Activity 1:
Students at Davea:
Measure valve guides and valve stems and record the measurements to a
spreadsheet
Student

Stem Diameter

Guide Diameter

Guide Clearance

INT

EXH

INT

EXH

INT

EXH

1

______

______

______

______

______

______

2

______

______

______

______

______

______

3

______

______

______

______

______

______

4

______

______

______

______

______

______

5

______

______

______

______

______

______

6

______

______

______

______

______

______

7

______

______

______

______

______

______

8

______

______

______

______

______

______

*Also enter the manufacturers' specifications for the cars
that you take the measurements.
FOR ALL STUDENTS:
 Compare the measurements with the manufacturers'
specifications and find the amount of tolerance (the range of variation
permitted in maintaining a specified dimension in machining a piece).
Compare the tolerance for several cars that are manufactured from the
same company. Do you find any trends in the variation of the tolerance
for certain manufactures?
 Where is the tolerance depended on? (e.g., size of the car?
weight of the car? etc.)
 Look carefully at the measurements of INT (and/or EXH)
(Stem Diameter, or Guide Diameter of Guide Clearance) for different
cars. Do you see and differences/similarities/trends?
 Compare the tolerances between Stem Diameter and Guide
Diameter for different car manufacturers. Do you see any
differences/similarities? Does this have to do with the engine
performance?
 Compare the "absolute" and "relative" tolerances of
different cars. For example, a relative tolerance has to do with the
idea that for small measurements there is limited range of variation;
for larger measurements, the tolerance is larger too. Is that true in
this situation, if you compare the Stem Diameter (and/or Guide
Diameter) from different car manufacturers?
(Optional lab for the high school students in DuPage county):
In this lab you will calculate the densities of pre1983 and post1983
pennies. You will find different densities since the older pennies
contain only copper, while the newer ones contain both copper and zinc,
making them less dense. With a partner, use a triplebeam balance to
find the mass of the pennies a graduated cylinder to measure their
volume (via water displacement). Then make use of the density formula D
= M/V, recording your answers in grams per cubic milliliter (g/mL). It
is recommended that about ten to fifteen pennies be used (of each type)
for better accuracy. (Instructor: Students who are very concerned about
accuracy may wish to find the mass and volume of the exact same
pennies, finding the mass first while they are still dry. A short
discussion before the lab regarding why it should not matter how many
pennies are used and why the answer does not need to be divided by the
number of pennies may be in order.)
With the other pairs of students in the class, there should be enough
density data to make a nice stemandleaf diagram. After you and your
partner calculate the density of your pennies, display your
calculations on the board in a table. An example is shown below.
Density Table (g/ml)

Pre1983

8.95

8.61

8.82

8.97

9.32

8.93

8.74

8.91

9.19

9.02

8.59

9.10

8.90

9.56

8.96

9.08

8.85

8.95

9.26

8.81

8.73

9.02

9.01

8.77


Post1983

8.04

8.09

7.84

8.17

7.95

8.07

7.67

8.05

8.10

7.99

8.08

8.18

8.06

8.16

8.03

7.89

7.83

7.85

7.90

8.00

7.66

7.9

8.19

7.75


You can then use the data to make a separate stemandleaf
diagram for the each type of penny as shown below. Grams and tenths of
grams together should make up the stems (left side of the table);
hundredths of grams will comprise the leaves.
StemandLeafDiagram for Pre1983 Pennies

85

9

86

1

87

3 4 7

88

1 2 5

89

0 1 3 5 5 6 7

90

1 2 2 8

91

0 9

92

6

93

2

94


95

6

 By looking at the stemandleaf diagram, describe how the
density measurements vary. What do you think is the best approximate
value for the density of older pennies to the nearest tenth of a g/mL?
Why? (Here "best" means the density that is most likely closest to the
true density of the pennies.)
 Using the spreadsheet software or a calculator, find the
mean (average) densities for the older and the newer pennies.
 How close were your measurement to the values found in
numbers 1 and 2 above? What does this probably say about the accuracy
of your measurement?
 What is the range of density data gathered by your class
for the newer pennies?
 What are some possible explanations for this range in data?
 What does the range suggest about the precision of your
measurements?
Activity 2:
Copper has a density of 8.96 g/mL, and zinc has a density of
7.14 g/mL. Use this information to answer the following questions.
 Using your stemandleafdiagram, estimate what proportion
of the newer pennies is zinc and what proportion is copper.
 If you were to ask several people at random to calculate
the densities of the pennies that they happened to have in their
pockets, would you expect them to report nearly identical answers? Why
or why not? How could you determined who had the highest proportion of
older pennies?
 Suppose that in the future the value of copper rises
relative to that of zinc, prompting the government to increase the zinc
content of pennies to 90%. About what would expect to find for the
density of these pennies? Explain.
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