Experiment: Modern Galileo ExperimentName: Trevor GustafsonLab Partners: Christian Sutherland, Chris JonesConducted on: Monday January the 14 starting at approximately 12:20 and ending at approximately 1:45
Intro
The purpose of this lab experiment was to determine the effect of gravity on a cart’s acceleration in three different scenarios: level, uphill, downhill. I predicted going into this experiment that on a level plain, the cart’s speed after a slight push would stay nearly constant with only a slight slowing. It was also predicted that a cart’s speed would dramatically increase when placed on a downhill slope. Finally it was predicted that a carts speed would dramatically decrease after being pushed up an uphill slope.
Preliminary questionsQuestion #1 - List some observations that led people of Galileo’s time to believe that heavier objects fall faster than lighter objects · Something like a feather floats around in the wind, and takes longer to fall than something like a rock which falls nearly straight down.Question #2 – Drop a textbook and crumpled piece of paper from the same height at the same time. Do this 3 times. Did the textbook hit first, last, or at the same time consistently? · Basically at the same time a): Why did this happen? The book is denser and thus wants to drop faster, but it also has more
air to overcomeQuestion #3 – Try this with a flat sheet of paper and the crumpled piece of paper. Do this 3 times. Did one hit first or last, or did they hit at the same time consistently. · The crumpled piece of paper hit sooner. a): Why did this happen? Because the air resistance caused the light piece of paper to slowly drift down to earth, but the crumpled piece of paper did not have as much air to overcome.
AnalysisQuestion #1 - Did each of your experimental graphs resemble their predicted graph? Was your hypothesis correct in each case? If not, why? What could the reason be? · The graphs were basically as predicted · Yes it was
Question #2 - Calculate the change in time between each of the points in your data table above. Enter these values in the right column of the data table. Do this for each experiment.
· See data Table 1 “Data collected from pushing a cart on a level surface” · See data Table 2 “Data collected from releasing a cart on a down hill slope” · See data Table 3 “Data collected from pushing a cart uphill”Question #3 – Calculate the change in position between each of the points in your data table above. Enter these values in the right column of the data table. Do this for each experiment. · See data Table 1 “Data collected from pushing a cart on a level surface” · See data Table 2 “Data collected from releasing a cart on a down hill slope” · See data Table 3 “Data collected from pushing a cart uphill”Question #4 – Calculate the average speed for each portion of the trip. Do this for each experiment. · See data Table 1 “Data collected from pushing a cart on a level surface” · See data Table 2 “Data collected from releasing a cart on a down hill slope” · See data Table 3 “Data collected from pushing a cart uphill”Question #5 – Plot the data of speed versus time. Do this and answer the questions below for each experiment · See graph – “CTC’s Straight Data Graph” · See graph – “CTC’s Downhill Data Graph” · See graph – “CTC’s Uphill Data Graph” a): Is there a general trend pattern in the data? If so, describe it · For the straight graph the data goes down left to right
· For the downhill graph the data goes up left to right
· For the uphill graph the data goes down left to right
b): Describe what is happening to the speed during the experiment. · During the straight experiment, the cart slowly slowed down. · During the downhill experiment, the cart steadily speed up · During the uphill experiment, the cart steadily slowed down
Conclusion
· A cart’s speed will decrees only slightly when pushed along a very smooth, level surface
· A cart’s speed will increase when released down a downhill slope
· After being given a push, a cart’s speed will decrees on an uphill slope
Tuesday, January 22, 2008
Tuesday, January 15, 2008
Modern Galileo Experiment
Experiment: Modern Galileo Experiment
Name: Trevor Gustafson
Partners: Christian Sutherland, Chris Jones
Conducted on: Monday January the 14 starting at approximately 12:20 and ending at approximately 1:45
Preliminary questions
Question #1 - List some observations that led people of Galileo’s time to believe that heavier objects fall faster than lighter objects
· Something like a feather floats around in the wind, and takes longer to fall than something like a rock which falls straight down.
Question #2 – Drop a textbook and crumpled piece of paper from the same height at the same time. Do this 3 times. Did the textbook hit first, last, or at the same time consistently?
· Basically at the same time
a): Why did this happen?
The book is denser and thus wants to drop faster, but it also has more inertia to overcome
Question #3 – Try this with a flat sheet of paper and the crumpled piece of paper. Do this 3 times. Did one hit first or last, or did they hit at the same time consistently.
