Lab+1+Measurement

Measurement Lab


 * Purpose:**

The purpose of this measuring exercise is to gain experience using several measuring instruments and use the data collected to calculate areas, volumes, densities, conversion factors, and percent error for various different shapes.


 * Hypothesis:**

Since time constraints (amount of class time) limit the number of trials carried out for each measurement, it is expected that the experimental, individual measurements and their averages will differ slightly from the accepted values. Plus, different people will be using the measuring tools, so human error may also have a hand in the differentiations from the expected values. Also, it is predicted that the measurements taken with the micrometer will yield the lowest percent error because its measuring units are smaller (millimeters) than those of the other measuring instruments (centimeters and inches).


 * Apparatus:**

The following are a list of measuring tools and the objects subject to their measurements that are used in this lab.
 * Paper note card
 * English-SI ruler
 * Two blocks of different sizes
 * Vernier Caliper
 * Electronic Scale
 * Two small spheres
 * Micrometer


 * Procedure:**

1. The two dimensions of the note card, length and width, are measured using a ruler. Each dimension is measured 10 times with the metric side of the ruler, and then another 10 measurements are done for each dimension in inches. The averages, deviations, average deviations, and percent deviation are calculated using the collected for each dimension and unit. Then, the average lengths and widths of matching units are multiplied together to find the area. Next, the average length in centimeters is divided by the average length in inches to determine the experimental conversion factor. Then, the percent error is calculated using the experimental conversion factor and the accepted conversion factor of 2.540.

2. Then, a block is chosen and the length, width, and height are all measured three times in both centimeters and inches with the same ruler. Then, another block is chosen and the process used to measure the first block is repeated for the second block. Next, the averages are calculated for the length, width, and height for both units. Then, the average length, width, and height are multiplied together to determine the volume of the block in both centimeters and inches. After calculating the volumes, the volume in centimeters is divided by the volume in inches to determine the experimental conversion factor. Then, both the experimental and accepted conversion factor, which is 16.39 (cm^3/in^3) are used to calculate the percent error. The same calculation process is used for the second block.

3. After that, a cylinder is selected and by placing it on an electronic scale, its experimental mass is recorded. Then, the cylinder’s length and diameter are measured in centimeters with the caliper three times. For future calculation purposes, each diameter measurement is divided by two to determine the radius. Then, the second cylinder is measured using the same process as the first cylinder. For the first cylinder, the average radius is calculated and used along with the average length to calculate the volume of the cylinder. Then, the mass in grams is divided by the volume in cubic centimeters to determine the experimental mass density. Then, the experimental mass density and the accepted mass density that coincides with the cylinder are used to calculate percent error. The calculation process is repeated for the second cylinder.

4. Next, a sphere is put on an electronic scale to determine its mass and has its diameter measured three times with a micrometer in millimeters, which are then converted to centimeters. The diameter was then divided by two to determine its radius. The second sphere was measured using the same method as the first. Then, the average radius is calculated and plugged into the equation for volume for a sphere, which is V= (4/3) π r^3. Then, the mass in grams was divided by the volume in cubic centimeters to determine the experimental mass density, which along with the coinciding accepted mass density, is used to calculate the percent error. These calculations are repeated for the second sphere.


 * Data: **


 * Figure 1: Note card Measurements ||
 * Trial || Length (cm) || Width (cm) || Length (in) || Width (in) ||
 * 1 || 18.21 || 6.63 || 7.16 || 2.63 ||
 * 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 || 2.50 ||
 * 5 || 18.13 || 6.59 || 7.125 || 2.625 ||
 * 6 || 18.20 || 6.60 || 7.156 || 2.594 ||
 * 7 || 18.18 || 6.61 || 7.1875 || 2.563 ||
 * 8 || 18.20 || 6.60 || 7.125 || 2.594 ||
 * 9 || 18.08 || 6.51 || 7.125 || 2.563 ||
 * 10 || 18.12 || 6.69 || 7.125 || 2.625 ||
 * Average || 18.151 || 6.598 || 7.141 || 2.594 ||

