8/31/2009USF Physics 100 Lecture 21 Physics 100 Fall 2009 Lecture 2 Getting Started

8/31/2009USF Physics 100 Lecture 22 Agenda Administrative matters Physics and the Scientific Method Notation and Units Functional Relationships Measurement and Error Trigonometry Review, Vectors

8/31/2009USF Physics 100 Lecture 23 Agenda (1) Administrative Prof. Benton is in Germany Substitute Lecturer this week: Terrence A. Mulera – HR 102 Office Hours: Today, AM and Wednesday, 1-2 PM and by appointment Contact Information:   Phone: (415) st Lab next week ? week of 14 September Homework ?

8/31/2009USF Physics 100 Lecture 24 Save a Tree, Use the Web Lecture 2 and Lecture 3 slides available on USF Wiki as a Power Point® presentation. Go to:

8/31/2009USF Physics 100 Lecture 25 Thanks for the cartoon to Moose’s, 1652 Stockton St., San Francisco, CA

8/31/2009USF Physics 100 Lecture 26 Physics and the Scientific Method Physics is a science Limited to that which is testable Concerned with how rather than why Best defined in terms of the “Scientific Method” Other concerns reserved to Philosophy, Metaphysics and Theology.

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8/31/2009USF Physics 100 Lecture 28 Example: Newtonian Gravitation Observations: Things fall, planets orbit in ellipses etc. Empirical Law: There is an attractive force between objects which have mass. Theory: Newton’s Law of Gravitation

8/31/2009USF Physics 100 Lecture 29 Testing: Good agreement with experiment and observation. Measurement of falling objects Celestial mechanics pre-1900 Refinement of Theory and Further Testing: 1905 – 1920 Einstein’s theory of general relativity Eddington’s observation of bending light Precession of Mercury’s orbit

8/31/2009USF Physics 100 Lecture 210 Future Refinement and Testing: Quantum gravity? CAVEAT: A scientific theory can never be proved, it can only be shown to be not incorrect to the limit of our ability to test it. Alternatively, if you can’t devise an experiment which may disprove your conjecture, your conjecture is not science. - Karl Popper ( )

8/31/2009USF Physics 100 Lecture 211

8/31/2009USF Physics 100 Lecture 212 Helen Quinn, What is Science, Physics Today (July 2009) Posted on Wiki

8/31/2009USF Physics 100 Lecture 213 Scientific Notation Very large and very small numbers with many zeros before or after the decimal point are inconvenient in calculations. For convenience we write them as a x 10 b e. g. 1.0 = 1.0 x = 1.0 x = 1.0 x = 1.0 x = 1.0 x 10 2

8/31/2009USF Physics 100 Lecture 214 Results usually presented as 1 digit to left of decimal with exponent adjusted accordingly Multiplication: (a 1 x10 b1 )(a 2 x10 b2 )=a 1 a 2 x10 b1+b2 Division: (a 1 x10 b1 )/(a 2 x10 b2 )= (a 1 /a 2 )x10 b1-b2 Exponents add and/or subtract Powers:

8/31/2009USF Physics 100 Lecture 215 Units Mostly rationalized mks units, i.e. distance in meters, mass in kilograms, time in seconds. Occasional use of cgs units, i.e. centimeters, grams, seconds and of “ English” units, i. e. ft., slugs, seconds Special units. e.g. light years, parsecs, fermis, barns introduced as needed

8/31/2009USF Physics 100 Lecture 216 Scales The “mundane” scale: Our everyday world. Where not using scientific notation is not too painful. The VERY LARGE SCALE: Astronomy, astrophysics, cosmology. The very small scale: Atomic, nuclear and sub nuclear Very large and very small are both important in current cosmological thinking.

