Evaluating Diverse Measuring Equipment - Lab Report Example

Summary Sheet Objective The core purpose of this study is to measure diverse objects’ lengths, masses, which will be essential in computing their volumes and densities with the aid diverse measuring lab equipments. Method Experiment’s procedure entailed taking lengths and diameters readings of copper wire together with diverse cylindrical objects to compute their densities besides their volumes (Wilson & Cecilia 243). This was via tabulating four independent readings coupled with taking their mean as the final and correct reading. Results Regardless of the experiment carried out with high level of keenness, readings’ deviations were inevitable owing to the unintentional tools’ errors. Besides, the mode of reading especially approximations and positioning of a person’s reading view could have also contributed to the errors. Table 1 Value of error = 0.354 Table 2 Percentage error = 1.96% Applications Knowledge concerning diverse measurements and their quantities is a very essential especially in fabrication sectors, for illustration, engineering besides other normal human activities. Calculations Measurement of Length, Mass, Volume and Density Introduction Measurement is an essential aspect mainly utilized in the scientific field to quantify diverse forms of matter. This entails determining the objects’, quantity of matter, volume and their densities (Wilson & Cecilia 242). However, an object’s exact measurement despite one being an expert, accuracy mainly relies on the equipments a person utilizes to take diverse measurements. This is due to the imperfections, which result from the equipments’ errors while a researcher is taking measurements of different types of matter or their parts. Therefore, it is essential for the researcher to have adequate knowledge regarding how to minimize errors via being able to manipulate the readings one attains while measuring. Since this varies across the equipments, where some are complex especially if one lacks proper knowhow regarding particular equipment (Wilson & Cecilia 39). The study’s focus encompasses measurements of diverse objects coupled with determining their lengths, mass, volume and densities. Objective: The core purpose of this study is to measure diverse objects’ lengths, masses, which will be essential in computing their volumes and densities by using diverse measuring equipments. Apparatus Triple beam balance English ruler’ Metric ruler Vernier Micrometer caliper Three cylindrical diverse metal rods Aluminum Brass Iron Length of a copper wire Method 1. The initial step was to take the readings of a copper wire with the help of a metric ruler. This is by placing the wire on the metric rule, reading the positions of the two sides and estimating the readings to approximately tenth of a millimeter. Then developing four sets of independent measurements to approximately 0.01cm in centimeters by estimating using diverse parts of the meter rule 2. The estimation of wire’s length to a tenth inch was by the use of English ruler. This entailed using diverse sections of the ruler coupled with developing set of four independent measurements. 3. The diameter of the copper wire was measured with the aid of a micrometer caliper where the measurements’ approximation was 0.0001cm. To increase the accuracy of the study, it entailed obtaining six independent recordings in a table. 