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IPL Lab Report

Summary of measurement errors, formulas for cylinder volume and density, and concepts of background radiation, standard deviation, standard error. Includes experiments measuring metal densities, radiation counts with error analysis.

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    O ; Northeastern University Report for Experiment #1 Measurement Anh Do Lab Partner: Deanna Guo, Maggie Chua TA: George Wanes 01/23/2023

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    Introduction Measuring an object can result in not the exact values. The difference between measurement and actual values is an error. Errors can happen within using any tools, even with the best and priciest tool the world could find. Some different tyqjes of errors are instrumental, systematic, and random. Instrumental error occurs when the calibration of the tool being used is incorrect - an example is weighing baking ingredients without taring the scale. Systematic error occurs consistently and repeatedly and can be associated with when using defective equipment - an example is repeating the same measured number previously’. Random error occurs in an unpredictable and with unknown reasons during an experiment - an example is a student reading off a ruler with a wrong number when measuring a stainless-steel cylinder. The differences between the three errors: random error happens by a known source that results in unanticipated outcome, and systematic error happens within the system with calculations that ends in imperfections, while instrumental error results from faulty equipment. The formula to calculate the volume of a cylinder: V = L 4 A derived quantity is what volume of the cylinder is called. Calculating the volume of a cylinder is also calculating how much space it can contain. When measuring its diameter and length, they have their own errors due to the measuring tool. The error in the cylinder is also caused by these measurement errors. The formula to calculate the density: ' = v Calculating density’ is mass divided by volume. For homogeneous substances, the density is independent for the size, mass, and shape. Density’ is also calculating how- heavy the object is compared to its proportion. Background radiation count rate is the measurement of radiation in the background of the environment. The Geiger counter was used to measure the radioactive in the background during the experiment. Standard deviation is the measurement of how much the data is being spread out compared to the mean. Standard error in the mean is comparing the mean of the population to the sample mean. These two correlated because when the standard deviation increases, the standard error also increases. In the first investigation, density’ was calculated using the measurements of length, diameter, and mass of the metals. The measurements were done using a scale and a mler. Then, all four were determined for the magnitude of errors - approximately’ equal to one-half of the smallest increment of the ruler and the scale. The Geiger counter was used to measure the number of background radioactive counts for the second investigation. Using this tool helps the understanding of how much amount of radioactivity' happens during the experiment and the factors of random error that can occur.

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    Investigation 1: Density of a Material First, the mass (g) of the four cylinders of rhe same material was weighted using a digital scale after zero the scale. The measurements for length (cm) and diameter (cm) of each cylinder were ±en measured using a ruler. The smallest increment of mas was 0.1 grams. The error was calculated as the smallest increment divided by 2: 6m g = 0 =0.055 The smallest increment of length and diameter was 1mm, so it was converted to 0.1 c m Because rhe same tool, ruler, was used, so rhe error for both values is ± e same. The calculation for the error for length and diameter was also the same way as the calculation for mass; the smallest increment divided b y 2 for both values. 6L cm ~ 6 D c m ~ -0.05cm The error was divided b y the measured data for each measurement, as shown in Table 1. Cylinde r # 1 #2 # 3 # 4 m(g) 21.4 9.5 13.9 2.6 6m (g) 0.05 0.05 0.05 0.05 6m/ m 0.0023 0.0053 0.0036 0.020 L (cm) 6.3 4.7 3.9 3.2 6L (cm) 0.05 0.05 0.05 0.05 6 L 1 0.008 0.012 0.013 0.016 D(ctn) 1.2 0.9 1.2 1.1 6D (cm) 0.05 0.05 0.05 0.05 6D.D 0.042 0.056 0.042 0.045 Table 1. Mass, Length, Diameter for each cylinder and ±eir respective errors calculated. After having measurements for the mass, length and diameter, the volume was calculated. The formula to calculate density 7 : 4 The below formula was used to calculate the error for volume. <5V ____ The table below contains the calculated volume and the error of the four cylinders. Cylinder # 1 #2 #3 # 4 V (cm3) 7 1 3.0 4.4 3.0

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