8/31/2009USF Physics 100 Lecture 217 Functional Relationships Mathematical representation of the relationship between quantities. y = f(x) y : dependent variable, ordinate x : independent variable, abscissa f x input y output

8/31/2009USF Physics 100 Lecture 218 As many forms as there are mathematical functions Forms of primary concern to us: Directly proportional Inversely proportional Proportional to the square Inversely proportional to the square

8/31/2009USF Physics 100 Lecture 219 A. Directly proportional Also called “linear” Form: y = mx + b x y Example: x = elapsed time y = distance traveled then m = velocity or speed b = initial distance or starting distance

8/31/2009USF Physics 100 Lecture 220 B. Directly Proportional to the Square Form: y = mx 2 Example: y = area of a square x = length of square’s edge m = 1 for this case

8/31/2009USF Physics 100 Lecture 221 C. Inversely Proportional Form: y = m/x y x Example: y = time to travel a distance x = velocity or speed m = 1 for this case

8/31/2009USF Physics 100 Lecture 222 D. Inversely Proportional to the Square Form: y = m/x 2 y x Example: y = gravitational attraction between m 1 and m 2. x = separation m = -Gm 1 m 2 m/x

8/31/2009USF Physics 100 Lecture 223 Polynomial Example: Motion in 1-D

8/31/2009USF Physics 100 Lecture 224 Calculus vs. Non-Calculus Notation x y Example: x = elapsed time y = distance traveled then m = velocity or speed b = initial distance or starting distance You do not need calculus for this course but sometimes I get sloppy with notation. For a linear function like the above

8/31/2009USF Physics 100 Lecture 225 is called the derivative of y w.r.t. x Now consider a non-linear function like y = x 2 There is a slope at each point of the curve but it is continually changing

8/31/2009USF Physics 100 Lecture 226 xx yy is the average slope over the range shown.

8/31/2009USF Physics 100 Lecture 227 Area under a curve f(x) x xx

8/31/2009USF Physics 100 Lecture 228 xixi is called the integral of f(x) from x = -5 to 5

8/31/2009USF Physics 100 Lecture 229 Measurement and Errors There is no such thing as an “exact” measurement. One must supply information about the reliability or exactness of a quoted measurement. Significant Figures: Inclusion of a particular number of digits => except possibly for the last one they are all known to be correct. e. g. page is 11 inches but probably not inches ”=> your measurement is good to about ” and probably not as bad as ”

8/31/2009USF Physics 100 Lecture 230 Another Way: Specifically call out limits of uncertainty. e. g. 4.0 ± 0.2 cm best estimate is 4.0 cm and true value is “likely” to be within 0.2 cm of this estimate Can also be written as 4.0 ± 5% cm or 4.0 cm ± 5%

8/31/2009USF Physics 100 Lecture 231 Statistical or Random Errors Fire a perfect shotgun at a target Sights aligned and you are a perfect shot. Result: symmetrical pattern of hits centered on target. Gaussian distribution of hits. Average is location of target. N r Repetition of experiment can reduce the effects of these types of errors.

8/31/2009USF Physics 100 Lecture 232. Systematic Errors Now knock shotgun’s sights out of line Result: Same sort of pattern as before but pattern as a whole is shifted systematically. N r Systematic errors can be corrected if they are understood. e. g. If shotgun shoots high and right, aim low and left.

8/31/2009USF Physics 100 Lecture 233 Mistakes Mistake in experimental procedure. e. g. Aim the shotgun at the wrong place

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8/31/2009USF Physics 100 Lecture 235 Total of 13 subjects divided into a 2 bin distribution. ½ (6.5) subjects’ BP lowered ½(6.5) subjects’ BP remained high. Poisson statistics: Error (random) in counting N events is Numbers should be quoted: 6.5 ± 2.5 Danger of small statistical universes

8/31/2009USF Physics 100 Lecture 236 Trigonometry Review  hypotenuse adjacent opposite Pythagorian Theorem: (hypotenuse) 2 = (opposite) 2 + (adjacent) 2 Trigonometric Functions:

8/31/2009USF Physics 100 Lecture 237 Vectors Scalars: Magnitude only e. g. mass, energy, temperature Vectors: Magnitude and direction e. g. force, momentum Graphically: Length represents magnitude Orientation represents direction 

8/31/2009USF Physics 100 Lecture 238 Graphical Addition of Vectors The parallelogram of forces

8/31/2009USF Physics 100 Lecture 239 Component Addition of Vectors x-axis y-axis AxAx AyAy AA A x = A cos  A A y = A sin  A Similarly, B x = B cos  B, etc.

8/31/2009USF Physics 100 Lecture 240 Add the components C x = A x + B x C y = A y + B y