Download 04-Density of Shot - Blue Valley Schools

Name (LAST, First) ________________, ____________
Date ___ / ___ / ______ Block 1 2 3 4 5 6 7 8
Experiment #4: The Density of Metal Shot
Introduction
Archimedes, a Greek physicist and mathematician who lived in
the third century B.C., was said to have discovered the
principle of water displacement while bathing, and
subsequently ran through the streets naked, shouting "Eureka!"
which is Greek for "I have found it!" This method may be
used by clothed scientists as well to determine the volume of
irregularly-shaped objects that will completely submerge in
water.
Obtain and weigh a small weighing dish. Place approximately
1.5 x 102 g of dry metal shot into the dish and weigh. Record
the masses to the nearest 0.01 g.
With this technique, the density of metal shot will be simple to
determine, but can the density of an unknown metal provide
enough information to identify it and distinguish it from other
metals?
Tilt the graduated cylinder to a 45° angle and slowly pour the
shot into the cylinder. Set the cylinder upright and record the
volume.
Obtain, from the supply shelf, a 100 mL graduated cylinder.
Fill approximately half-full with tap water. Record this volume
to correct number of significant digits (estimate the last digit,
±0.1mL). When reading volume, read the level at the bottom
of the meniscus.
Pour the shot into the recovery bucket and rinse the cylinder
1.
2.
3.
4.
Prelab Assignment
Read about Density:
a. Use the index in your text to find appropriate pages.
b. See web resources below for Water Displacement and
Reading Volume.
152.3 g of shot is placed into a graduated cylinder. The
volume of water in the cylinder is initially 55.4 mL, which
rises to 68.6 mL with the addition of the shot. The sample
consisted of 123 spherical shot.
a. Calculate the density of the shot.
b. Determine the average mass, volume, and diameter
for an individual shot.
In your Work Record, create a blank table for data. The
column headings should be “Description” and “Value”.
Create a separate, blank table for calculations.
kg
with tap water. Calculate density 

place your value in the class data table.
1.
2.
3.
Experimental Question
Can density be used to identify a particular type of metal?
Experiment Overview
You will collect mass and volume data for a sample of metal
shot and then calculate the density of this unknown metal. You
will then attempt to determine the identity of the metal.
Procedure
4.
5.
Calculations
Calculate the specific gravity for your sample.
Data Analysis
For the class density data calculate the mean, standard
deviation, 95% range, and percent sigma.
Results
Using a table of metal densities as a reference, find all
metals that have a density within the 95% range. These are
the metals, with 95% surety, that your sample could be.
This also means that there is a 5% chance that the actual
density is outside of the 95% range. Record the identity
and correct density for each metal within this range.
Determine the percent error between your experimental
value and the correct density for each possibility. Repeat,
using average class density in place of your experimental
density.
Comment on accuracy and precision. Support each answer
with appropriate numerical evidence.
Web resources: (Extra credit if you find a web resource that I will plan on using next year.)
Water Displacement Method:
http://ch185.semo.edu/comp2obj/comp2obj.html
Meniscus and Reading Volume:
http://www.uwplatt.edu/chemep/chem/chemscape/labdocs/catofp/measurea/scales/scales.htm
Density Information: You are going to have to search.
http://www.chemicalelements.com/index.html
http://micronmetals.com/
http://www.atlanticmetals.com
http://en.wikipedia.org/wiki/Periodic_table
http://www.mcelwee.net/#%5B%5BDensities%20of%20Various%20Materials%5D%5D
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 for the shot and
m3 
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Name (LAST, First) ________________, ____________
Date ___ / ___ / ______ Block 1 2 3 4 5 6 7 8
TI-83 Skills
Entering the data, 1 dimension, Statistics:
Buttons to press: STAT / EDIT
Notes:
 Enter your data in the appropriate lists. For this I will assume that L1 contains the data to be analyzed.
 To clear a list, do NOT use the DEL button. Position the cursor on the L1 symbol, press CLEAR, then
press ENTER. The list should be emptied but remain.
Statistics, One Variable
Buttons to press: STAT / CALC / 1: 1-Var Stats / L1 / ENTER
The command you should see on the screen:
1-Var Stats L1
The results should look like this (I have included a definition and description):
Symbol Pronounced
x
x-bar
x
x
Sx
σx
n
minX
Q1
Med
Q3
maxX
sigma x
2
Definition
arithmetic mean
Description
center of the data
summation of all x values
sigma x squared summation of all x2 values
sigma x
minimum x
que one
median
que three
maximum x
standard deviation of a sample
standard deviation of a population
number of x values
minimum x value
1st quartile score
middle score
3rd quartile score
maximum x value
spread
middle value
Laboratory Statistical Calculations
Simple Statistics:
x is the arithmetic mean, a measure of central tendency.
σ is standard deviation, a measure of data spread.
95% Range: Acceptable range within Spread of Data:
95% Range
Upper bound of acceptable values: x + 2 σ
Lower bound of acceptable values: x – 2 σ
 The range within which 95% of the data values lie. The 95% that falls within the range is usually assumed
to be good data. The 5% that falls outside of the range is usually assumed to be in error.
 The correct, or accepted, value has a 95% chance of falling within this range.
There is a 5% chance that the correct value is outside of this range.
Accuracy: Relative Error and Percent Error
Measured = experimentally measured value, either an individual value or the mean of the measured values.
Accepted = value accepted as correct
Relative Error = Measured – Accepted
Percent Error = %e = Relative Error / Accepted * 100
In first-year physics a percent error value between – 5% and +5% inclusive is usually considered to be
acceptable. This indicates data points that are close to the accepted value. A value greater than 5% usually
indicates sloppy lab technique and/or failure to follow instructions. |%e| ≤ 5% implies accurate measurement(s).
Precision: Percent Sigma
Percent Sigma = %σ =

x
x 100
In first-year physics a percent sigma value less than or equal to 5% is usually considered to be acceptable. This
indicates data points that are grouped close to each other. |%σ| ≤ 5% implies precise measurements.
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