2. 1 1 st Pre-Lab Quiz 2 nd Pre-Lab Quiz 3 rd Pre-Lab Quiz 4 th Pre-Lab Quiz

3. 2 Physics 2BL Instructor: Prof. Avi Yagil E-Mail: 2BL@physics.ucsd.edu Course web site: http://2bl.ucsd.edu/ My research is in Experimental High Energy Physics

4. 3 Research Area: Experimental High Energy Physics The Large Hadron Collider The CMS DetectorThe Tunnel CMS lowered to the cavern CMS tracker installed

5. 4 PHYSICS 2BL - LABORATORY METHODS OF PHYSICS Instructor:Professor Avi Yagil 5512 Mayer Hall Extension TAs Coordinator: Damien delToro Web Page: http://2bl.ucsd.edu/ Office Hour: Monday 11:00-12:00 or catch me after class. Lecture: Monday 15:00-15:50 Final exam: Monday, Nov 30, 15:00-16:50, York 2622. >>> 10th week of classes <<< Text: J. R. Taylor, An Introduction to Error Analysis.

6. 5 Course Logistics Please use course web site: 2BL.UCSD.edu All announcements will be made there –All course materials posted there: Lecture notes Experiments Guidelines (including all quiz questions) HW solutions Note Schedule! (do not miss the final exam - no excuses!!) In next few slides details on: –Text book –Grading and Grading Policy –Lab reports and your lab notebooks –Importance of homework exercises ==>If you have any special needs/issues, please come see me!

7. 6 Textbook “Introduction to Error Analysis”, by Taylor. No experimental information but good intro on how to handle data once your experiment produces some… Source of your homework problems (similar to final) Many helpful examples! Important Physics background: Fundamentals of Physics Halliday, Resnick & Walker 7 th Ed.

8. 7 Grading Pre-Lab Quizzes20% Lab #1 10% Lab #2 10% Lab #3 10% Lab #4 10% Final exam 40% 100% Lab Grade, Details: pre-lab quiz - 5% written lab report: description of the experiment, presentation of the data, error analysis, discussion and conclusions - 10% Preparation is key for labs! Quizzes made of questions contained in the experiment guidelines - posted on course web site. ==> You will know the questions in advance! They are meant to prepare you for the labs. Total quiz score - 20% of total grade - don’t miss it.

9. 8 Each Lab contributes 15% to the final grade. Pre-Lab Quiz 5% Final Report 10% (structure and guidelines)10% Introduction 2 What quantities are to be measured? What is the necessary precision? What is the essential physics? Methodology 4 Apparatus (sketches are useful) Key Equations (derive or give source) Error analysis (derive for all expressions) Data and experimental details 4 Analysis of the data and experimental conclusions Discussion: Dominant sources of error Discrepancies with published results Possible improvements Final report See course web site for detailed Lab notebook guidelines! Buy 2 quad-rule notebooks (The cheapest kind) See Experiment-Specific Grading Rubric !!

10. 9 Homework Exercises Practice problems listed under the link: “Lectures & Assignments Schedule” on course Web page. –Self Graded: Solutions posted to Web Page –All problems are from the text book –They will help you understand and practice the new concepts The problems in the final exam will be similar to the problems from your homework and will test your understanding of the error analysis. Solving them on your own will prepare you for the Final!

11. 10 Grading Policy Absolute Grading scale: >95 A+ >85% A >70%B >50%C >40% D <40 F To remove possible section-dependent biases: Will look at correlation between: - Lab/Quiz grades - Final performance Across sections.

12. 11 How to do well in the course? Show up to all lectures and labs Read before the lectures the recommended reading Before each lab: –Review lecture slides –Read experiment guidelines –Answer all quiz questions within. Do the homework/practice problems Prepare for final –Come to review session Ask questions!

