09-01-04

Section 30

Amanda Collins

John ?

This laboratory experiment looks at the mass and diameter of seven steel

ball bearings, using a vernier caliper to determine diameter, and an

electronic analytical balance to determine mass. Graphical data analysis

then allows us to observe the relationships between mass and diameter and

to obtain a trendline in order to determine the diameter of an unknown ball

bearing.

Section I

Data Table 1: Mass and Diameter (D) of Ball Bearings

|Mass (g) |Diameter (mm) |D^2 |D^3 |1/D |1/D ^2 |1/D^3 |log(D) |10^D | |1

|1.05 |6.3 |39.69 |250.047 |0.15873 |0.025195263 |0.003999 |0.799340549

|1995262.315 | |2 |2.04 |7.8 |60.84 |474.552 |0.128205 |0.016436555

|0.002107 |0.892094603 |63095734.45 | |3 |3.52 |9.4 |88.36 |830.584

|0.106383 |0.011317338 |0.001204 |0.973127854 |2511886432 | |4 |5.6 |11

|121 |1331 |0.090909 |0.008264463 |0.000751 |1.041392685 |1E+11 | |5 |6.19

|11.3 |127.69 |1442.897 |0.088496 |0.007831467 |0.000693 |1.053078443

|1.99526E+11 | |6 |7.96 |12.4 |153.76 |1906.624 |0.080645 |0.006503642

|0.000524 |1.093421685 |2.51189E+12 | |7 |11.9 |14.1 |198.81 |2803.221

|0.070922 |0.005029928 |0.000357 |1.149219113 |1.25893E+14 | |

Graph 1 with trendline:Graph 2 with trendline:

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Graph 3 with trendline:Graph 4 with trendline:

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Graph 5 with trendline:Graph 6 with trendline:

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Graph 7 with trendline:Graph 8 with trendline:

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Section II

Using our straight line formula from Graph 2, y=26.133x – 18.832, the

predicted value for the diameter of the unknown ball bearing is y = 32.1

mm. This value is inaccurate, possibly due to errors in measurement of the

ball bearings.

1. Density of each ball bearing:

1: 0.17 g/mm3

2: 0.26 g/mm3

3: 0.37 g/mm3

4: 0.51 g/mm3

5: 0.548 g/mm3

6: 0.642 g/mm3

7: 0.844 g/mm3

2. The average density of the steep ball bearings is 0.48 g/mm3. If the

known density of steel is 0.785 g/mm3, the average obtained by our

measurements is inaccurate.

3. Three significant figures ought to be reported for the slope and y

intercept in the trendline analysis, using the equation from Graph 2, due

to the value for x having three figures.