· The crumpled piece of paper hit sooner.
a): Why did this happen?
Because the air/ inertia resistance caused the light piece of paper to take slowly drift down to earth
Analysis
Question #1 - Did each of your experimental graphs resemble their predicted graph? Was your hypothesis correct in each case? If not, why? What could the reason be?
· The graphs were basically how I had predicted?
· Yes it was
Question #2 - Calculate the change in time between each of the points in your data table above. Enter these values in the right column of the data table. Do this for each experiment.
· See data Table 1 “Data collected from pushing a cart on a level surface”
· See data Table 2 “Data collected from releasing a cart on a down hill slope”
· See data Table 3 “Data collected from pushing a cart uphill”
Question #3 – Calculate the change in position between each of the points in your data table above. Enter these values in the right column of the data table. Do this for each experiment.
· See data Table 1 “Data collected from pushing a cart on a level surface”
· See data Table 2 “Data collected from releasing a cart on a down hill slope”
· See data Table 3 “Data collected from pushing a cart uphill”
Question #4 – Calculate the average speed for each portion of the trip. Do this for each experiment.
· See data Table 1 “Data collected from pushing a cart on a level surface”
· See data Table 2 “Data collected from releasing a cart on a down hill slope”
· See data Table 3 “Data collected from pushing a cart uphill”
Question #5 – Plot the data of speed versus time. Do this and answer the questions below for each experiment
· See graph – “CTC’s Straight Data Graph
· See graph – “CTC’s Downhill Data Graph
· See graph – CTC’s Uphill Data Graph
a): Is there a general trend pattern in the data? If so, describe it
*
b): Describe what is happening to the speed during the experiment.
· During the level experiment, the cart slowly slowed down.
· During the downhill experiment, the cart steadily speed up
· During the uphill experiment, the cart steadily slowed down
Question for Chris-
Do we need to right a formal hypothesis or is our predicted graph our hypothesis? Where would we write a hypothesis?
In Questions 2-3 we’re just supposed to reference the table right?
Question 4 is only concerning each portion and not the average of the whole trip, right?
We should number our graphs
Name: Trevor Gustafson
Partners: Christian Sutherland, Chris Jones
Conducted on: Monday January the 14 starting at approximately 12:20 and ending at approximately 1:45
Preliminary questions
Question #1 - List some observations that led people of Galileo’s time to believe that heavier objects fall faster than lighter objects
· Something like a feather floats around in the wind, and takes longer to fall than something like a rock which falls straight down.
Question #2 – Drop a textbook and crumpled piece of paper from the same height at the same time. Do this 3 times. Did the textbook hit first, last, or at the same time consistently?
· Basically at the same time
a): Why did this happen?
The book is denser and thus wants to drop faster, but it also has more inertia to overcome
Question #3 – Try this with a flat sheet of paper and the crumpled piece of paper. Do this 3 times. Did one hit first or last, or did they hit at the same time consistently.
· The crumpled piece of paper hit sooner.
a): Why did this happen?
Because the air/ inertia resistance caused the light piece of paper to take slowly drift down to earth
Analysis
Question #1 - Did each of your experimental graphs resemble their predicted graph? Was your hypothesis correct in each case? If not, why? What could the reason be?
· The graphs were basically how I had predicted?
· Yes it was
Question #2 - Calculate the change in time between each of the points in your data table above. Enter these values in the right column of the data table. Do this for each experiment.
· See data Table 1 “Data collected from pushing a cart on a level surface”
· See data Table 2 “Data collected from releasing a cart on a down hill slope”
· See data Table 3 “Data collected from pushing a cart uphill”
Question #3 – Calculate the change in position between each of the points in your data table above. Enter these values in the right column of the data table. Do this for each experiment.
· See data Table 1 “Data collected from pushing a cart on a level surface”
· See data Table 2 “Data collected from releasing a cart on a down hill slope”
· See data Table 3 “Data collected from pushing a cart uphill”
Question #4 – Calculate the average speed for each portion of the trip. Do this for each experiment.
