • Convert units (consistency) • Set up equations: Plug in numbers if not comfortable with solving sets of equations If confident, plug in numbers at last moment 6) Check whether answers make sense 7) In exams: once you have solved a problem, check calculations one more time at the end of exam. Especially important if you tend to make small mistakes

  27. Greek Alphabet We will use some of those…

  28. 2D Geometrical Objects

  29. 3D Geometrical Objects

  30. Solving Quadratic Equations In general there are 2 solutions. In physics problems, One of them is usually not realistic and is thrown out.

  31. h A = wh p = 2w+2h 24 = wh so w = 24/h 22 = 2w + 2h = (2x24/h) + 2h = (48/h) + 2h -2h2 + 22h - 48 = 0 w Calculate the length of the shorter of two sides of a rectangle, which has an area of A = 24 m2 and a perimeter of p = 22 m. Example of two equations and two unknowns.

  32. Dimensional Analysis Dimensions should be treated as algebraic quantities • If you know the dimensions you want in the end of a calculation, it helps you plan your work and check your math • Example: • Calculate the distance traveled in 10 seconds by an object starting at rest and traveling at constant acceleration • Given : x = (1/2) a t2 • What are the units for a (acceleration)? • [m] = [?]  [s2] • Rearrange to get units for a: • [?] = [m] / [s2] )= m/s2 Units of acceleration go here Check your math: [m] = [m/s2]  [s2] = [m]

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