Lab
Density of a Paper Clip
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Purpose
To allow the student to become familiar with obtaining measurements with a triple beam balance and a graduated cylinder. Data analysis techniques are reinforced with the density being graphically calculated as the slope of the line Mass vs Volume.
Vocabulary
cubic centimeter
density
grams
mass
mean
median
meniscus
milliliters
mode
volume
Beams
Use the "positions" of poises (counterweights) to calculate the "mass on the pan." State your answers to 2 decimal places.
A
B
Graduated cylinders
Record the volume of "water" present in each of the cylinders specified. In each case, estimate your final significant digit.
C
D
E
F
C
D
E
F
Mass of a paper clip.
By using multiples of six (6) clips measure the mass of each collection of clips. Remember that each member of the group must measure each collection of clips. As a group you should reach a consensus to read each value to either one or two decimal places. Keep track of your significant digits and place units on every measurement! Be certain that you only use LARGE paper clips. A copy of this chart must be kept in your notebooks.
Number of Clips
Reader #1
Reader #2
Average Mass
6
12
18
24
30
36
42
48
54
60
Volume of a paper clip.
By using multiples of six (6) clips measure the volume of each collections of clips. Also, note that the all clips must be TOTALLY submerged before you read the volume of water. Since your graduated cylinders are marked off in 1 ml increments, you can only estimate one (1) decimal place. Remember that each member of the group must measure each collection of clips. Also, remember to keep track of your significant digits and to place units on every measurement!
Completely submerge 6 paper clips at a time in the water and record the new water level. Then, subtract the original water level from the new water level to determine the amount of water displaced by each cumulative collection of paper clips. After each group member has made his/her measurement, calculate the average change in water volume for each group of clips. ALERT: since 1 ml of water is displaced by each cm
^{3}
of solid paper clips, this average value needs to be expressed in cm
^{3}
.
Original water levels:
Start as close to 85.0 ml as possible; each person's starting point can be slightly different if necessary. Record all of your water levels readings for your graduated cylinder in the chart below.
Number of Clips
Reader #1
Reader #2
Average Volume of Clips
original water _____ ml
original water _____ ml
new water
level
net water
displaced
new water
level
net water
displaced
6
12
18
24
30
36
42
48
54
60
Graphical Analysis.
EXCEL will now graph your data. Minimize your browser, double click My Computer, double click the shared drive called colwell/bay on Lederman, double click your period's folder and then finally double click 1-density.xls. You will most likely be asked to open the file as "read only" - that is fine. As soon as the file is open, use File Save As to rename the file as
LastnameLastnameDensity.xls
in your period's folder. This copy of the file now belongs uniquely to your group. Remember that there are to be no spaces in the file name.
What is the name of your density file?
Input your final AVERAGE values for Volume and Mass for each of the 10 collections of paper clips. As you enter your data, its graph will grow. Volume, measured in cm
^{3}
to 1 decimal place, will be placed on the x-axis and Mass, measured in grams to 2 decimal places, will be placed on the y-axis. When your graph is finished, be certain that any points that are obviously out-of-line have been rechecked for accuracy -- either in measurement, or for a mistake in typing.
Your graphs will be printed from my teacher station. Student stations do not have permissions to print to a local or network printer.
when you receive your printout, you are to write the equation of the line in the form "y = mx + b" along the graph's trend line. Be careful to use the correct "variables" -- M for "y" and V for "x" as well as the specific numerical values for your line's slope, "m," and y-axis intercept, "b." Since
M = DV
your group's experimental density is represented by the slope of your regression or trend line.
What is the equation of your line?
Basic Statistics
When your group has calculated its value for the density of the paper clip material, go to the board and record your value so that the rest of the class can compare it with theirs.
Once again, minimize your browser, double click My Computer, double click the shared drive called colwell/bay on Lederman, double click your period's folder and then finally double click 1-densitystatistics.xls. You will most likely be asked to open the file as "read only" - that is fine. As soon as the file is open, use File Save As to rename the file as
LastnameLastnameDensityStatistics.xls
in your period's folder. This copy of the file now belongs uniquely to your group. Remember that there are to be no spaces in the file name.
What is the name of your statistics file?
Your data is to be placed in column B on the sheet called
RawData
.
When all of the data has been recorded, we will rank them from smallest to largest and complete the statistics on median and mode.
Refer to the following information for the next three questions.
Individual Group Results
Basic Statistics for your PERIOD
Mode (most frequent value)
Median (middle value)
Mean (average value)
Standard Deviation
We will now use an EXCEL spreadsheet to calculate the variance and standard deviation for the density of a paper clip.
Click on the worksheet called
Analysis
. It will open with the format shown below. This spreadsheet has already been programmed to calculate the mean, (value-mean), (value-mean)2, variance and standard deviation. All you need to do initially is type in your group's information in cells
E1-E8
and the density values recorded on the board (or from your RawData worksheet) in
column B
.
The statistics quantity called the
variance
(s
^{2}
) has already been programmed in cell
B96
. Its formula is
The
standard deviation
for the data has already been programmed in cell
B97
. Its formula is
After you have entered all of the data in ascending order, you will need to enter the total number of datapoints in
B93
. We will then record the values for the median in
E15
and the mode in
E18
. When the spreadsheet is completed, resave your file
What was the standard deviation for your EXCEL statistics spreadsheet?
Conclusion
Copy the following diagram on the bottom of your printout of Mass vs Volume. Place your group's value in its correct position on your diagram and write a conclusion stating where your group's result fell along this number line.
My group's density of _____ g/cm
^{3}
fell within ________ standard deviation(s) of the mean.
Lab Report
When finished, this lab report should include: a title page, Data Charts I, II, and the EXCEL graph of Mass vs Volume with your conclusion.
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