· See data Table 1 “Data collected from pushing a cart on a level surface”
· See data Table 2 “Data collected from releasing a cart on a down hill slope”
· See data Table 3 “Data collected from pushing a cart uphill”
Question #5 – Plot the data of speed versus time. Do this and answer the questions below for each experiment
· See graph – “CTC’s Straight Data Graph
· See graph – “CTC’s Downhill Data Graph
· See graph – CTC’s Uphill Data Graph
a): Is there a general trend pattern in the data? If so, describe it
*
b): Describe what is happening to the speed during the experiment.
· During the level experiment, the cart slowly slowed down.
· During the downhill experiment, the cart steadily speed up
· During the uphill experiment, the cart steadily slowed down
Question for Chris-
Do we need to right a formal hypothesis or is our predicted graph our hypothesis? Where would we write a hypothesis?
In Questions 2-3 we’re just supposed to reference the table right?
Question 4 is only concerning each portion and not the average of the whole trip, right?
We should number our graphs
Friday, January 11, 2008
A comparison of a pennies mass to the year it was minted
A comparison of a pennies mass to the year it was minted
By Trevor Gustafson
Introduction:
This experiment was done to discover the relationship between a penny’s weight and the year it was minted. My hypothesis going into this experiment was that “The longer a penny is in circulation, the lighter it will become. See figure 1:“Predicted results of the comparison of a pennies mass to the year it was minted.”
Materials used:
· 1 penny from the 1960’s
· 2 pennies form different years in the 1970”s
· 3 pennies from different years in the 1980’s
· 3 pennies from different years in the 1990’s
· 1 penny from the 2000’s
· 1 scale
· a pencil
· a notebook
· a piece of graphing paper
Procedure:
· 1 Create a hypothesis
· 2 Graph predicted outcome
· 3 Weigh individual pennies and mark findings on a chart
· 4 Mark individual data along with class data on a second chart
· 5 Mark individual data along with class data on a graph
Results:
· See attached Figure 1. “Predicted results of the comparison of a pennies mass to the year it was minted.”
· See attached Table 1. “Personal data concerning the comparison of a pennies mass to the year it was minted.”
· See attached Figure 2. “Group data concerning the comparison of a pennies mass to the year it was minted
· See attached Table 2. “Group data concerning the relationship of a pennies mass to the year it was minted.”
Analysis
1 Plot both the class data and your individual data on the same graph. Show the mass of each penny in grams on the y-axis and the year the penny was minted on the x-axis. Highlight the points that correspond to your individual data.
· See Figure 2: “Group data concerning the comparison of a pennies mass to the year it was minted”
2 Are the experimental results consistent with your hypothesis? If not, propose a new hypothesis
· No.
· The older pennies were actually heavier than the newer pennies
· The change was not gradual, but happened suddenly during the year 1982 (during 1982, some of the pennies were lighter and some were heavier)
· My new hypothesis is
“Something besides wear must have played a part in the sudden weight change of the penny during 1982.”
3 What effect might aging have on the mass of a nickel, a dime, or a quarter?
· Those coins are made of different materials so we can’t know what affect aging would have on them from this experiment.
4 Would using a balance that was many times more sensitive have made a difference in your conclusion about the effect of aging on a penny?
· The greater sensitivity might possibly have yielded different results.
5 What improvements might you have expected in you graph if only one student had done all the weighing on a single balance.
· Taking out variables such as multiple students and balances might have yielded a more consistent graph.
6 Compare your individual graph to the graph of class data. Why might you expect better results with the entire class data set than with your individual data set?
· Because most of the dots up until 1982, including my own, fell on 3.1 and most of the dots after 1982, including my own, fell on 2.5, It’s possible that the few odd ball points on the graph may have been miss-calculations.
Conclusion
· A pennies weight does not decrease by more than one decimal point of a gram the longer it has been in circulation.
· The coins minted before 1982 were actually heaver than the ones minted after 1982.
· Something caused the pennies to suddenly become lighter during and after 1982.
· Something besides wear must have played a part in the sudden weight change
By Trevor Gustafson
Introduction:
This experiment was done to discover the relationship between a penny’s weight and the year it was minted. My hypothesis going into this experiment was that “The longer a penny is in circulation, the lighter it will become. See figure 1:“Predicted results of the comparison of a pennies mass to the year it was minted.”