Area= Length x width= 18.151 x 6.598= 119.76 cm^2 7.141 x 2.594= 18.524 in^2

Length (cm): Average deviation= .065 cm Percent deviation= .358% Percent deviation= (average deviation/ mean value) x 100= .065/18.151 x 100= .358

Width (cm) Average deviation= .0348 cm Percent deviation= .527%

Length (in) Average deviation= .019 in Percent deviation= .266%

Width (in) Average deviation= .032 in Percent deviation= 1.22%

Experimental Conversion factor= avg. length in cm/ avg. length in inches= 18.151/ 7.141= 2.543 cm/in

Accepted value= 2.540 cm/in

Error= I accepted value- experimental I= 2.543-2.540= .003

Percent error= (error/ accepted value) x 100 = .118%


 * Figure 2: Block 1 Measurements ||
 * Trial || Length || Width || Height || Length || Width || Height ||
 * No. || Cm || Cm || Cm || In || In || In ||
 * 1 || 8.45 || 3.30 || 2.50 || 3.344 || 1.313 || 1 ||
 * 2 || 8.49 || 3.32 || 2.49 || 3.313 || 1.313 || 1 ||
 * 3 || 8.54 || 3.31 || 2.51 || 3.313 || 1.25 || 1 ||
 * Average || 8.49 || 3.31 || 2.50 || 3.32 || 1.29 || 1 ||

Average Volume= length x width x height= 8.49 x 3.31 x 2.50= 70.255 cm^3 3.32 x 1.29 x 1= 4.283 in^3 Experimental Conversion Factor= Volume in cm/ Volume in inches= 16.403 cm^3/in^3

Accepted Value= 16.39 cm^3/in^3

Error= .013

Percent Error= .079%


 * Figure 3: Block 2 Measurements ||
 * Trial || Length || Width || Height || Length || Width || Height ||
 * No. || 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 || 3.44 || 1.656 || 0.75 ||
 * 3 || 8.71 || 4.20 || 1.88 || 3.4375 || 1.656 || 0.75 ||
 * Average || 8.753 || 4.207 || 1.887 || 3.438 || 1.667 || 0.732 ||

Volume (cm^3)= 69.487 cm^3 Volume (in^3)= 4.195 in^3

Experimental Conversion Factor= 16.564 (cm^3/in^3)

Accepted Value= 16.39 (cm^3/in^3)

Error= .174 (cm^3/in^3)

% Error= 1.062%


 * Figure 4: Cylinder 1 Measurements ||
 * Trial || Length (cm) || Diameter (cm) || Radius (cm) ||
 * 1 || 9.68 || 1.58 || 0.79 ||
 * 2 || 9.69 || 1.58 || 0.79 ||
 * 3 || 9.68 || 1.59 || 0.795 ||
 * Average || 9.68 || 1.58 || 0.792 ||

Volume= ( π radius^2) x height= 3.14 x (.792^2) x height= 19.0696 cm^3

Mass= 22.880 grams

Experimental Mass Density= mass/ volume= 22.880/ 19.0696= 1.174 g/ cm^3

Accepted Mass Density= 1.24 g/ cm^3

Error= .0402 g/cm^3

% Error= 3.24%


 * Figure 5: Cylinder 2 Measurements ||
 * Trial || Length (cm) || Diameter (cm) || Radius (cm) ||
 * 1 || 6.10 || 1.62 || 0.81 ||
 * 2 || 6.10 || 1.63 || 0.815 ||
 * 3 || 6.10 || 1.63 || 0.815 ||
 * Average || 6.10 || 1.63 || 0.813 ||

