Review and Graphical AnalysisReview and Graphical AnalysisWHS Honors Physics WHS Honors Physics

Part 2Part 2

Essential QuestionsEssential Questions

What is Physics?What is Physics? What is the “scientific method”?What is the “scientific method”? What are the standard units of measure used in physics?What are the standard units of measure used in physics? What is Data?What is Data? In measurement, what is the difference between accuracy In measurement, what is the difference between accuracy

and precision?and precision? How does one perform calculations using scientific notation How does one perform calculations using scientific notation

and significant figures?and significant figures? What is the proper way to construct a graph from What is the proper way to construct a graph from

experimental data?experimental data? What is dimensional analysis and how is it used to verify the What is dimensional analysis and how is it used to verify the

answer to an equation?answer to an equation?

What is the purpose of any Experiment?What is the purpose of any Experiment?

Ultimately, the purpose of any experiment is to Ultimately, the purpose of any experiment is to determine the relation between two determine the relation between two variablesvariables… the … the independentindependent and and dependentdependent

We gather We gather data data to determine the relationto determine the relation Raw data is usually organized using a data tableRaw data is usually organized using a data table

How has the average human height varied over time?How has the average human height varied over time? Year Av. height (m)

1920 1.71

1960 1.76

1980 1.80

1995 1.83

Can you tell the relation by just looking at this data?

Can you tell the relation by just looking at this data?

http://www.maths.mq.edu.au/numeracy/tutorial/graph.htm

Independent variable usually on the left

Dependent variable usually on the right

Always include units

Graphical AnalysisGraphical Analysis

A graph is one of the most effective representations A graph is one of the most effective representations of the relationship between two variables.of the relationship between two variables.

Year Av. height (m)

1920 1.71

1960 1.76

1980 1.80

1995 1.83

Average Height compared to Year

Y-Axis… Dependent Variable

X-Axis… Independent Variable

In Physics, Axis In Physics, Axis scales should start scales should start at zeroat zero

Graphing GuidelinesGraphing GuidelinesAlways give your graph a title.

Always label the x and y axes and give units.

Scales should start at (0,0).

Scale increments must be consistent (2, 4, 6 not 1, 5, 12)

Use symbols to identify data points ( , , , + )

Use a “Best Fit” line or curve… Never connect the dots! Omit obvious “outliers”

Determining the RelationDetermining the Relation

Average Height compared to Year• “Linear” or “Direct” relation

• y=mx + b

•To find “m” and “b” pick two points on the “best fit” line

• use “point-slope” formulas

•After taking Honors Algebra, you should be expert at this… but, not all relations are linear

)( 11

12

12

xxmyy

xx

yym

+ (1924, 1.71)

(1992, 1.82) +

4.1)(0016.)(

1.30016.71.1

)1924(0016.71.1

0016.068

11.0

19241992

71.182.1

yearmheight

yearheight

yearheight

year

meters

years

metersm

What will be the average height in feet and inches in 2050?

Basic Relations between VariablesBasic Relations between Variables

““Linear” or “Direct”Linear” or “Direct” y=mx+by=mx+b As x increases, y increases proportionally.As x increases, y increases proportionally. y is directly proportional to xy is directly proportional to x

““No Relation”No Relation” y=constanty=constant Changes in x have no effect on yChanges in x have no effect on y

y

x

y

x

y

x

y

x

Basic Relations between VariablesBasic Relations between Variables

““y is proportional to the square of xy is proportional to the square of x” ” y=mxy=mx22+b +b (y=Ax(y=Ax22+Bx+C on DataStudio)+Bx+C on DataStudio)

b moves the graph up or downb moves the graph up or down

To find m and b, you must “linearize” the To find m and b, you must “linearize” the datadata

Square the “x” data values, don’t change the ySquare the “x” data values, don’t change the y Create a graph of xCreate a graph of x22 and y… should be linear and y… should be linear Use point-slope formulas to find m and b Use point-slope formulas to find m and b

y

x

y

x

Example of “Square” Relation Example of “Square” Relation

Time (s) Position (m)

0 4

0.5 3.6

1.0 1.9

1.5 -0.5

2.0 -4.0

Time2 (s) Position (m)

0 4

.25 3.6

1.0 1.9

2.25 -0.5

4.0 -4.0

0.40.2

4.0m(time(s))s

m2.0(m)Position

2

22

tp

Basic Relations between VariablesBasic Relations between Variables

““Inverse” Inverse” As x increases, y decreasesAs x increases, y decreases ““y is inversely proportional to x”y is inversely proportional to x”

To find m and b:To find m and b: Invert the “x” data values, don’t change the yInvert the “x” data values, don’t change the y Create a graph of 1/x and y… should be Create a graph of 1/x and y… should be

linearlinear Use point-slope formulas to find m and b Use point-slope formulas to find m and b

y

x

y

x bx

1my

Basic Relations between VariablesBasic Relations between Variables

““Square of y is proportional to x”Square of y is proportional to x” “ “y is proportional to the square root of x”y is proportional to the square root of x” b moves the graph left or rightb moves the graph left or right

To find m and b:To find m and b: Square the“y” data values, don’t change the xSquare the“y” data values, don’t change the x Create a graph of x and yCreate a graph of x and y22… should be linear… should be linear Use point-slope formulas to find m and b Use point-slope formulas to find m and b

bmxy2

y

x

y

x

Summary… 5 Basic RelationsSummary… 5 Basic Relations

No Relation…No Relation… y directly proportional to xy directly proportional to x

y=mx+by=mx+b y proportional to the square of xy proportional to the square of x

Square x-values and replotSquare x-values and replot y=mxy=mx22+b+b

y squared proportional to xy squared proportional to x Square y-values and replotSquare y-values and replot yy22=mx+b=mx+b

y inversely proportional to xy inversely proportional to x Invert the x-values and replotInvert the x-values and replot

y

x

y

x

y

x

y

x

y

x

bx

1my

Graphical AnalysisGraphical Analysis

The world is complex… variable relations may be The world is complex… variable relations may be more complicated than the 5 basicmore complicated than the 5 basic You may need to linearize the data more than onceYou may need to linearize the data more than once Graphs may be shifted and or flippedGraphs may be shifted and or flipped Don’t confuse the “square root” relation with an upside Don’t confuse the “square root” relation with an upside

down “square” relationdown “square” relation On all graphs, consider what you think the dependent On all graphs, consider what you think the dependent

variable should likely be when the independent variable should likely be when the independent variable is zero… should your graph go through the variable is zero… should your graph go through the origin?origin?

Check units (or dimensions)… does your relation give Check units (or dimensions)… does your relation give the correct units for the final answerthe correct units for the final answer

Essential QuestionsEssential Questions

What is Physics?What is Physics? What is the “scientific method”?What is the “scientific method”? What are the standard units of measure used in physics?What are the standard units of measure used in physics? What is Data?What is Data? In measurement, what is the difference between accuracy In measurement, what is the difference between accuracy

and precision?and precision? How does one perform calculations using scientific notation How does one perform calculations using scientific notation

and significant figures?and significant figures? What is the proper way to construct a graph from What is the proper way to construct a graph from

experimental data?experimental data? What is dimensional analysis and how is it used to verify the What is dimensional analysis and how is it used to verify the

answer to an equation?answer to an equation?

Questions?Questions?