Materials used:
· 1 penny from the 1960’s
· 2 pennies form different years in the 1970”s
· 3 pennies from different years in the 1980’s
· 3 pennies from different years in the 1990’s
· 1 penny from the 2000’s
· 1 scale
· a pencil
· a notebook
· a piece of graphing paper
Procedure:
· 1 Create a hypothesis
· 2 Graph predicted outcome
· 3 Weigh individual pennies and mark findings on a chart
· 4 Mark individual data along with class data on a second chart
· 5 Mark individual data along with class data on a graph
Results:
· See attached Figure 1. “Predicted results of the comparison of a pennies mass to the year it was minted.”
· See attached Table 1. “Personal data concerning the comparison of a pennies mass to the year it was minted.”
· See attached Figure 2. “Group data concerning the comparison of a pennies mass to the year it was minted
· See attached Table 2. “Group data concerning the relationship of a pennies mass to the year it was minted.”
Analysis
1 Plot both the class data and your individual data on the same graph. Show the mass of each penny in grams on the y-axis and the year the penny was minted on the x-axis. Highlight the points that correspond to your individual data.
· See Figure 2: “Group data concerning the comparison of a pennies mass to the year it was minted”
2 Are the experimental results consistent with your hypothesis? If not, propose a new hypothesis
· No.
· The older pennies were actually heavier than the newer pennies
· The change was not gradual, but happened suddenly during the year 1982 (during 1982, some of the pennies were lighter and some were heavier)
· My new hypothesis is
“Something besides wear must have played a part in the sudden weight change of the penny during 1982.”
3 What effect might aging have on the mass of a nickel, a dime, or a quarter?
· Those coins are made of different materials so we can’t know what affect aging would have on them from this experiment.
4 Would using a balance that was many times more sensitive have made a difference in your conclusion about the effect of aging on a penny?
· The greater sensitivity might possibly have yielded different results.
5 What improvements might you have expected in you graph if only one student had done all the weighing on a single balance.
· Taking out variables such as multiple students and balances might have yielded a more consistent graph.
6 Compare your individual graph to the graph of class data. Why might you expect better results with the entire class data set than with your individual data set?
· Because most of the dots up until 1982, including my own, fell on 3.1 and most of the dots after 1982, including my own, fell on 2.5, It’s possible that the few odd ball points on the graph may have been miss-calculations.
Conclusion
· A pennies weight does not decrease by more than one decimal point of a gram the longer it has been in circulation.
· The coins minted before 1982 were actually heaver than the ones minted after 1982.
· Something caused the pennies to suddenly become lighter during and after 1982.
· Something besides wear must have played a part in the sudden weight change
Thursday, January 10, 2008
Conclusion
Conclusion
Under the small magnitude of one decimal point, there was no gradual decrees the more the penny was in circulation. The data reveals that there was a sudden drop in weight around 1982. Upon research I discovered that the us Mint changed its standars for minting pennies from copper to zinc.
Under the small magnitude of one decimal point, there was no gradual decrees the more the penny was in circulation. The data reveals that there was a sudden drop in weight around 1982. Upon research I discovered that the us Mint changed its standars for minting pennies from copper to zinc.
Study for quiz
Direct proportionality = whatever you do to one side you do the same to the other side. (eg. Hours times wage)
Proportionality symbol = <><
Points on graph = (2,10) (6,30) slope = (30-10) / (6-2) = 5
Inverse proportionality = as one number is multiplied by a number, the other number is divided by that number.
People Time
1
24 24*1=24)
2
12 (12*2=24)
3
8 (8*3=24)
Time = K/people where K is constant
0.000378 = 3.78 *10 (-4)
(1.2*10 (3) ) * (4*10 (11) ) = (1.2 * 4) * ( 10 (3) * 10 (11) )
(3.75 * 10(5) ) / (1.25 * 10(8) ) = (3.75 / 1.25) * (10(5) / 10(8) )
Deci = .2
Centi = .02
Milli = .002
Kilo = 2000Mega = 2000000
In 1800 John Palton discovered that matter always combines in same weight ratio
1 ibs hydrogen = 8ibs Oxygen
Sodium 23 : chlorine 35
Robert Brown said that all atoms are moving in a random fashion = Brownian Motion
-Dust particles/pollen strains moved randomly under microscope
- Every atom wants to be distributed evenly
Einstien created an equation to fit Brownian motion
112- 116 different matters-but almost everything is made from 90 matters
Greek = Atom = something that cannot be split up anymore
Better Definition = Atom = smallest particle of one of the ELEMENTS that maintains the chemical and physical properties of that ELEMENT
Molecule = the smallest particle of a TYPE OF MATTER that maintains the chemical and physical properties of that TYPE OF MATTER
- H2 0 = 2 parts Hydrogen and 1 part oxygen = 1 molecule
- Nobility gases don’t mix with anything else
- Molecule Nitrogen = N2 = Not useful until broken by plants(?)
