Density of pre- and by hcj

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									                            Density of pre- and
                            post-1982 Pennies
                                    Mr. Amendola

                                        Abstract
The mass of 29 pre and 29 post-1982 pennies was measured, and their respective
volumes were measured by water displacement. Experimental density of 29 pre 1982
pennies was 8.6 g/mL, while that of post-1982 pennies was 5.5 g/mL. Class results
showed the average density of a pre-1982 penny as 9.0 g/mL, while that of a post-1982
penny was 7.2 g/mL.
                         Density of Pre- and Post 1982 Pennies

Introduction

The composition of pennies minted prior to 1982 differs from those minted after 1982.
Density is physical property that is characteristic of the metal or alloy. The purpose of
this experiment was to determine the density of both pre- and post 1982- pennies via
water displacement. Class data is used to avoid anomalous data points.

Materials:

100 mL graduated cylinder.
20 pre-1982 pennies
20 post-1982 pennies
analytical balance

Method:

The mass of 20 pre-1982 pennies was measured using an analytical balance and recorded.
50.0 mL of water was added to a 100 mL graduated cylinder. The pennies were added
and the new volume was recorded. The procedure was repeated using 20 post-1982
pennies. Data is found in Table 1. Class data is recorded in Table 2.

Data
                Table 1: Individual Mass and Volume Measurements
                             Pre-1982 Pennies         Post 1982 Pennies

Mass                           89.682 g                        72.625 g


Volume Water                   50.0 mL                         50.0 mL


Volume of Water and            60.4 ml                         63.3 mL
pennies

Volume Pennies                 10.4 mL                         13.3 mL



Density                        8.6 g/mL                        5.5 g/mL
                     Table 2: Class Mass and Volume Measurements
                     Pre-1982 Pennies               Post-1982 Pennies
Lab Pair             mass (g)         volume (mL)   mass (g)         volume (mL)
1                    123.243          14.4          62.752           8.8
2                    30.788           3.1           50.102           6.9
3                    46.28            11.0          37.60            5.0
4                    61.70            7.0           25.00            3.5
5                    39.996           4.9           32.570           4.9
6                    61.379           8.1           45.066           6.2
7                    92.679           10.0          75.116           10.0
8                    76.10            8.6           12.523           1.5
9                    83.363           8.9           67.681           9.5
10                   98.641           6.1           80.447           11.3
11                   73.8             9.0           60.0             8.0
12                   89.682           10.4          72.625           13.3

Analysis
The data in Table 2 was plotted in Graph 1 and a linear correlation between mass and
volume was found. The slope of the best fit line represents the density of the substance,
and the calculation of each slope is provided below.

Pre-1982 Penny

          y   100.0 g - 15.0 g        g
slope                          8.5
          x 11.67 mL - 1.67 mL       mL


Post 1982 Penny

          y   105.0 g - 15.0 g        g
slope                          7.2
          x 14.67 mL - 2.0 mL        mL

The density of each lab was calculated by the following method and results are presented
in Table 3. The data for 29 Pre-1982 Pennies is shown in the example calculation. The
remainder of results were calculated in the same manner.

             mass
density 
            volume

            89.682 g         g
density              8.62
            10.4 mL         mL
                               Table 3: Class density results
                  Lab Pair      Density of Pre Density of Post
                                1982 Pennies    1982 Pennies
                                (g/mL)          (g/mL)
                  1                         8.6                 7.1
                  2                         9.9                 7.3
                  3                         4.2                 7.5
                  4                         8.8                 7.1
                  5                         8.2                 6.6
                  6                         7.6                 7.3
                  7                         9.3                 7.5
                  8                         8.8                 8.3
                  9                         9.4                 7.1
                  10                       16.2                 7.1
                  11                        8.2                 7.5
                  12                        8.6                 5.5
                  AVERAGE                   9.0                 7.2

As expected the average density for the class is close the slope of the best fit line in each
case.

The error was calculated using the following formula. The actual density of a pre 1982
penny is 8.6 g/mL and that of a post 1982 penny is 6.9 g/mL. Source:
http://www.1728.com/projects.htm.


            accepted value - experimental value
% error                                          x 100% 
                        accepted value

For pre-1982 pennies the class error is given below. Error for both individual and class
results were calculated in the same manner and are located in Table 4.

                   g         g
            8.6        9.0
                  mL        mL
% error =                      x100%  4.5%
                        g
                   8.6
                       mL

                      Table 4: Error for Individual and class densities
                                  Individual                   Class
Pre1982                           0.00%                        4.5%
Post 1982                         20.%                         4.3%
Conclusion/Discussion:
Pre 1982 pennies densities were determined to have a density of 9.0 g/mL, while post
1982 pennies were 7.2 g/mL. Note that the number of pennies does alter the mass, but
does not affect the density. This is illustrated in the graph. The mass/volume
relationship is linear, meaning the slope is constant. The slope of each line represents the
density of the substance. The average values in the table for density should have been
identical to the slope of the best fit line for each type of penny. This was the case for post
1982 pennies, but not for pre 1982 pennies. The like cause of this was that the best fit
line was hand drawn, rather than computed by linear regression. For this reason, the
average density values are more reliable in this experiment.

Individual results for post-1982 pennies were inaccurate (20. % error, Table 4). The
inaccuracy was likely caused by incorrectly reading the meniscus on the graduated
cylinder. Results could have been improved by each group measuring the density three
times and reporting an average value.

								
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