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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)

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Experiment

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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.

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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

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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

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Classification of Physical Quantities in Experiment

Measure Quantities VS Derived Quantities

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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.

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Example: Determination of Gravitational Constant gExperiment: Gravitational Constant g = ?

tMeasure t with timer

2

22

2),(

2

1),,0(

2

1),,(

t

stsg

gttgVsgttVtgVs ooo

Derive g from

• kinematic relation, and

• numerical values of (s,t)

Measure s with measuring tape

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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. *

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Definition of An Experiment via A Functional Form

);;(parametersconstant parameters VariablevariablestIndependenvariablesDependent

cpxfy

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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.

);;(parametersconstant parameters VariablevariablestIndependenvariablesDependent

cpxfy

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Example

Experiment:

Determination of displacement s Dependent variable

as a function of time t Independent variable

at various Vo’s Variable parameter

and constant g Constant parameter

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2

1);;(

2

1),,( gttVgVtsgttVtgVs oooo

t sg

Vo

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);;(

);;(parametersconstantparametersvariablevariablestindependenvariablesdependent

gVtfs

cpxfy

o

Dependent variables

0

500

1000

1500

2000

2500

0 2 4 6 8 10

t (s)

s (m

) s (v=0)

s (v=2)

Line – Theoretical Relations

Point markers – Experimental data points

Line – Curve-fit to experimental data points

Vo1 = 0 m/s

g

s (m)

t (s)

Independent variables

Variable parametersVo2 = 2 m/s

Constant parameters

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Definition of An Experiment Via A Functional Form

);;(

);;(parametersconstantparametersvariablevariablestindependenvariablesdependent

gVtfs

cpxfy

o

Vo1

g

s (m)

t (s)Independent variables

Variable parameters

Vo2

Constant parameters

Dependent variables

Graphical presentation of results

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Definition of Experiment and Functional Form

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Experiment 1 VS Experiment 2

p1

R

(k/m3)

T (K)

p2

Experiment 2: );;( GasRTpf

Experiment 1: );;( GasRpTf

VS

T1

R

(k/m3)

p (pa)

T2

Are they the same?

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Three-Column Table of Objectives

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Three-Column Table of Objectives

Statement Functional Form Graphical Presentation of

Results

To investigate how x

depends on t for ….);;( mktfx

m

x

k

t

);;( kmtfx

??

?

?

??

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Experiment and Data Reduction Diagram (DRD)

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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:

);;( cpxfy

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Key Idea of DRD

3. Data Reduction Diagram (DRD):

Construct a data reduction diagram (DRD) for each of the final variables:

DRD-y DRD-x DRD-p DRD-c

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Example of DRD

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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.

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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.

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Experiment and Data Reduction Diagram (DRD)

DRD-y DRD-x DRD-p DRD-c

);;( cpxfy

There must be DRD for all physical quantities in the definition of an experiment.

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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)

),;;( gVpsfV o

V

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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)

),;;( gVpsfV o

V

s (m)

V Vo,g(m/s)

(s, )V

2)(

gssV Theory: is determined from s:V

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

),( VsV

DRD-y DRD-x DRD-p DRD-c

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Example: DRD-y DRD- V

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DRD: Box for Derived Quantities

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DRD: Box for Measured Quantities

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DRD-y: DRD-V

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Example

Experiment: Performance of a fan

),;;( atmatm TpNQfp

DRD-p

DRD-Q

DRD-N

DRD-patm

DRD-Tatm

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DRD-y: DRD-p

Measuring instruments

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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

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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).

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