Graphing with Computers Pressure and Density. What is Pressure? Pressure = Force = lbs area in 2 Let me propose the following experiment.

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Presentation transcript:

Graphing with Computers Pressure and Density

What is Pressure? Pressure = Force = lbs area in 2 Let me propose the following experiment

Pressure Experiment A series of 1 lbs, 1 in 2 disks are placed on a scale What would the data Look like?

Data From Experiment Total Pounds Total Inches squared

This is a direct proportion. The pounds varies directly as the in 2 We can use a “best fit” line to describe the relationship

Best Fit Line I use excel to determine the equation for the line. y = 1.0 x What units does y represent?x?So the equation really is lbs = in 2 R 2 = correlation coefficient This tells us how well the Line is described. Perfect correlation = 1

Best Fit Line The line describes the ratio or proportion The ratio is the slope or pounds / in 2 In the is example it is equal to 1 –This means for every pound added, one in 2 is added R 2 = 1 tells us there is perfect correlation in our data Our accuracy and precision are perfect Our data was unrealistic Let’s throw in some error and see what happens

Data From Experiment Total Pounds Total Inches squared

Notice the data is not in perfect line. We can draw in a best fit line, but it is more accurate to let the computer do it

Notice the slope is not perfectly 1 any more! R 2, our correlation coefficient is close to one. Good enough! The equation of y = mx +b turns into pounds =.9956 in 2 + 0

Let’s Review Plot the data. Determine the type of proportion (direct) Draw a best fit line Determine the slope of the line The slope is the relationship –It describes the proportion or ratio of the two variables

Density What are the units of density? g/mL Given an unknown material –We can measure the grams –We can measure the mL by displacement –We can determine the density by using a graph!

Graphing with Computers Plot the data Determine the type of proportion –linear or direct Draw a best fit line –Also called doing a linear regression Determine the slope of the line

What are the units of the slope? g/ml What are the units of density? g/ml

Let’s Switch to Excel Use excel to graph and draw best line Linear regressions are really easy !