4. Individual volumes and densities’ computations followed the obtaining of fundamental measurements coupled with appropriate averaged recordings. Results Table 1 Standard deviation = √ (Sum of square deviations/ (n-1)) = √ (0.125/ (4-1)) = 0.2041 Value of error = 0.354 Table 2 Standard deviation = √ (Sum of square deviations/ (n-1)) = √ (0.0099815/ (4-1)) = 0.057681 Percentage error = 1.96% Table 5 Object used Density computed, g/cm3 Density from table IV Percent error Aluminum cylinder 2.814 2.7 6.333 ZN cylinder 7.165 7.14 1.62 SN cylinder 7.060 7.4317 5.07 Copper wire 510 8.96 1.083 Irregular solid 12.0357 12.2867 2.043 Despite the experiment carried out with high level of keenness to shun any possible errors that may emanate from carelessness or readings’ improper taking, they were inevitable. Mainly, the source of errors in this study that have prompted the results to deviate from the ordinary expected readings is due to, Equipments’ prior errors, which were inherent in them, hence during the experiment they were inevitable. Sometimes there might be unintentional and excessive force when adjusting the anvils or jaws to touch the edges of diverse objects. There was high possibility of diverse materials particles, for instance, dust that was on the measuring edges or objects. Probably there was incorrect reading positioning view of the reader especially when using meter rulers to take the lengths of diverse wires. Applications The knowhow concerning diverse measurement tools and quantities are of great importance in all human aspects. Since diverse activities, normally their completions cannot be effective without proper knowledge regarding how they should appear, which is also evident in various specializations (Wilson & Cecilia 39). For illustration in the engineering where each activity entails taking measurements and readings meant for fabrication of diverse products. Data Table 1: Measurement of wire length using a Metric Ruler Ruler Readings Lengths Deviations Deviations squared Left End Right End 134mm 201mm 67 -0.5 0.25 130mm 298mm 68 0.5 0.25 140mm 207.5mm 67.5 0 0 20mm 87.5mm 67.5 0 0 Average Values 67.5 0 0.125 Value of error = 0.354 Mean = Total lengths/frequency (n) = 67.5 mm Then computing standard deviation Frequency (n) = 4 Sum of deviations = -0.5 +0.5 = 0 Sum of squared deviations = 0.25 + 0.25 = 0.125 Therefore, standard deviation = √ (Sum of square deviations/ (n-1)) = √ (0.125/ (4-1)) = 0.2041 Table 2: Measurement of a wire length using an English Ruler Ruler Readings Lengths Deviations Deviations squared Left End Right End 5 7.625 2.625 -0.83 0.006889 5.5 8.28 2.78 0.072 0.005184 6.75 9.4 2.65 -0.058 0.003364 1.125 3.9 2.775 0.067 0.004489 Average Values 2.707 0.0285 0.0099815 Value of error = 0.071 Then computing standard deviation Frequency (n) = 4 Sum of squared deviations = 0.006889 + 0.005184 + 0.003364 + 0.004489 = 0.0099815 Therefore, standard deviation = √ (Sum of square deviations/ (n-1)) = √ (0.0099815/ (4-1)) = 0.057681 Table 3: The length and diameter of metal cylinders using a vernier caliper Zero reading 1 2 3 4 Average Length, Aluminum cylinder 8.65 8.65 8.65 8.64 8.647 Length, ZN cylinder 3.50 3.49 3.50 3.50 3.503 Length, SN cylinder 3.37 3.35 3.38 3.37 3.37 Diameter, Aluminum cylinder 1.90 1.89 1.90 1.91 1.9 Diameter, ZN cylinder 1.90 1.89 1.90 1.90 1.8975 Diameter, SN cylinder 1.91 1.89 1.89 1.89 1.895 Table 4: Diameter of a copper wire using a micrometer caliper 1 2 3 4 5 6 Average Zero reading 0.000 0.000 0.000 0.000 Reading with wire 0.327 0.328 0.325 0.325 0.326 0.328 0.326 Diameter wire 0.327 0.328 0.325 0.325 0.326 0.328 