Name: ___________________________
Group Members:
___________________________
___________________________
___________________________
Introduction to Procedure and
Measurements
Purpose and Objectives
The purpose of this experiment involves a well-known, geometric quantity which relates to the
nature of space. In Euclidean geometry, the ratio of the circumference of a circle to its diameter is
shown to be a constant, π. According to modern theories about the structure of space, Euclidean
geometry might not describe the universe on a large scale. Then, the ratio of circumference to
diameter would not be π. If you measure two quantities, their relationship may be determined by
plotting one against the other. If a straight line that passes through the origin describes the data,
then the ratio of the quantities is a constant given by the slope.
After performing the experiment and analyzing the data, you should be able to do the following:
1. Record data with the inclusion of uncertainty.
2. Calculate averages and deviations.
3. Propagate uncertainty
Equipment
5 Circular objects
Vernier Caliper
Graphing paper
Pencil and ruler
Calculator
String
Procedure
Use 5 circular objects and plot the circumference versus the diameter. Measure these quantities
several times so that you can estimate the random uncertainty by the average deviation. Indicate the
uncertainty on the plot by using error bars. Discuss with your group to determine the best way to
measure the circumference. Use a Vernier caliper to measure the diameter for small enough objects..
Record all possible sources of random uncertainty. If the data indicates that the relationship of
circumference to diameter can be described by a straight line, use Excel or Graphical Analysis to
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1-1b Introduction to Procedure and Measurements
determine the equation of the best-fit straight line to the data, along with uncertainties on the slope
and intercept.
An ordinary vernier caliper has jaws you can place around an object, and on the other side jaws
made to fit inside an object. These secondary jaws are for measuring the inside diameter of an
object. Also, a stiff bar extends from the caliper as you open it that can be used to measure depth.
The basic steps are as follows:
1. Preparation to take the measurement, loosen the locking screw and move the slider to check
if the vernier scale works properly. Before measuring, do make sure the caliper reads 0 when
fully closed. If the reading is not 0, adjust the caliper’s jaws until you get a 0 reading. If you
can’t adjust the caliper, you will have to remember to add to subtract the correct offset from
your final reading. Clean the measuring surfaces of the vernier caliper and the object, then
you can take the measurement.
2. Close the jaws lightly on the item which you want to measure. If you are measuring
something round, make sure you are measuring the full diameter. An ordinary caliper has
jaws you can place around an object, and on the other side jaws made to fit inside an object.
These secondary jaws are for measuring the inside diameter of an object. Also, a stiff bar
extends from the caliper as you open it that can be used to measure depth.
How to Read a Vernier Caliper
Figure 1 Read the centimeter mark on the fixed scale to the left
of the 0-mark on the vernier scale. (10mm on the fixed caliper)
Figure 2 Find the millimeter mark on the fixed scale that is just
to the left of the 0-mark on the vernier scale. (6mm on the fixed
caliper)
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1-1b Introduction to Procedure and Measurements
Figure 3 Look along the ten marks on the vernier scale and the
millimeter marks on the adjacent fixed scale, until you find the
two that most nearly line up. (0.25mm on the vernier scale)
Figure 4 To get the correct reading, simply add this found digit
to your previous reading. (10mm + 6mm + 0.25mm= 16.25 mm)
Information and pictures from http://www.tresnainstrument.com/how_to_read_a_vernier_caliper.html
Questions
1. What is the relationship between circumference and diameter?
2. Is a straight line a good fit to the data points? Explain. (The words “error bars” should
occur in your explanation.)
3. Does the value of the slope make sense? the intercept?
4. Based on the results from your experiment, what do you predict the diameter of the earth
to be (along with uncertainty) from the know circumference of 24,902 miles?
5. Is Euclidean geometry valid for the objects used in the experiment?
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1-1b Introduction to Procedure and Measurements