Lab+1

The purpose of this lab was to allow students to practice making precise measurement of a card, cylinder, and sphere, with a ruler, Vernier caliper, and a micrometer. It was also expected for students to use the correct number of significant figures and to use different formulas with ease. These previously learned formulas included percent error, average deviation, volume, and mass density.
 * Lab #1: Measurement**
 * Purpose/Background:**

It is hypothesized that all of the measurements made in this lab will be very near the actual values. This is expected because all of the measuring equipment being used is generally very accurate. It is expected that the percent error will generally be about 5% to 10%. In a perfect world the percent error would be 0% although this is not realistic because at some point the measurement must be estimated because it is impossible to measure some very small units of measurement.
 * Hypothesis:**


 * Apparatus:**
 * Card
 * Ruler
 * Vernier caliper
 * Micrometer
 * 2 cylinders
 * 2 blocks
 * 2 spheres
 * Balance

//Part A//: Get a notecard and using a ruler take ten measurements of the length and width of your card in centimeters. Then, measure the card in inches. Calculate the mean, average deviation, and percent deviation. Lastly, calculate the area of the card and find the error and percent error using the accepted value which is 2.54 cm/in. 3
 * Procedure:**

//Part B:// Choose a block and measure the dimensions of it with a ruler in inches and centimeters three times and record the data. Next, find the average length, width, and height of the block in both inches and centimeters and then calculate the volume of the block in cubic centimeters and inches. Find the experimental conversion factor by dividing the average volume of the block in cubic centimeters by the volume in cubic inches. Use the accepted value, which is 16.39 cm^3/in^3, to find the error and percent error. Choose a second block of a different size and repeat these steps.

//Part C:// Choose a cylinder and measure the length and diameter three times with a Vernier caliper. Calculate the average radius and length and use this to calculate the volume of the cylinder. Then, using a balance, find the mass of the cylinder and record the number in grams. Calculate the mass density and compare the value to the accepted value which is 1.24 g/cm^3 for one and 1.36 g/cm^3 for another. Use these values to calculate the error and percent error. Repeat these steps for a second cylinder.

//Part D:// Choose a sphere and measure the diameter three times using a micrometer. Use a balance to find the mass of the sphere. With this value, calculate the mass density of the sphere and compare this value to the accepted values which is 2.7 g/cm^3 and find the error and percent error.

//Part A// Note Card Length: Mean value: 20.25 cm Average deviation: .009 cm % deviation: .9%
 * Data:**
 * Trial || Length L || Width W || Length L || Width W ||
 * No. || Cm || Cm || In || In ||
 * 1 || 20.26 || 10.00 || 8.00 || 3.94 ||
 * 2 || 20.30 || 10.00 || 8.00 || 3.95 ||
 * 3 || 20.24 || 10.00 || 8.00 || 3.97 ||
 * 4 || 20.23 || 10.00 || 8.00 || 3.95 ||
 * 5 || 20.23 || 10.00 || 8.00 || 3.94 ||
 * 6 || 20.25 || 10.00 || 8.00 || 3.94 ||
 * 7 || 20.22 || 10.00 || 8.00 || 3.94 ||
 * 8 || 20.28 || 10.00 || 8.00 || 3.94 ||
 * 9 || 20.27 || 10.00 || 8.00 || 3.96 ||
 * 10 || 20.25 || 10.00 || 8.00 || 3.94 ||

Mean value: 8 in Average deviation: 0 in % deviation: 1.3%

Width: Mean value: 10 cm Average deviation: 0 cm % deviation: 0%

Mean value: 3.95 in Average deviation: .012 in % deviation: 1.2%

Area: Area: 202.5 cm² Area: 31.60 in² Experimental conversion factor 2.53 cm/in Accepted value 2.540 cm/in Error .01 cm/in % Error .394 %

//Part B// Block 1
 * Trial || Length L || Width W || Height H || Length L || Width W || Height H ||
 * No. || Cm || Cm || Cm || In || In || In ||
 * 1 || 10.15 || 5.35 || 1.19 || 4.13 || 2.13 || .49 ||
 * 2 || 10.15 || 5.35 || 1.19 || 4.13 || 2.13 || .49 ||
 * 3 || 10.15 || 5.35 || 1.19 || 4.13 || 2.13 || .49 ||

Average Volume: 64.6 cm³ Average Volume: 4.3 in³ Experimental conversion factor: 15 cm³/in³ Accepted Value: 16.39 cm³/in³ Error: 1.39 cm³/in³ % error: 8.5%

Block 2
 * Trial || Length L || Width W || Height H || Length L || Width W || Height H ||
 * No. || Cm || Cm || Cm || In || In || In ||
 * 1 || 7.71 || 5.25 || 2.59 || 3.04 || 2.10 || 1.0 ||
 * 2 || 7.71 || 5.25 || 2.59 || 3.04 || 2.10 || 1.0 ||
 * 3 || 7.71 || 5.25 || 2.59 || 3.04 || 2.10 || 1.0 ||