Volume= 12.667 cm^3

Mass= 17.045 grams

Experimental Mass Density= 1.354 g/cm^3

Accepted Mass Density= 1.36 g/ cm^3

Error= .006 g/cm^3

% Error= 0.441%


 * Figure 6: Sphere 1 Measurements (Yellow Plastic Material) ||
 * Trial || Length (cm) || Diameter (cm) || Radius (cm) ||
 * 1 || 2.540 || 2.540 || 1.270 ||
 * 2 || 2.534 || 2.534 || 1.267 ||
 * 3 || 2.523 || 2.523 || 1.2615 ||
 * Average || 2.532 || 2.532 || 1.266 ||

Volume= (4/3) π radius^3= (4.3) x 3.14 x 1.266^3= 8.499 cm^3

Mass= 9.860 grams

Experimental Mass Density= 1.160 g/ cm^3

Accepted Mass Density= 1.15 g/ cm^3

Error= 0.01 g. cm^3

% Error= 0.870%


 * Figure 7: Sphere 2 Measurements (Steel Material) ||
 * Trial || Length (cm) || Diameter (cm) || Radius (cm) ||
 * 1 || 2.533 || 2.533 || 1.2665 ||
 * 2 || 2.521 || 2.521 || 1.2605 ||
 * 3 || 2.519 || 2.519 || 1.2595 ||
 * Average || 2.524 || 2.524 || 1.2620 ||

Volume= 8.419 cm^3

Mass= 65.775 grams

Experimental Mass Density= 7.813 g/ cm^3

Accepted Mass Density= 7.8 g/cm^3

Error= .013 g/ cm^3

% Error= 0.167%


 * Analysis:**

Area= Length x width= 18.151 x 6.598= 119.76 cm^2

Percent deviation= (average deviation/ mean value) x 100= .065/18.151 x 100= .358

Experimental Conversion factor= avg. length in cm/ avg. length in inches= 18.151/ 7.141= 2.543 cm/in

Error= I accepted value- experimental I= 2.543-2.540= .003

Percent error= (error/ accepted value) x 100 = .118%

Average Volume of Block= length x width x height= 8.49 x 3.31 x 2.50= 70.255 cm^3

Experimental Conversion Factor= Volume in cm/ Volume in inches= 16.403 cm^3/in^3

Volume of Cylinder= ( π radius^2) x height= 3.14 x (.792^2) x height= 19.0696 cm^3

Experimental Mass Density= mass/ volume= 22.880/ 19.0696= 1.174 g/ cm^3

Volume of Sphere= (4/3) π radius^3= (4.3) x 3.14 x 1.266^3= 8.499 cm^3

The largest percent error calculated was 3.24% for cylinder 1 and the lowest was 0.079% for Block 1. Since the highest percent error is only 3.24%, I can conclude that my results are relatively accurate. The percent error calculations ranged from 0.079% to 3.24%, which means that there was a slight variation from the accepted quantities, but not a considerable variation. Although the data differs slightly from the averages, the conversion factors and densities are still close to the accepted values, but there was still an element of error. Some of this differentiation from the accepted may come from a limited number of trials, a scale that is not zeroed, or a measuring tool that is not calibrated. These measuring tools could include the caliper or the micrometer.

** Conclusion: ** The hypothesis was partially supported by the data. The data did vary slightly from the average, but the measurements made with the micrometer did not have the lowest percent error. In fact, the lowest percent error was 0.079%, which came from measurements made with the ruler for block 1. This may be because the sphere needs to be put in the micrometer where it measures its diameter, but it could have easily been placed somewhere where the instrument was measuring a chord. The highest percent error was only 3.24%, which came from cylinder 1. Since cylinder 1 was measured with the Vernier caliper, then the caliper may not have been calibrated. If this experiment could be repeated, it might produce more accurate data if more trials were carried out, more time was spent assuring that the sphere’s diameter was being measured instead of a chord, and the calipers were calibrated more often. In the end, it all comes down to allowing more time for experimentation.