Liquids and solids have constant volume while gas has a variable Volume
Gas and liquids have variable shapes while solids have constant shapes
Solids and liquids are non compressible while gas is compressible
Solids stay in same location to themselves while gas and liquids are free to move about (gas actually moves more though)
Solid Liquid Gas
-----------------------------à Increase temperature/increase movement
If you compress gas, becomes liquid. Once released, turns back into gas.
Humans are carbon based beings
1 Combustion Produces Heat
2 Respiration Produced BY aminals
(opposites)3 Photosynthesis Produced by plants
Atom =
Electrons - outer rim
Nucleus - inner rim
Protons - inside inner rim - Charge
Nutrons - Inside inner rim - No charge
Proportionality symbol = <><
Points on graph = (2,10) (6,30) slope = (30-10) / (6-2) = 5
Inverse proportionality = as one number is multiplied by a number, the other number is divided by that number.
People Time
1
24 24*1=24)
2
12 (12*2=24)
3
8 (8*3=24)
Time = K/people where K is constant
0.000378 = 3.78 *10 (-4)
(1.2*10 (3) ) * (4*10 (11) ) = (1.2 * 4) * ( 10 (3) * 10 (11) )
(3.75 * 10(5) ) / (1.25 * 10(8) ) = (3.75 / 1.25) * (10(5) / 10(8) )
Deci = .2
Centi = .02
Milli = .002
Kilo = 2000Mega = 2000000
In 1800 John Palton discovered that matter always combines in same weight ratio
1 ibs hydrogen = 8ibs Oxygen
Sodium 23 : chlorine 35
Robert Brown said that all atoms are moving in a random fashion = Brownian Motion
-Dust particles/pollen strains moved randomly under microscope
- Every atom wants to be distributed evenly
Einstien created an equation to fit Brownian motion
112- 116 different matters-but almost everything is made from 90 matters
Greek = Atom = something that cannot be split up anymore
Better Definition = Atom = smallest particle of one of the ELEMENTS that maintains the chemical and physical properties of that ELEMENT
Molecule = the smallest particle of a TYPE OF MATTER that maintains the chemical and physical properties of that TYPE OF MATTER
- H2 0 = 2 parts Hydrogen and 1 part oxygen = 1 molecule
- Nobility gases don’t mix with anything else
- Molecule Nitrogen = N2 = Not useful until broken by plants(?)
Liquids and solids have constant volume while gas has a variable Volume
Gas and liquids have variable shapes while solids have constant shapes
Solids and liquids are non compressible while gas is compressible
Solids stay in same location to themselves while gas and liquids are free to move about (gas actually moves more though)
Solid
-----------------------------à Increase temperature/increase movement
If you compress gas, becomes liquid. Once released, turns back into gas.
Humans are carbon based beings
1 Combustion Produces Heat
2 Respiration Produced BY aminals
(opposites)3 Photosynthesis Produced by plants
Atom =
Electrons - outer rim
Nucleus - inner rim
Protons - inside inner rim - Charge
Nutrons - Inside inner rim - No charge
Wednesday, January 9, 2008
A comparison of a pennies mass to the year it was minted
A comparison of a pennies mass to the year it was minted
By Trevor Gustafson
Introduction:
This experiment was done to discover the relationship between a pennies weight and the year it was minted. My assumption going into this experiment was that the pennies weight would slowly decrease over time due to wear.
Materials used:
· 1 penny from the 1960’s
· 2 pennies form different years in the 1970”s
· 3 pennies from different years in the 1980’s
· 3 pennies from different years in the 1990’s
· 1 penny from the 2000’s
· 1 scale
· 1 pencil
· 1 notebook
Procedure:
· Create a hypothesis
· Graph predicted outcome
· Weigh individual pennies and mark findings on a chart
· Mark findings along with classmates findings on a graph
Results:
· See attached Figure 1. “Predicted results of the comparison of a pennies mass to the year it was minted.”