13. 12 Academic Integrity Please read the section on UCSD Policy on Integrity of Scholarship in: http://www.ucsd.edu/catalog/front/AcadRegu.html Cite everything that isn’t your original thought. Acknowledge your partner’s contributions and do not plagiarize their work. But do discuss the problems and experiments with other students. Collaboration is important. –You work on the experiments in teams, but the lab report has to be written by you! –For details, please see http://2bl.ucsd.edu/courseoverview.phphttp://2bl.ucsd.edu/courseoverview.php If in doubt, ask us! End of Logistical Intro…

14. 13 Today’s Lecture: Logistics –Schedule –Text book, lab notebooks, calculator… –HW, Quizzes, Final exam Course general introduction, overview How do we report a measurement result? –Significant Figures Introduction to Error Propagation

15. 14 Course Structure at a Glance 4 Experiments Two weeks of Labs for each One lecture before each experiment (during first Lab week). Describe: What is the goal of the experiment? What do we measure? What do we deduce/compute? Experimental issues Second lecture between two Lab Sections. Discuss: Issues arising with current experiment Focus on interpretation of the data –Error propagation –Introduction to Statistical analysis A different kind of lab course: –Main Goal: Introduction to data analysis, interpretation of data Learn how to deal with data Uncertainties associated with data from any Physical source –Experiments: Intended to introduce you to Physical measurement issues –No ideology: Basic, everyday knowledge crucial for Scientists and Engineers

16. 15 The Four Experiments Determine the average density of the earth Weigh the Earth, Measure its volume –Measure simple things like lengths and times –Learn to estimate and propagate errors Non-Destructive measurements of densities, inner structure of objects –Absolute measurements Vs. Measurements of variability –Measure moments of inertia –Use repeated measurements to reduce random errors Construct and tune a shock absorber –Adjust performance of a mechanical system –Demonstrate critical damping of your shock absorber –Test a theoretical model, experimentally. Measure coulomb force and calibrate a voltmeter. –Reduce systematic errors in a precise measurement. Excellent write-ups. Use them!

17. 16 The correct way to state the result of measurement is to give a best estimate of the quantity and the range within which you are confident the quantity lies: Best Estimate ± Uncertainty or Writing: L = 1.7 ± 0.2 cm Means that: - your best estimate for the length is 1.7 cm and - you estimate its range to be from 1.5 to 1.9 cm (measured value of x ) = Stating Result of a Measurement Significant Figures

18. 17 Rule #1 for stating uncertainties: experimental uncertainties should almost always be rounded to one significant figure. (measured g ) = 9.85 ± 0.09328 m/s 2 - WRONG (measured g ) = 9.85 ± 0.09 m/s 2 - CORRECT Rule #2 for stating uncertainties: the last significant figure in any stated answer should be of the same order of magnitude (in the same decimal position) as the uncertainty. L = 1.668 ± 0.3 cm - WRONGL = 1.7 ± 0.3 cm - CORRECT What should we do with this one? (measured g ) = 9.85387 ± 0.11328 m/s 2 - 9.9 ± 0.1 m/s 2 ? If the 1 st significant figure in the uncertainty is 1 it is a good idea to keep two figures,  g = 0.11 and (measured g ) = 9.85 ± 0.11 m/s 2 Example:

19. 18 Examples Someone tells you that a block of ice has a mass of: 5.28352 +/- 0.6257345 kg How would you report its weight? W = mg g = 10 m/sec 2  m ~ 0.6 kg --> m ~ 5.3 kg W = 53 +/- 6 Newtons

20. 19 Accuracy and Precision Accuracy: Close to target Precision: Close to each other Distance from true value - Accuracy Spread between trials - Precision (reproducibility, repeatability…) (statistical) (systematic)

21. 20 Errors Uncertainties (not mistakes!) inevitable and intrinsic part of any experiment Errors and Uncertainties How do we estimate uncertainties??

