Lab+1+-+Measurements

= __Lab 1 - Measurements__ = The purpose of this lab was to discover and determine the accuracy of different measuring apparatuses.
 * Purpose**

It is hypothesized that individual measurements will vary slightly from the others, producing very minimal percent error; because of this, it is expected that experimental values for conversion factors and densities will differ only slightly from the expected values. This slight variation may be caused by small deviations in the measuring instruments in terms of their precision or the ways that they were read by observers. Also, the objects being measured could have possible deviations in their dimensions due to possible minor manufacturing faults. If there were no errors, then it would be expected that the experimental values would be exactly identical to the accepted values for the conversions factors and the densities of the objects.
 * Hypothesis**


 * Apparatus**
 * 1 ruler (empirical and metric)
 * 1 Vernier caliper
 * 1 micrometer
 * 1 scale
 * 1 piece of paper
 * 2 blocks
 * 2 spheres
 * 2 cylinders

For each side of the ruler, the piece of paper was measured 10 times. The cylinders’ and blocks’ lengths and widths were measured three times with calipers. The two spheres’ diameters were measured three times using a micrometer. The cylinders, spheres, and blocks were all weighed using an electronic scale. After the measurements were taken, the average dimensions were calculated to find the average area (for the paper) and volume (for the cylinders and spheres). After that, the densities for each cylinders and spheres were calculated from the average values and compared to the accepted densities. From there, the error and percent error were calculated.
 * Procedure**


 * **Figure 1.1 - Paper Dimensions** ||
 * **Trial** || **Length (L)** || **Width (W)** || **Length (L)** || **Width (W)** ||
 * **Number** || **cm** || **cm** || **in** || **in** ||
 * 1 || 18.21 || 6.63 || 7.156 || 2.625 ||
 * 2 || 18.11 || 6.62 || 7.156 || 2.625 ||
 * 3 || 18.29 || 6.61 || 7.125 || 2.625 ||
 * 4 || 17.99 || 6.52 || 7.125 || 2.500 ||
 * 5 || 18.13 || 6.59 || 7.125 || 2.625 ||
 * 6 || 18.20 || 6.60 || 7.156 || 2.594 ||
 * 7 || 18.20 || 6.60 || 7.125 || 2.594 ||
 * 8 || 18.18 || 6.61 || 7.188 || 2.563 ||
 * 9 || 18.08 || 6.51 || 7.125 || 2.563 ||
 * 10 || 18.12 || 6.69 || 7.125 || 2.625 ||
 * Average || 18.15 || 6.60 || 7.141 || 2.594 ||


 * **Figure 1.2 - Block 1 Dimensions** ||
 * **Trial** || **Length (L)** || **Width (W)** || **Height (H)** || **Length (L)** || **Width (W)** || **Height (H)** ||
 * **Number** || **cm** || **cm** || **cm** || **in** || **in** || **in** ||
 * 1 || 8.45 || 3.30 || 2.50 || 3.344 || 1.313 || 1.000 ||
 * 2 || 8.49 || 3.32 || 2.49 || 3.313 || 1.313 || 1.000 ||
 * 3 || 8.54 || 3.31 || 2.51 || 3.313 || 1.250 || 1.000 ||
 * Average || 8.49 || 3.31 || 2.50 || 3.323 || 1.292 || 1.000 ||


 * **Figure 1.3 - Block 2 Dimensions** ||
 * **Trial** || **Length (L)** || **Width (W)** || **Height (H)** || **Length (L)** || **Width (W)** || **Height (H)** ||
 * **Number** || **cm** || **cm** || **cm** || **in** || **in** || **in** ||
 * 1 || 8.80 || 4.21 || 1.89 || 3.438 || 1.688 || 0.667 ||
 * 2 || 8.75 || 4.21 || 1.89 || 3.438 || 1.656 || 0.750 ||
 * 3 || 8.71 || 4.20 || 1.88 || 3.438 || 1.656 || 0.750 ||
 * Average || 8.75 || 4.21 || 1.89 || 3.438 || 1.667 || 0.722 ||


