1. 1 2103-390 Mechanical Engineering Experimentation and Laboratory I  Experiment  Definition of Experiment and Functional Form  Three-Column Table of Objectives  Classification of Physical Quantities in Experiment  Measured Quantities  Derived Quantities  Data Reduction Diagram (DRD)

2. 2 Experiment

3. 3 Goals and Roles of Experiment Goal:Extract knowledge and useful information regarding the system of interest with reasonable justification.  new knowledge,  used in product design and development,  qualify a product according to some standard,  falsify/verify a theory, call for a new theory,  hint toward the structure or mathematical form of a theory,  etc. Activity: Class Discussion Give examples and discussions of uses of experiment in these various roles.

4. 4 5C: Some Qualifiers in Experimentation Observation - Ask the Right Question / Critical Thinking / Creativity 5C = Clear, Convincing, Coherent, Concise, and Consistent 1) Clear Problem Statement / Question 2.2) Convincing Supporting Evidences / Experimental Results 2.1) Convincing Justification Method 2) Convincing Justification 3) Clear, Convincing/Justified, and Coherent Conclusions

5. 5 Report: Conclusions What are conclusions? Conclusions are convictions based on evidence. From The American Institute of Physics: AIP Style Manual, Fourth Edition: http://www.aip.org/pubservs/style/4thed/toc.html

6. 6 Classification of Physical Quantities in Experiment Measure Quantities VS Derived Quantities

7. 7 How can we find the gravitational constant g? Experiment: Gravitational Constant g = ? Activity: Class Discussion Give examples and discussions of uses of experiment in these various roles.

8. 8 Example:Determination of Gravitational Constant g Experiment: Gravitational Constant g = ? t Measure t with timer Derive g from kinematic relation, and numerical values of (s,t) Measure s with measuring tape

9. 9 Classification of Physical Quantities in Experiment  Measured Quantities: Numerical values from measurement with measuring instruments  Derived Quantities: Numerical values from relations (definition, theoretical relation, etc.)  Basically in sciences/engineering, the numerical value of a physical quantity is either  measured with a measuring instrument, or  derived through a physical relation. * We do not want anybody to make up any number if it is meant to be useful physically. *

10. 10 Definition of An Experiment via A Functional Form

11. 11 Theoretical Approach and Relation VS Experimental/Empirical Approach and Relation Determination of the dependency of y on x under the condition ( p, c )  Theoretical Approach =The determination of the dependency of on under the condition is via theoretical derivation.  Experimental/Empirical Approach =The determination of the dependency of on under the condition is via (experiment with: observation and measurement on) the physical system itself.

12. 12 Example  Experiment: Determination of displacement s  Dependent variable as a function of time t  Independent variable at various V o ’s  Variable parameter and constant g  Constant parameter t s g VoVo

13. 13 Dependent variables Line – Theoretical Relations Point markers – Experimental data points Line – Curve-fit to experimental data points V o1 = 0 m/s g s (m) t (s) Independent variables Variable parameters V o2 = 2 m/s Constant parameters

14. 14 Definition of An Experiment Via A Functional Form V o1 g s (m) t (s) Independent variables Variable parameters V o2 Constant parameters Dependent variables Graphical presentation of results

15. 15 Definition of Experiment and Functional Form

16. 16 Experiment 1 VS Experiment 2 p1p1 R  (k/m 3 ) T (K) p2p2  Experiment 2:  Experiment 1: VS T1T1 R  (k/m 3 ) p (pa) T2T2 Are they the same?

17. 17 Three-Column Table of Objectives

18. 18 Three-Column Table of Objectives StatementFunctional Form Graphical Presentation of Results To investigate how x depends on t for …. m x k t ? ? ? ? ? ?

19. 19 Experiment and Data Reduction Diagram (DRD)

20. 20 Key Idea of DRD

21. 21 Key Idea of DRD KEY IDEA in Constructing a Set of DRDs for an Experiment 1.Question/Relation: Set the goal that we want to answer the question ‘whether and how.’ 2. Graphical representation of results: We then know that the graphical representation of the relation should look like below:

22. 22 Key Idea of DRD 3. Data Reduction Diagram (DRD): Construct a data reduction diagram (DRD) for each of the final variables: DRD-y DRD-xDRD-pDRD-c

23. 23 Example of DRD

24. 24

25. 25 DRD: Key Idea Know and specify clearly and specifically the sources of the numerical value in the unit of a physical quantity - both at the source and derived levels - that source-level: either enters our experiment at the source level, derived-level: or is derived through a relation in our intermediate data analysis step.

26. 26 DRD: Key Idea The reason is that if we suspect that something is wrong with our final (numerical) result:, we can trace back each and every data analysis step, step- by-step, from the end result to the sources. Note that a step here refers to a step of numerical transformation. For example, a unit conversion – though may be simple enough – is also considered a step since there is a transformation of numerical value, from one value to another.

27. 27 Experiment and Data Reduction Diagram (DRD) DRD-y DRD-xDRD-pDRD-c There must be DRD for all physical quantities in the definition of an experiment.

28. 28 Experiment:Determine average velocity as a function of distance s for various bodies (p) at constant Vo and g. [ Theory: ] Experiment and Data Reduction Diagram (DRD)

29. 29 Experiment:Determine average velocity as a function of distance s for various bodies (p) at constant Vo and g. Experiment and Data Reduction Diagram (DRD) s (m) V o,g (m/s) (s, ) Theory: is determined from s: Experiment: We must determine the numerical values of and s independently  coordinates We also need to determine p  ball, feather We also need to determine c  Vo, g DRD-y DRD-xDRD-pDRD-c

30. 30 Example:DRD-y  DRD-

31. 31 DRD: Box for Derived Quantities

32. 32 DRD: Box for Measured Quantities

33. 33 DRD-y:DRD-

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35. 35 Example Experiment:Performance of a fan DRD-  p DRD-Q DRD-N DRD-p atm DRD-T atm

36. 36 DRD-y:DRD-  p  Measuring instruments

37. 37 What can we derived from DRD? 1.List of all variables in our experiments 1.Measured quantities 2.Derived quantities 3.Referenced quantities 2.List of all relations in our experiments 3.List of all required instruments 4.Data collection worksheet (DCW) 5.Data analysis work sheet (DAW) 6.Uncertainty analysis

38. 38 What can DRD help?  To get an overview of an experiment  To identify weak points (e.g., validity of the reference sources, data analysis steps)  To diagnose the experiment (e.g., when something’s wrong).

39. 39