0.326 Table 5: Determination of Density Object used Mass, g Length, cm Diameter, cm Volume, cc(cm3) Density computed, g/cm3 Density from table IV g/cm3 Percent error Aluminum cylinder 70.35 g 8.647 1.9 25 cm3 2.814 2.7 6.333 ZN cylinder 71.65 g 3.503 1.8975 10 cm3 7.165 7.14 1.62 SN cylinder 70.60 g 3.37 1.895 10 cm3 7.060 7.4317 5.07 Copper wire 5.10 g 6.75 0.326 1 cm3 9.0565 8.96 1.083 Irregular solid 84.25g 7 cm3 12.0357 12.2867 12.2867 Density = Mass (g)/ volume (cm3) Therefore, Aluminum cylinder = 70.35/ 25 = 70.35 g/cm3 ZN cylinder = 71.65/ 10 = 7.165 g/cm3 SN cylinder = 70.60/ 10 = 7.060 g/cm3 Copper wire = 510/1 = 510 g/cm3 Irregular solid = 84.25/7 = 12.0357 g/cm3 Calculations No. 1 Table 6: Measurement of wire length using a Metric Ruler Ruler Readings Lengths Deviations Deviations squared Left End Right End 134mm 201mm 67 -0.5 0.25 130mm 298mm 68 0.5 0.25 140mm 207.5mm 67.5 0 0 20mm 87.5mm 67.5 0 0 Average Values 67.5 0 0.125 Length of the copper wire = (∑ of the individual lengths) / No. of significant figures = (67+68+67.5+67.5) / 4 = 67.5 mm No. 2 Table 7: Measurement of a wire length using an English Ruler Ruler Readings Lengths Deviations Deviations squared Left End Right End 5 7.625 2.625 -0.83 0.006889 5.5 8.28 2.78 0.072 0.005184 6.75 9.4 2.65 -0.058 0.003364 1.125 3.9 2.775 0.067 0.004489 Average Values 2.707 0.0285 0.0099815 Length of the copper wire = (∑ of the individual lengths) / No. of significant figures = (2.625+2.78+2.65+2.775+2.707) / 4 = 2.707 No. 3 Number of centimeters in 1 Inc Calculated value = 2.49 Accepted value = 2.54 Difference between the calculated and accepted values = 2.54 – 2.49 = 0.05 cm The computing the % error = 0.05/2.54 *100 = 1.96% No. 4 Table 8: The length and diameter of metal cylinders using a vernier caliper Zero reading 1 2 3 4 Average Length, Aluminum cylinder 8.65 8.65 8.65 8.64 8.647 Length, ZN cylinder 3.50 3.49 3.50 3.50 3.503 Length, SN cylinder 3.37 3.35 3.38 3.37 3.37 Diameter, Aluminum cylinder 1.90 1.89 1.90 1.91 1.9 Diameter, ZN cylinder 1.90 1.89 1.90 1.90 1.8975 Diameter, SN cylinder 1.91 1.89 1.89 1.89 1.895 Average/ mean = (∑ of the individual lengths) / No. of significant figures Therefore, Length, Aluminum cylinder = 8.65+8.65+8.65+8.64 = 8.647cm Length, ZN cylinder = 3.50+3.49+3.50+3.50 = 3.503cm Length, SN cylinder = 3.37+3.35+3.38+3.37 = 3.37 Diameter, Aluminum cylinder = 1.90+1.89+1.90+1.91 = 1.90cm Diameter, ZN cylinder = 1.90+1.89+1.90+1.90 = 1.8975 Diameter, SN cylinder = 1.91+1.89+1.89+1.89 = 1.895 No. 5 Table 9: Diameter of a copper wire using a micrometer caliper 1 2 3 4 5 6 Average Zero reading 0.000 0.000 0.000 0.000 Reading with wire 0.327 0.328 0.325 0.325 0.326 0.328 0.326 Diameter wire 0.327 0.328 0.325 0.325 0.326 0.328 0.326 No. 6 Table 10: Measurement of wire length using a Metric Ruler Ruler Readings Lengths Deviations Deviations squared Left End Right End 134mm 201mm 67 -0.5 0.25 130mm 298mm 68 0.5 0.25 140mm 207.5mm 67.5 0 0 20mm 87.5mm 67.5 0 0 Average Values 67.5 0 0.125 Value of error = 0.354 Mean = Total lengths/frequency (n) = 67.5 mm Then computing standard deviation Frequency (n) = 4 Sum of deviations = -0.5 +0.5 = 0 Sum of squared deviations = 0.25 + 0.25 = 0.125 Therefore, standard deviation = √ (Sum of square deviations/ (n-1)) = √ (0.125/ (4-1)) = 0.2041 Table 11: Measurement of a wire length using an English Ruler Ruler Readings Lengths Deviations Deviations squared Left End Right End 5 7.625 2.625 -0.83 0.006889 5.5 8.28 2.78 0.072 0.005184 6.75 9.4 2.65 -0.058 