Comprehension of the Propagation of Errors with the Help of Formulas - Lab Report Example

Lab Partner’s Group Number Section Number DD Month YYYY of the Experiment: LAB REPORT: VOLUMES OBJECTIVE SECTION The aim of the experiment was to comprehend the propagation of errors with the help of formulas. The volumes of objects with regular shapes were measured together with graph linearization in order to define the clay’s density. The physics quantities that were measured include Width, Height, and Length of the objects. The aim of determining the density of clay was to practice the propagation of errors and to come up with a linearized graph in determining the quantity if physics. EXPERIMENTAL DATA In the first experiment, the height, thickness, and inner diameter of the hollow cylinder was collected. Additionally, the data on the height and the diameter of the bullet shaped object was collected and tabulated. In the second experiment, the data on the sphere’s mass was collected as mass 1 to mass 5. The fourth experimental that was needed in the experiment was the diameter for the five spheres which were taken as diameter 1 to diameter 6 DATA ANALYSIS SECTION We took the density of the clay as Mass per Unit of Volume. The formula that was used in calculating this was with an SI unit of . In the experiment, the propagation of errors was calculated from the approach of partial derivatives. The formula for this was The standard errors for the experiment were demonstrated by . The standard error was obtained through the computation of standard deviation from the various measurement. We later calculated the standard deviation with the help of a graphical analysis program. The standard deviation was denoted as N is taken to mean the measurement’s number of x. x and y are taken to represent their mean values. The uncertainties in the end outcome were reported with one significant number. It was assumed that the final average value is equated to the number of decimal points found in the uncertainty. The equipment that were used in the experiment include; a plastic bag, hollow cylinder, bullet shaped object, Vernier’s calipers, balance, and a set of masses. In the first experiment we determined the volumes and the standard error for the hollow cylinder, bullet shaped object, and the triangle prism (Price, 889). The following equation was used to calculate the volume of the hollow cylinder h was taken to mean the cylinder’s height, t was the wall’s thickness, while d was the inner diameter. The volume for the bullet shaped object was calculated using the formula h was the bullet shaped object height while D was the diameter of the base. The Vernier calipers was used to measure the pertinent dimension of the object. The dimension of the Vernier was 0.05mm. The five measurement of the provided object was measured. After taking the five measurement, the mean values for the dimensions were also determined. The standard deviations for the dimensions for the hollow cylinders was then determined. The standard deviation for the mean was calculated from the standard deviations of the dimensions. The dimensions errors for the objects was taken to be 0.05 mm. This is taken to be the Vernier caliper’s precision. The mean values were used in calculating the volume of the objects. The propagation of errors was found from . In the second part of the experiment, we made a single measurement for clay spheres mass having nominal diameters between 1-7 cm. The mass measurement errors were recorded in the electronic balance. The sphere was rollers after taking the measurements. The Vernier caliper was used in taking the five independent reading the sphere’s diameter. The sphere was rolled after every measurement. After rolling the sphere the measurements were recorded, followed by the calculation of the mean value(Price, 889). The table was then prepared in the Logger GA/Pro. In the table, the first column was taken to mean the mass, the second column was the mean diameters. While the third column was the 5 diameter measurement done the sphere that was selected. RESULTS SECTION The experimental results is signed and will be attached at the end of the paper. The full data are tabulated in Tables 1, Table 2, Table 3, and Table 4. When calculating the volumes for the hollow cylinder it was reported that the mean value of height, thickness, and inner diameter were 127.46 mm, 5.13mm, and 76.63 mm respectively. Their respective standard deviations include 0.1949 for height, 0.004472 for thickness, and 0.2775 for inner diameter. In the second table the mean value for bullet shaped object’s height and its diameter is 70.01 and 35.14 mm respectively. Their standard error was 0.05. In the second experiment, the masses 1-5 for the clay spheres were 8.86g, 8.09g, 17.47g,28.76g, 51.57g, and 102.65g. Additionally after measuring the diameters of the sphere using Vernier calipers, the mean values for the six measurements were 16.28mm, 20.59mm, 23.56mm, 31.19mm, 39.37mm, and 50.24mm. DISCUSSION AND CONCLUSION The purpose of the first experiment is to comprehend how errors can be propagated with the help of formulas. In the second section of the experiment, the clay’s density was determined. The aim of this was to practice the propagation of errors and to practice on how to build linearized graphs in determining the quantity in physics. Some of the physics concepts that was tested include the width, height, and the length of boxes. The tested concept answered the question the error in the volume of the box after multiplying the mean values of the quantities. Additionally, the experiment was meant to answer how errors can be propagated (Price, 889). When calculating the volumes for the hollow cylinder it was reported that the mean value of height, thickness, and inner diameter were 127.46 mm, 5.13mm, and 76.63 mm respectively. Their respective standard deviations include 0.1949 for height, 0.004472 for thickness, and 0.2775 for inner diameter. In the second table the mean value for bullet shaped object’s height and its diameter is 70.01 and 35.14 mm respectively. Their standard error was 0.05. In the second experiment, the masses 1-5 for the clay spheres were 8.86g, 8.09g, 17.47g,28.76g, 51.57g, and 102.65g. Additionally after measuring the diameters of the sphere using Vernier calipers, the mean values for the six measurements were 16.28mm, 20.59mm, 23.56mm, 31.19mm, 39.37mm, and 50.24mm. The Vernier calipers was used to measure the pertinent dimension of the object. The dimension of the Vernier was 0.05mm. The five measurement of the provided object was measured. After taking the five measurement, the mean values for the dimensions were also determined. The standard deviations for the dimensions for the hollow cylinders was then determined. The standard deviation for the mean was calculated from the standard deviations of the dimensions. The dimensions errors for the objects were taken to be 0.05 mm. This is taken to be the Vernier caliper’s precision. The table was then prepared in the Logger GA/Pro. In the table, the first column was taken to mean the mass; the second column was the mean diameters. While the third column was the 5 diameter measurement done the sphere that was selected. In the second part of the experiment, we made a single measurement for clay spheres mass having nominal diameters between 1-7 cm. The mass measurement errors were recorded in the electronic balance. The sphere was rollers after taking the measurements. The Vernier caliper was used in taking the five independent reading the sphere’s diameter. The sphere was rolled after every measurement. After rolling the sphere the measurements were recorded, followed by the calculation of the mean value. One of the difficulties that we faced in the experiment is making the mass Vs the diameter graph. It was not easy for the group members to apply the curve fit in identifying the parameters. Additionally, we also experienced problems in checking and confirming the cubic relationship that exists between the sphere’s diameter and its mass. Consequently, in finding the relationship between mass and diameter in cube was difficult. For this reason finding a proper relationship was quite difficult. For instance, in the experiment I got 2.8 due to human error when taking the measurement. This posed as a greatest challenge during the experiment. Some of the statistical errors that affected the experiment was errors in the conversion of decimal place into the appropriate one. This posed as error because it was based on estimation. This problem can be redesigned by using equipment that only records results in the appropriate number of decimal places. The systematic error that affected the measurement is correct positioning of the balance to start from a zero calibration. It was difficult to place the initial measurement as zero was due to instability in the adjustment knob of the balance. The deviations of the experimental result were attributed to the idealization inherent of the available theories. The theory has failed to factor the systematic, human, and statistical errors that are prone to happen when measuring the data for the measured variables (Price, 889). References Price, Joseph E. Optional Formal Lab Reports For An Introductory Physics Course. American Journal of Physics 44.9 (1976): 889. Web. Works Cited Read More