AP Physics
Lab Activity - Graphing
Background
Graphs are used for many purposes but in the scientific world, graphs are used for four main purposes:
1. Determine the value of a constant
2. Determine that a value is a constant
3. Interpolate an answer
4. Extrapolate a prediction
Case 1: Determine the value of a constant.
Generally speaking, determining the value of a constant from a graph yields a precise answer because
the scatter-plot graphing process (making a line graph) averages out all but the most egregious errors in
data collection. Egregious errors, sometimes called outliers, are visually obvious as the data is plotted
and should not be used when determining the best-fit straight line (after an appropriate explanation has
been noted either on the data table or in the lab journal).
If the value in question can be found in a formula of the form
ValueOfInterest =
StuffYouCanMeasure
OtherStuffYouCanMeasure
then a simple line graph can be made where the slope of the best-fit line is the value of interest.
One should note that not all best-fit lines hit the origin. If you can make the claim that when the x-value
is zero (0) then the y-value must be zero (0), you can anchor your best-fit line through (0,0); just be
certain that you can justify the claim.
As an example, the formula for density (which I am sure you recognize) is D =
M
. Since slope is
V
rise Δy
=
, plotting a graph of mass vs volume causes the slope of the
run Δx
Δy M
⎛
⎞
=
= D⎟ .
best-fit straight line to represent density ⎜ slope =
Δx V
⎝
⎠
calculated by slope = m =
Remember, plotting mass vs volume means that mass is plotted on the y-axis and volume is plotted on
the x-axis.
This is probably the most common purpose of a graph in physical sciences. Watch for these “the slope is
meaningful” moments.
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Case 2: Determine that a value is a constant.
In Case 1, we assumed that the data would yield a best-fit straight line because the point of the graph
(sorry….) was to determine the value of a constant. The process of determining if a value is a constant
uses the same thinking but in reverse.
To determine if a value is a constant, plot the points (see Case 1) to see if the best-fit line is indeed
straight. Simple.
Case 3: Interpolate an answer.
Interpolation is the process of finding or estimating a term inside the
bounds of existing terms. In graphing terms, that is to use a point on a
best-fit line through existing data to determine a value between the
smallest and largest data points.
Case 4: Extrapolate a prediction.
To extrapolate is to estimate the value of a variable outside of the observed
range of data. In graphing terms, that is to extend the best-fit line beyond
the last data point to determine the value of a variable.
The Assignment
Measure the circumference and diameter of a variety of circular objects. Graph this data to determine
the value of π. (As you have no doubt surmised, this is employing Case 1 – a “the slope is meaningful”
moment; if your data is properly graphed, the slope of your graph should be π).
A data table and graph paper are provided. Measure a minimum of 10 significantly different objects.
Remember that the cross-section of a sphere is a circle.
Tips on making good graphs
• Always title the graph. Ex: Mass vs Volume of Wood Objects
• Label both axis, including units
• Scale each axis from zero (0); no “broken” axis
• Make the graph as large as possible for the space provided; size the scale accordingly.
• A best-fit line should equally miss all data points. (One vision of this is that there will be as many
data points above the line as there are below the line.)
• Slope of the best-fit straight line is taken between two points on the line; never use the original
data points.
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Just in case your creativity is slumbering today, here are a few possibilities for measuring circumference
and diameter. Note: You are not obligated to use these methods.
Measuring Circumference
Left: a string is wrapped around the item and a mark is made crossing both strings.
Right: the string is then held flat and the distance between the marks is measured.
Left: a mark is made on the end of the cylinder and on the paper.
Right: the cylinder is rolled 1 revolution; measurement is taken from original mark to new mark.
Measuring Diameter
(This works well for measuring the diameter of a sphere.)
Left: The object is sandwiched between the wall and a book;
measurement is taken (obviously) between the wall and the
book.
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AP Physics
Lab Activity - Graphing
Name ___________________________________
Please drop this page off at the High
School Main Office when finished
(there is a folder there) or e-mail as
attachment.
Lab Partner ____None_____________________
Per ____ Due Date _2:00PM 31 August 2012____
Data Table 1
Trial
#
Item
1
Penny
2
Quarter
Size (cm)
1.89
Diameter
Method of Measurement
Vernier caliper
Size (cm)
5.94
Circumference
Method of Measurement
rolling
3
4
5
6
7
8
9
10
After completing your graph on the grid provided on back, use the space here to show your calculation
of π. Show all work, including units; be neat and organized.
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