Average Volume: 6.4 cm^3 Average Volume: 105 in^3 Experimental conversion factor: 16 cm^3/in^3 Accepted Value: 16.39 cm^3/in^3 Error: .39 cm^3/in^3 % error: 2.4%

//Part C// Cylinder 1
 * Trial || Length L || Diameter D || Radius R ||
 * No. || Cm || Cm || Cm ||
 * 1 || 9.19 || 2.16 || 1.08 ||
 * 2 || 9.19 || 2.16 || 1.08 ||
 * 3 || 9.19 || 2.16 || 1.08 ||

Volume: 33.68 cm³ Mass: 25.62 g Experimental mass density: .76 g/cm³ Accepted mass density: 1.24 g/cm³ Error: .48 g/cm³ % Error: 38.71 %

Cylinder 2
 * Trial || Length L || Diameter D || Radius R ||
 * No. || Cm || Cm || Cm ||
 * 1 || 6.15 || 1.65 || .83 ||
 * 2 || 6.15 || 1.65 || .83 ||
 * 3 || 6.15 || 1.65 || .83 ||

Volume: 13.15 cm³ Mass: 17.05 g Experimental mass density: 1.30 g/cm³ Accepted mass density: 1.36 g/cm³ Error: .06 g/cm³ % Error: 4.41 %

//Part D// Sphere 1
 * Trial || Length L || Diameter D || Radius R ||
 * No. || Cm || Cm || Cm ||
 * 1 || 1.65 || 1.65 || .83 ||
 * 2 || 1.65 || 1.65 || .83 ||
 * 3 || 1.65 || 1.65 || .83 ||

Volume: 2.35 cm³ Mass: 6.03 g Experimental mass density: 2.57 g/cm³ Accepted mass density: 2.7 g/cm³ Error: .13 g/cm³ % Error: 4.81 %

Sphere 2
 * Trial || Length L || Diameter D || Radius R ||
 * No. || Cm || Cm || Cm ||
 * 1 || 2.52 || 2.52 || 1.26 ||
 * 2 || 2.52 || 2.52 || 1.26 ||
 * 3 || 2.52 || 2.52 || 1.26 ||

Volume: 8.38 cm³ Mass: 20.06 g Experimental mass density: 2.39 g/cm³ Accepted mass density: 2.7 g/cm³ Error: .31 g/cm³ % Error: 11.48 %


 * Analysis:**

Mean Value= (20.26+20.30+20.24+20.23+20.23+20.25+20.22+20.28+20.27+20.25)/10 Average Deviation= |average-each value| Percent Deviation= average deviation x100 Error= 2.53-2.54=.01 % Error= (2.53-2.54)/2.54 x100=.394%

Volume= length x width x height Expiremental conversion factor=64.6cm³/4.3in³=15cm³/in³ Error= 15cm³/in³-16.39cm³/in³=1.39cm³/in³ % error= (15-16.39)/16.39 x100=8.5%

Volume of cylinder- V=πr²L Expiremental conversion factor= 25.62g/33.68cm³=.76g/cm³ Error=.76-1.24=.48g/cm³ % error=(.76-1.24)/1.24 x100=38.71% Expiremental conversion factor= 17.05g/13.15cm³=1.30g/cm³ Error= 1.36-1.30=.06g/cm³ % error=(1.30-1.36)/1.36 x100=4.41%

Volume of sphere- V=3/4πr³ Expiremental mass density = 6.03g/2.35cm³=2.67g/cm³ Error=2.7-2.57=.13g/cm³ % error=(2.57-2.7)/2.7 x100=4.81% Expiremental mass density = 20.06g/8.38cm³=2.39g/cm³ Error=2.7-2.39=.31g/cm³ % error=(2.39-2.7)/2.7 x100=11.48%

The analysis shows that most of the measurements and calculations are mostly accurate with a few exceptions. The largest error is 38.71% which is not very accurate at all, but the others were near 5%-10%. The error could be due to inaccurate readings or measuring tools or simply because at some point an estimation was required.

The hypothesis that stated the percent error would be 5%-10% was not supported. The percent error for cylinder 1 and sphere 2 were both over 10%. Sphere 2 had a percent error of 38.71% which was way off. The others were in the range from 5%-10% except for cylinder 1 which was 11.48% which was very close. The measuring tools were mostly accurate with a few exceptions. In the future, measuring tools can be made more accurate and easier to read more precisely so there is less error. The lab could be altered so that the objects are more clearly labeled so there can be no confusion as to what material is which. This would help determine the accepted mass density more accurately. In general, this was a good lab to practice measuring with several different tools and using different important formulas.
 * Conclusion:**