Purpose: to determine the relationship between the circumference and the diameter of cylindrical objects; to determine the accuracy of measurement; to
compare accuracy and precision
Materials:
Procedure
1.
2.
3.
4.
five cylindrical objects, i.e. metal tubing, salt containers, etc
string (non-elastic)
metric ruler
graph paper or graphing program
Lab
TIME !
Obtain at least five cylindrical objects for measurement.
Construct a data table that lists the name of the object, the circumference (C) (cm), the diameter (d) (cm), and a column that shows the
result of dividing C by d. C and d MUST be measured…not calculated.
Make measurements using an estimated digit with the school metric ruler (Each measurement should have one decimal place in cm.)
Carefully measure the diameter and the circumference of each object and record.
Questions/Analysis:
1.
2.
3.
4.
5.
For each object, divide the circumference by the diameter. Place this value in the appropriate column in your data table. Do you notice any pattern
or similarities between the resulting numbers? What unit does the resulting number have?
Construct a graph using the program Graphical Analysis. This program is found on the classroom computers; you can borrow a CD to take home
with you and load the program on your home computer. If a CD is not available, you can ask your instructor to email you a zip file of the program.
The blog has a document that will explain HOW to use the program, called Graphical Analysis Tutorial.
Make sure that each axis is properly labeled and contains units: Circumference (cm) and Diameter (cm). There are several ways to do this – the
easiest is to double-click on the X at the top of the data table and type in the label in the “Name” field and type the units (no parentheses) in the
“Units” field. DO NOT type the units in the Name field. Repeat for the Y axis.
Give the graph a title; usually the format Y vs. X, in this case Circumference vs. Diameter. Line graphs in science are generally titled this way. To
title the graph: double-click on the graph, type in your title. Uncheck all boxes under the Appearance column on that screen EXCEPT for point
protectors. Click DONE at the bottom of the screen. To make the best-fit straight line, click on the button on the top task bar that says R=. This
stands for REGRESSION which is the best fit straight line. When the line is drawn, you will also get a Statistics box. The following will be given:
slope (m), y-intercept (b) and a correlation coefficient. The correlation coefficient is a good measure of the precision of the data. The closer the
value is to 1.00, the better the data because it is a measure of how close the data points lie to the average line drawn.
Calculate a percentage error using the following formula:
|EXP – THEO| x 100
THEO
In this case, the EXPerimental value is the slope from the graph. The THEOretical value
is 3.14. Absolute value is used so that all percentage errors are positive.
6.
Why is the theoretical value for this lab 3.14?
7.
The percentage error you found is called the ACCURACY…how close the experimental value is to the standard or theoretical value. PRECISION
is the reproducibility of the measurements. When you divided C by d in question #1, were the values close to each other? If they were close,
precision was good; if they were random, precision was poor. Describe your precision.
8.
Using a dartboard as an example, describe how a dart thrower, using three throws, could have the following:
(A)
good accuracy and good precision
(B)
poor accuracy and good precision
(C)
poor precision and poor accuracy
9.
In this lab, your accuracy could be good with the precision being poor. Explain using your graph to support your argument.
Data Table:
Object
Circumference
15
Diameter
5
C/d = slope
3
#1
12
4
3
#2
#3
30
10
3
#4
36
12
3
9
3
3
#5