0.003364 1.125 3.9 2.775 0.067 0.004489 Average Values 2.707 0.0285 0.0099815 Value of error = 0.071 Then computing standard deviation Frequency (n) = 4 Sum of squared deviations = 0.006889 + 0.005184 + 0.003364 + 0.004489 = 0.0099815 Therefore, standard deviation = √ (Sum of square deviations/ (n-1)) = √ (0.0099815/ (4-1)) = 0.057681 No. 7 Number of centimeters in 1 Inc Calculated value = 2.49 Accepted value = 2.54 = 2.54 – 2.49 = 0.05 The calculated standard deviations both in Table 1, Table 2 are 0.2041 and 0.057681 respectively whereas the accepted value is 2.54, which is out of range. No. 8 Volume = πr2L Aluminum cylinder = 3.14*(1.9/2)2*8.647 = 24.5043 cm3 ZN cylinder = 3.14*(1.8975/2)2*3.503 = 9.8750 cm3 SN cylinder = 3.14*(1.895/2)2*3.37 = 9.4998 cm3 Copper wire = 3.14*(0.326/2)2*6.75 = 0.5631 cm3 Irregular solid = 7 cm3 No.9 Density = Mass/Volume Aluminum cylinder = 70.35/24.5043 = 2.8710 g/cm3 ZN cylinder = 71.65/9.8750 = 7.2557 g/cm3 SN cylinder = 70.60/9.4998 = 7.4317 g/cm3 Copper wire =5.10/0.5631 = 9.0570 g/cm3 No.10 Object used Mass, g Length, cm Diameter, cm Volume, cc(cm3) Density computed, g/cm3 Density from table IV g/cm3 Percent error Aluminum cylinder 70.35 g 8.647 1.9 25 cm3 2.8710 2.7 6.333 ZN cylinder 71.65 g 3.503 1.8975 10 cm3 7.2557 7.14 1.62 SN cylinder 70.60 g 3.37 1.895 10 cm3 7.060 7.4317 5.07 Copper wire 5.10 g 6.75 0.326 1 cm3 9.0570 8.96 1.083 Irregular solid 84.25g 7 cm3 12.0357 12.2867 2.043 Questions 1. Several observations on each measurements aids to increase accuracy of a particular reading, which is essential when computing. 2. a. The smallest part of a centimeter for effective reading is 0.01cm with a meter stick. b. The smallest part of a centimeter for effective reading is 0.1mm with a vernier caliper c. Therefore, the more liable is 0.1mm of vernier caliper since its approximation is minimal to affect the accuracy of a reading. 3. The smallest part of a centimeter, which a researcher can estimate or read using a micrometer caliper is 0.05cm. 4. 5. a. The purpose of average deviation is to predict how far the value usually is from the mean of a given set data. b. The standard deviation’s function is to establish the set data’s dispersion from the mean. 6. When measuring length and diameter of a cylindrical object it is essential to take the latter readings. This is because diameter usually determines the content of matter contained in an object. 7. Micrometer has a high accuracy compared to vernier caliper where its approximation is not closely to the exact readings taken. 8. Biggest volume is that of a an Aluminum cylinder is 24.5043 cm3 then in, a. Cubic millimeters 1 Cm3 = 1000 mm3 Therefore, 24.5043*1000 = 24504.3 mm3 b. Liters 1 Cm3 = 0.000001m3 Therefore, liters = 24.5043*0.000001 = 2.4x10-7Liters c. Kilograms 1 liter = 1kg Therefore 2.4x10-7 liters = 2.4x10-7kg. 9. Circular sheet of copper Diameter = 30.0cm =0.3m Thickness = 1mm = 0.001m Volume = 3.14*(0.3/2)2*0.001 = 7.065x10-5 M3 1 M3= 1000 kg 7.065x10-5 M3*1000 = 7.065x10-2kg Then weight = 7.065x10-2Kg*9.8N/Kg = 6.9237x10-1Newtons 10. Diameter = 4cm and radius will be 2cm Volume =3.14*r2*L a. Therefore L= Volume / (3.14*r2) b. The sphere has radius of 1.20cm. Then its volume will be, = 3.14*(4/3)*r3 which is 3.14*(4/3)* 1.203 = 7.23456cm3 Therefore the distance will be, L = Volume / (3.14*r2) = 7.23456/ (3.14*1.22) = 1.6 cm Work Cited Wilson, Jerry, D. & Cecilia, A. H. Hall. Physics Laboratory Experiments. Boston, MA: Brooks/Cole, Cengage Learning, 2009. Print. Read More