Errors, Uncertainties and Measurements

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Abstract

Measurements are subject to errors which can sometimes deviate from the true value of an object. The experiment determined the %error (g/cm3) for density and different measuring data of a sphere through various measuring devices. It also aims to determine the deviation data of the sphere.

Results and Discussion

Table 1. Diameter and Density of Sphere
| Diameter of Sphere (cm)|
Trial| Foot Rule| Vernier Caliper| Micrometer Caliper|
1| 1.35 cm| 0.16 cm| 1.580 cm| .005 cm| 1.5865 cm| .0002 cm| 2| 1.50 cm| 0.01 cm| 1.585 cm| 0.00 cm| 1.5865 cm| .0002 cm| 3| 1.45 cm| 0.05 cm| 1.585 cm| 0.00 cm| 1.5853 cm| .0014 cm| 4| 1.55 cm| 0.04 cm| 1.590 cm| .005 cm| 1.5860 cm| .0007 cm| 5| 1.55 cm| 0.04 cm| 1.585 cm| 0.00 cm| 1.5865 cm| .0002 cm| 6| 1.50 cm| 0.01 cm| 1.585 cm| 0.00 cm| 1.5855 cm| .0012 cm| 7| 1.50 cm| 0.01 cm| 1.580 cm| .005 cm| 1.5865 cm| .0002 cm| 8| 1.50 cm| 0.01 cm| 1.590 cm| .005 cm| 1.5915 cm| .0048 cm| 9| 1.55 cm| 0.04 cm| 1.580 cm| .005 cm| 1.5865 cm| .0002 cm| 10| 1.60 cm| 0.09 cm| 1.590 cm| .005 cm| 1.5860 cm| .0007 cm| Mean Diameter| 1.51 cm| 1.585 cm| 1.5867 cm|

Average Deviation (a.d.)| 0.046| .0030| .00098|
Average Deviation of the Mean (A.D.)| 0.015| .0016| .00031| Volume (cm3)| 1.803 cm3| 2.089 cm3| 2.092 cm3|
Mass (g)| 16.41 g| 16.41 g| 16.41 g|
Experimental Value of Density (g/cm3)| 9.101 g/cm3| 7.855 g/cm3| 7.844 g/cm3| Accepted Value of Density (g/cm3)| 7.8 g/cm3| 7.8 g/cm3| 7.8 g/cm3| %Error for Density| 16.705%| 0.705%| 0.564%|

The diameter of a sphere using foot rule, vernier caliper and micrometer caliper is shown in Table 1. In order to get the accurate and precise measurements of each, ten trials are made. Micrometer caliper’s experimental value of 7.844 g/cm3 shows the most accurate and precise measurement based on the accepted value of density, which is 7.8 g/cm3. Vernier caliper...
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