Review and Graphical Analysis WHS Honors Physics Part 2

Essential Questions  What is Physics?  What is the “scientific method”?  What are the standard units of measure used in physics?  What is Data?  In measurement, what is the difference between accuracy and precision?  How does one perform calculations using scientific notation and significant figures?  What is the proper way to construct a graph from experimental data?  What is dimensional analysis and how is it used to verify the answer to an equation?

What is the purpose of any Experiment?  Ultimately, the purpose of any experiment is to determine the relation between two variables… the independent and dependent  We gather data to determine the relation Raw data is usually organized using a data table Raw data is usually organized using a data table How has the average human height varied over time? YearAv. height (m) Can you tell the relation by just looking at this data? Independent variable usually on the left Dependent variable usually on the right Always include units

Graphical Analysis  A graph is one of the most effective representations of the relationship between two variables. YearAv. height (m) Average Height compared to Year Y-Axis… Dependent Variable X-Axis… Independent Variable In Physics, Axis scales should start at zero

Graphing Guidelines Always 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 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 + (1924, 1.71) (1992, 1.82) + What will be the average height in feet and inches in 2050?

Basic Relations between Variables  “Linear” or “Direct” y=mx+b y=mx+b As x increases, y increases proportionally. As x increases, y increases proportionally. y is directly proportional to x y is directly proportional to x  “No Relation” y=constant y=constant Changes in x have no effect on y Changes in x have no effect on y

Basic Relations between Variables  “ y is proportional to the square of x ” y=mx 2 +b (y=Ax 2 +Bx+C on DataStudio) y=mx 2 +b (y=Ax 2 +Bx+C on DataStudio) b moves the graph up or down b moves the graph up or down  To find m and b, you must “linearize” the data Square the “x” data values, don’t change the y Square the “x” data values, don’t change the y Create a graph of x 2 and y… should be linear Create a graph of x 2 and y… should be linear Use point-slope formulas to find m and b Use point-slope formulas to find m and b

Example of “Square” Relation Time (s)Position (m) Time 2 (s)Position (m)

Basic Relations between Variables  “Inverse” As x increases, y decreases As x increases, y decreases “y is inversely proportional to x” “y is inversely proportional to x”  To find m and b: Invert the “x” data values, don’t change the y Invert the “x” data values, don’t change the y Create a graph of 1/x and y… should be linear Create a graph of 1/x and y… should be linear Use point-slope formulas to find m and b Use point-slope formulas to find m and b

Basic Relations between Variables  “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 right b moves the graph left or right  To find m and b: Square the“y” data values, don’t change the x Square the“y” data values, don’t change the x Create a graph of x and y 2 … should be linear Create a graph of x and y 2 … should be linear Use point-slope formulas to find m and b Use point-slope formulas to find m and b

Summary… 5 Basic Relations  No Relation…  y directly proportional to x y=mx+b y=mx+b  y proportional to the square of x Square x-values and replot Square x-values and replot y=mx 2 +b y=mx 2 +b  y squared proportional to x Square y-values and replot Square y-values and replot y 2 =mx+b y 2 =mx+b  y inversely proportional to x Invert the x-values and replot Invert the x-values and replot y x y x y x y x y x

Graphical Analysis  The world is complex… variable relations may be more complicated than the 5 basic You may need to linearize the data more than once You may need to linearize the data more than once Graphs may be shifted and or flipped Graphs may be shifted and or flipped Don’t confuse the “square root” relation with an upside down “square” relation Don’t confuse the “square root” relation with an upside down “square” relation On all graphs, consider what you think the dependent variable should likely be when the independent variable is zero… should your graph go through the origin? On all graphs, consider what you think the dependent variable should likely be when the independent variable is zero… should your graph go through the origin? Check units (or dimensions)… does your relation give the correct units for the final answer Check units (or dimensions)… does your relation give the correct units for the final answer

Essential Questions  What is Physics?  What is the “scientific method”?  What are the standard units of measure used in physics?  What is Data?  In measurement, what is the difference between accuracy and precision?  How does one perform calculations using scientific notation and significant figures?  What is the proper way to construct a graph from experimental data?  What is dimensional analysis and how is it used to verify the answer to an equation?

Questions?