10/18/10
Relationship between Mint Date of Pennies and Density
Question:
What is the relationship between the mint date of pennies and their densities?
Hypothesis:
There is an increasing linear relationship between the density and the mint date. I’ll
accept this if the true values fall on the line, meaning the line should go through the error bars around
the measurements.
Materials:
one 100 mL graduated cylinder
one triple-beam balance
pennies ranging from 1954-2009
water
paper towels
20 Dixie cups
Calculator
Variables:
Independent Variable: mint date
Dependent Variable: density
Control Group: none, internal comparison
Controlled Variables: To make sure the collected data was accurate, we controlled some of the
variables, such as weighing method, same graduated cylinder/ balance, air temperature, water
temperature. By making sure the environment of the pennies was the same, we ensured that
they didn’t expand or contract due to temperature so the volumes would be collected fairly. By
using the same weighing method, we kept the uncertainty level around the same.
Procedure: We organized a large stack of pennies by year and each group took about 5 years of
pennies. Using a triple beam balance, we measured the mass of all the pennies for one specific year
three times. Then, using a 100 mL graduated cylinder, we measured the volume of the pennies. To do
this, we used the water displacement method. We filled the cylinder with 50 mL of water and then
dropped in all the pennies for one year and shook out any air bubbles. We measured the volume of each
year 3 times. Then, we used the formula density= mass/volume to find 3 densities for each year, and
then averaged those densities to find the average density of each year of pennies.
Data:
Mass 1 (g)
Mass 2
Mass 3
Volume 1 (mL)
Volume 2
Volume 3
Density 1 (g/mL)
Density 2
Density 3
Average Density
1961
9.39 ± .01
9.40 ± .01
9.35 ± .01
3.1 ± .2
2.5 ± .4
2.4 ± .4
3.03
3.76
3.9
3.563333333
1974
69.27 ± .01
69.19 ± .01
69.27 ± .01
8.5 ± .2
8.1 ± .4
7.1 ± .4
8.15
8.54
9.76
8.816666667
1975
67.82 ± .03
67.82 ± .03
67.92 ± .02
7.9 ± .1
8.5 ± .2
8.5 ± .2
8.5848
7.9788
7.9906
8.184733333
1976
43.36 ± .03
43.12 ± .02
43.20 ± .02
5.5 ± .2
9.1 ± .5
4.5 ± .4
7.8836
4.7384
9.6
7.407333333
1977
58.02 ± .01
58.05 ± .01
58.05 ± .01
7.2 ± .5
6.5 ± .4
6.8 ± .3
8.06
8.93
8.54
8.51
Uncertainty/ Error: No experiment is without error, so error/ uncertainty was considered. During
measurement, we could only be certain up to the tenths place while measuring mass and the ones place
while measuring volume, so we estimated how much uncertainty we had on each measurement and
showed that with the plus or minus sign. Then we took 3 mass measurements and 3 volume
measurements for each year of pennies, so we found 3 densities and then took the average of those
densities. To determine the uncertainty of the average graphs, we then found the average deviation. An
example of how we did that is exemplified here:
(8.15 + 8.54 + 9.76)/3= 8.1666
|8.15-8.1666|=0.0166 |8.54-8.1666|=0.3734 |9.76-8.1666|=1.5934
(0.0166 + 0.3734 + 1.5934)/3= 0.66
Average Deviation= 0.66 g/mL
Also, the graph is not 100% accurate because some mint dates did not supply their data or supplied an
insufficient amount of information. These years included 1955-1957, 1963, 1971, 1990 and 1992. Also, I
remove one year of pennies information because the data didn’t make logical sense because the density
was 19.1 g/mL, which is considerably larger than all of the other data and is close to the density of the
one of the densest elements in the periodic table, gold, which has a density of 19.3 g/mL. I figured that
the density of a penny wouldn’t be only slightly less than gold, so I removed that data point.
Calculations: Besides average deviation, we also used the formula density=mass/volume to find the
density of each set of pennies and also used averaging (measurement 1 + ms. 2 + ms. 3/3= average) to
find average density.
Example (Density: 1977)Mass= 58.02 g Volume=7.2
58.02/7.2= 8.1 g/mL
Example (Average Density: 1975)(8.5848 + 7.9788 + 7.9906)/3= 8.1847 g/mL
Graph:
Average Density
12
Average Density (g/mL)
10
8
6
4
2
0
1950
1960
1970
1980
1990
2000
2010
2020
Mint Date
Evaluation of Hypothesis: My hypothesis was incorrect because I had predicted that the density of the
pennies would have an increasing linear relationship to the mint date. The trendline on the graph above
shows that from 1960 to 1982, the densities were slightly increasing and averaged around 8.4 g/mL, but
at 1983, there is a sharp drop in density from 8.7 g/mL to 7.39 g/mL and continues to decrease over
time. In 2008, we found the density to be 6.98 g/mL, which clearly shows a decrease in density when
that is compared to the density of the 1982 penny, which was 8.7 g/mL. This data disproves my
hypothesis and allows me to conclude that the density of pennies was increasing linearly until 1982
when the composition of the pennies changed, so then it began to decrease at a steady rate.
Explanation: The decrease in density over time of the pennies can be explained by the composition of
the pennies. Between 1960 and 1982, pennies were composed of copper with only about 5% zinc, but
after 1982, pennies were made with a zinc core and a light copper coating on the outside. Pennies now
are about 97.5% zinc and only 2.5% copper, and since the density of copper is 8.96 g/mL and the density
of zinc is only 7.14 g/mL, pennies nowadays have a lower density than they did before 1982.
Importance: This experiment shows that in 1982, the amount of copper in pennies drastically decreased
from 95% to 2.5%. The questions is: why did they change the composition of pennies? It’s because the
price of copper, along with other metals, was increasing as a result of demand. Copper was used for
wiring, pipes, electrical circuits and many other things in homes and cars, as well as being used for
pennies. As a result of this, the price of copper increased, so the government was spending more and
more minting pennies. To save money, they changed the composition of pennies so that it looked the
same, with a copper coating on the inside but zinc at its core.