Relationship between Mint Date of Pennies and Density

Transcription

1 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 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

2 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) 9.39 ± ± ± ± ±.01 Mass ± ± ± ± ±.01 Mass ± ± ± ± ±.01 Volume 1 (ml) 3.1 ± ± ± ± ±.5 Volume ± ± ± ± ±.4 Volume ± ± ± ± ±.3 Density 1 (g/ml) Density Density Average Density 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

3 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: ( )/3= = = = ( )/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 , 1963, 1971, 1990 and 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= g Volume= /7.2= 8.1 g/ml

4 Average Density (g/ml) Example (Average Density: 1975)- ( )/3= g/ml Graph: Average Density 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.

5 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 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.