PHYS 100
Dr. Labroo
Introductory Physics Laboratory
V_S01
Experiment 1: Measurement and Uncertainty
Objectives:
1. Demonstrate the limitation of human senses as measuring devices.
2. Learn about experimental errors and uncertainties.
3. Learn some basic graphing techniques.
Suggested Reading:
Chapter 1 of the text.
Equipment and Supplies:
20 Pennies, beam balance, cm scale ruler, and graph paper.
Introduction:
Physics and most other sciences often rely on accurate measurements that lead to a
quantitative description of an observable physical quantity. We will demonstrate that if one
depends solely on one’s senses as a measuring device, important discoveries could go unnoticed.
Therefore, objective measurements are important in science.
Every measurement has an uncertainty associated with it. A good scientist will therefore
report a measurement along with its uncertainty (or error). This uncertainty is usually related to
the limitation of the measuring instrument and to other random factors. When measured
quantities are used to calculate another quantity, this uncertainty propagates.
In the first part of this experiment you will measure the mass of some pennies and plot a
histogram of your results. The results may be surprising! In the second part, you will learn how
an uncertainty in the measurement of length leads to uncertainty in the area of a surface.
Procedure:
Part I
1. Adjust your beam balance so that it is perfectly balanced with no mass placed on it.
This is called zeroing the balance.
2. Find the mass of a penny to the nearest tenths of a gram and record your measurement
in the data sheet provided to you.
3. Repeat for all of the pennies.
4. Note that the pennies most likely do not have identical masses. To verify any pattern,
plot a histogram of your results. A histogram is a plot of the frequency or occurrence
of a measurement in a series of measurements.
5. Label the horizontal axis as the mass and the vertical axis as the number of times a
particular measurement occurred (frequency). The horizontal axis should range from
the smallest to the largest mass in tenths of a gram while the vertical axis should be
numbered from 0 to 10.
Part II
1. Take your data sheet page and measure its length and width using a centimeter scale
ruler. Record your measurements and the uncertainty associated with it. Usually,
uncertainty is the smallest reading an instrument can take.
2. Calculate the maximum and minimum possible areas of the page.
3. Uncertainty in the calculated quantity (area) is half the difference between the
maximum and the minimum possible areas.
Uncertaint y in Area 
Max. Area - Min. Area 
2
Questions:
1. Does your histogram from Part I reveal any information about the pennies that was
not apparent by just looking at them?
2. How do you account for the measured differences of the masses of the coins? Is there
a correlation between the masses and the year of production?
3. In part II, if you had used an instrument with a smaller measurement uncertainty,
would your uncertainty in area be smaller also?
4. Sometimes it is more convenient to express the uncertainty as a percentage of the
measured quantity. Can you calculate the % Uncertainty in Area from your data?
Show all the calculations.
5. Based on the lessons learned in this experiment, suggest some ways to minimize
experimental error.
Report Requirements:
Brief summary of the experiment, data, graph, calculations and answers to the above
questions.
PHYS 100 Laboratory
Data Sheet
Name:
Experiment 1
, Partners:
Part I
Year
Part II
Measured Length (cm):
Measured Width (cm):
Measured Area (cm2):
Uncertainty (Smallest reading on the instrument) in cm:
Maximum Length:
Maximum Width:
Minimum Length:
Minimum Width:
Maximum possible area (cm2):
Minimum possible area (cm2):
Calculated uncertainty in area (cm2):
Note:
Maximum Length or Width = Measured Length or Width + Uncertainty
Minimum Length or Width = Measured Length or Width – Uncertainty
Maximum Area = Maximum Length x Maximum Width
Minimum Area = Minimum Length x Minimum Width
20
Mass
(g)
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
Penny