· See attached Table 1. “Personal data concerning the comparison of a pennies mass to the year it was minted.”
· See attached Figure 2. “Group data concerning the relationship of a pennies mass to the year it was minted
· See attached Table 2. “Group data concerning the comparison of a pennies mass to the year it was minted.”
Analysis
1 Plot your data on graph paper as a scatter plot. Show the mass of each penny in grams on the y-axis and the year the penny was minted on the x-axis. Plot both the class data and your individual data on the same graph. Highlight the points that correspond to your individual data
· See Figure 2: “Group data concerning the relationship of a pennies mass to the year it was minted”
2 Are the experimental results consistent with you hypothesis? If not, propose a new hypothesis
· No.
· The older pennies were actually heavier than the newer pennies
· The change was not gradual, but happened suddenly around 1982
· My new hypothesis is
“When measuring the pennies to one decimal point, it appears that circulation has very little effect on a pennies weight. Something outside of circulation, such change in manufacturing the penny, must have played a part in the pennies weight.”
3 What effect might aging have on the mass of a nickel, a dime, or a quarter
· Those coins are made of different materials so we can’t know what affect aging would have on them from this experiment.
4 Would using a balance that was many times more sensitive have made a difference in your conclusion about the effect of aging on a penny?
· Possible. The greater sensitiveness might have yielded different results.
5 What improvements might you have expected in you graph if only one student had done all the weighing on a single balance.
· Taking out variables such as multiple students and balances would probably had yielded a more consistent graph.
6 Compare your individual graph to the graph of class data. Why might you expect better results with the entire class data set than with your individual data set?
· Because most of the dots up until 1982 fell on 3.1 and most of the dots after 1982 fell on 2.5. I believe that the few odd ball points on the graph may have been miss-calculations
By Trevor Gustafson
Introduction:
This experiment was done to discover the relationship between a pennies weight and the year it was minted. My assumption going into this experiment was that the pennies weight would slowly decrease over time due to wear.
Materials used:
· 1 penny from the 1960’s
· 2 pennies form different years in the 1970”s
· 3 pennies from different years in the 1980’s
· 3 pennies from different years in the 1990’s
· 1 penny from the 2000’s
· 1 scale
· 1 pencil
· 1 notebook
Procedure:
· Create a hypothesis
· Graph predicted outcome
· Weigh individual pennies and mark findings on a chart
· Mark findings along with classmates findings on a graph
Results:
· See attached Figure 1. “Predicted results of the comparison of a pennies mass to the year it was minted.”
· See attached Table 1. “Personal data concerning the comparison of a pennies mass to the year it was minted.”
· See attached Figure 2. “Group data concerning the relationship of a pennies mass to the year it was minted
· See attached Table 2. “Group data concerning the comparison of a pennies mass to the year it was minted.”
Analysis
1 Plot your data on graph paper as a scatter plot. Show the mass of each penny in grams on the y-axis and the year the penny was minted on the x-axis. Plot both the class data and your individual data on the same graph. Highlight the points that correspond to your individual data
· See Figure 2: “Group data concerning the relationship of a pennies mass to the year it was minted”
2 Are the experimental results consistent with you hypothesis? If not, propose a new hypothesis
· No.
· The older pennies were actually heavier than the newer pennies
· The change was not gradual, but happened suddenly around 1982
· My new hypothesis is
“When measuring the pennies to one decimal point, it appears that circulation has very little effect on a pennies weight. Something outside of circulation, such change in manufacturing the penny, must have played a part in the pennies weight.”
3 What effect might aging have on the mass of a nickel, a dime, or a quarter
· Those coins are made of different materials so we can’t know what affect aging would have on them from this experiment.
4 Would using a balance that was many times more sensitive have made a difference in your conclusion about the effect of aging on a penny?
· Possible. The greater sensitiveness might have yielded different results.
5 What improvements might you have expected in you graph if only one student had done all the weighing on a single balance.
· Taking out variables such as multiple students and balances would probably had yielded a more consistent graph.
6 Compare your individual graph to the graph of class data. Why might you expect better results with the entire class data set than with your individual data set?
· Because most of the dots up until 1982 fell on 3.1 and most of the dots after 1982 fell on 2.5. I believe that the few odd ball points on the graph may have been miss-calculations
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