Accuracy, Precision, Variation and Tolerance Module

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## Day 2 Lesson: Tolerance, An Automotive Lab

#### Activity 1:

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

 Stem Diameter Guide Diameter Guide Clearance Student 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:
1. 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?
2. Where is the tolerance depended on? (e.g., size of the car? weight of the car? etc.)
3. 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?
4. 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?
5. 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 pre-1983 and post-1983 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 triple-beam 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 stem-and-leaf 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)

 Pre-1983 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

 Post-1983 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 stem-and-leaf 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.

Stem-and-Leaf-Diagram for Pre-1983 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

1. By looking at the stem-and-leaf 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.)
2. Using the spreadsheet software or a calculator, find the mean (average) densities for the older and the newer pennies.
3. 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?
4. What is the range of density data gathered by your class for the newer pennies?
5. What are some possible explanations for this range in data?
6. What does the range suggest about the precision of your measurements?

#### 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.

1. Using your stem-and-leaf-diagram, estimate what proportion of the newer pennies is zinc and what proportion is copper.
2. 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?
3. 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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