22. 21 10 -3 m 10 -4 m 10 -5 m Sometime its easy…

23. 22 x best x best -  x x best +  x 024681012141618202224 Measurements & Errors Measurements & Uncertainties x Statistically - Take a few measurements of some variable x 1. Find the most likely value - “best” 2. Estimate the spread - uncertainty We will learn how to do this estimate

24. 23 Error Propagation - A glimpse ahead As part of the first experiment, you’ll need to determine the acceleration of gravity, g. You’ll do it using a simple pendulum, measuring its: -Length l : -Period T : And determine g by solving: what is the resulting uncertainty on g,  g ?? how do we estimate  T,  l ?? Error propagaion…

25. 24 x best x best -  xx best +  x q best = q(x best ) q(x best –  x) q(x best +  x) Error Propagation - An intuitive view We measured some quantity: q is an arbitrary function of x:

26. 25 General Formula for error propagation For independent, random errors

27. 26 A Quick Review of Partial Differentiation First, consider “differentiation.” For a real ‐ valued function of a single real variable, the derivative at a point equals the slope of the tangent line to the graph of the function at that point. Differentiation is a method to compute the rate at which a quantity, y, changes with respect to the change in another quantity, x, upon which it is dependent. This rate of change is called the derivative of y with respect to x. A partial derivative of a function of several variables is its derivative with respect to one of those variables with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Slide stolen from Mike Riley

28. 27 Partial Differentiation: Example Consider the volume V of a cone; it depends on the cone's height h and its radius r according to the formula: The partial derivative of V with respect to r is: –It describes the rate with which a cone's volume changes if its radius is varied and its height is kept constant. The partial derivative with respect to h is: –It represents the rate with which the volume changes if its height is varied and its radius is kept constant. Slide stolen from Mike Riley

29. 28 Special Cases & Examples These are meant to illustrate the general rule. They all are private cases of it. Whenever in doubt use the general rule!!

30. 29 Error Propagation - Sum What is the perimeter of this figure? y w z x p = w + x + y + z 1. Estimate errors from x, y, z, w. - They all are likely to be on the order of precision of the ruler, 1/32” or ~0.75 mm. 2. Propagate these to compute the error on p. How would you calculate the error on p? You measure x, y, z, w and compute p.

31. 30 Error Propagation - Sum (cont) y w z x p = w + x + y + z We estimated the errors on x, y, z, and w as: What is our estimate of error on p? Since But, since  x,  y,  z and  w are all error estimates ==> we do not know their signs! Therefore, we could do: Worst case, if all have same sign! We would normally use the rule of addition in quadrature: Independent, random errors. Consider:

32. 31 Another Example of Error Propagation - Product Take x, y and q as x best, y best, q best Measure (x+  x) and (y+  y) Compute (q+  q) Subtract q from both sides of the above equation. (Notice partial derivatives) (neglect  x  y) q

33. 32 Another Example of Error Propagation - Product Here again, we don’t know the signs. Sometimes these contributions will cancel, sometimes add up. We can compute errors two ways: 1) Maximum possible error 2) If the uncertainties  x,  y are independent & random:

34. 33 Fractional Errors For products like q=xy, we can add the fractional errors on the measurements (  x/x) to get the fractional error on the result (  q/q) : Simple Derivation This also works for ratios like.

35. 34 Example

36. 35 Quick Summary Uncertainties in Sums and Differences: Uncertainties in Products and Ratios: General Rule: For independent random errors

37. 36 h l  ==> Find h. always use radians when calculating the errors on trig functions Given that: Example

38. 37 Next Week Our first experiment: Determine the average density of the earth Weigh the Earth, Measure its volume –Measure simple things like lengths and times –Estimate and propagate errors Next week’s lecture will cover the details before your Lab sessions. Please: –Read the material: Experiment #1 Guidelines Grading Rubric for Experiment #1 Both on course web page –Refresh your memories of the physics –Work out HW assignment #1. No labs this week Prepare for Quiz next week! TA’s and you are on same page!

39. 38 Some more examples…

40. 39 1. 1) (measured height ) = 2) (measured time ) = 3) (charge ) = 4) (wavelength ) =

41. 40 2. 5) (momentum ) =

42. 41 Fractional Uncertainties 3.

43. 42 4. Find the fractional error on Our basic formula. Shorthand notation for addition in quadrature