 * **Figure 1.4 - Cylinder 1 Dimensions** ||
 * **Trial** || **Length (L)** || **Diameter (D)** || **Radius (R)** ||
 * **Number** || **cm** || **cm** || **cm** ||
 * 1 || 9.68 || 1.58 || 0.79 ||
 * 2 || 9.69 || 1.58 || 0.79 ||
 * 3 || 9.68 || 1.59 || 0.80 ||
 * Average || 9.68 || 1.58 || 0.79 ||


 * **Figure 1.5 - Cylinder 2 Dimensions** ||
 * **Trial** || **Length (L)** || **Diameter (D)** || **Radius (R)** ||
 * **Number** || **cm** || **cm** || **cm** ||
 * 1 || 6.10 || 1.62 || 0.81 ||
 * 2 || 6.10 || 1.63 || 0.82 ||
 * 3 || 6.10 || 1.63 || 0.82 ||
 * Average || 6.10 || 1.63 || 0.81 ||


 * **Figure 1.6 - Sphere 1 Dimensions** ||
 * **Trial** || **Length (L)** || **Diameter (D)** || **Radius (R)** ||
 * **Number** || **cm** || **cm** || **cm** ||
 * 1 || 2.540 || 2.540 || 1.270 ||
 * 2 || 2.534 || 2.534 || 1.267 ||
 * 3 || 2.523 || 2.523 || 1.262 ||
 * Average || 2.532 || 2.532 || 1.266 ||


 * **Figure 1.7 - Sphere 2 Dimensions** ||
 * **Trial** || **Length (L)** || **Diameter (D)** || **Radius (R)** ||
 * **Number** || **cm** || **cm** || **cm** ||
 * 1 || 2.533 || 2.533 || 1.267 ||
 * 2 || 2.521 || 2.521 || 1.261 ||
 * 3 || 2.519 || 2.519 || 1.260 ||
 * Average || 2.524 || 2.524 || 1.262 ||

Paper: L x W = 18.15cm x 6.60cm ≈ 120cm2 Block: L x W x H = 8.49cm x 3.31cm x 2.50cm ≈ 70.3cm3 Cylinder: πr2 x L = π(.81cm)2 x 6.1cm ≈ 4πcm3 | 17.045g/4πcm3 ≈ 1.3446g/cm3 Sphere: 4/3πr3 = 4/3π(1.262cm)3 ≈ 8.422cm3 | 65.775g/8.422cm3 ≈ 7.809g/cm3 % error = [|expected value - experimental value|/(expected value)] x 100% = [|16.39cm3/in3 - 16.37cm3/in3|/(16.39cm3/in3)] x 100% ≈ 0.122% error For each of the objects, the appropriate formula was used for finding its surface area or volume. The percent error was measured by using the average area/volumes to calculate an experimental value. From there, that value along with the expected values were plugged into the percent error equation to determine the percent error. Since it was found that the highest percent error was around 5.32% and the lowest error was around 0.122%, it can be inferred that the measurements taken were relatively accurate. Sources of error may have come from slightly uncalibrated instruments (Vernier caliper, micrometer, or incorrectly zeroed scale) or misreading the instruments that required reading by the human eye (ruler, Vernier caliper, and micrometer).
 * Analysis**

The original conclusion was supported based on the percent errors that were calculated in the studies. With the smallest error being near 0.122% and the largest being near 5.32%, it can be concluded that the percent errors were relatively small which indicates that the original data readings were very accurate and close to the actual measurement of the objects. Looking at the original measurements for both of the cylinders measured (see Figures 1.4 and 1.5), two of the three measurements in each column were the same. The third measurement was only 0.01cm away from the other measurements. For cylinder 2, the percent error was calculated to be about 1.135%, which is very low. This goes to show that with precise instruments and using the average measurement of several trials proves to be more accurate at determining the true measurements and physical features (density in this case) about the objects. With instruments that were even more accurate (such as the micrometer), the percent error was nearly 1/10 less of the percent error of some of the objects measured with a simple ruler or Vernier caliper. Sphere 2’s raw measurements (see Figure 1.7) deviated only 0.014cm from the other measurements in the same set at most, producing one of the lowest errors of 0.122%. © Kevin Trinh 2011
 * Conclusions**