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Diploma in ILT,ES,FT/Applied Physics-G5601/Lab Expt.//SGS EXPERIMENT 1 INTRODUCTORY LAB ON ERROR AND MEASUREMENT INTRODUCTION: The purpose of this experiment is to familiarize you with the basic measurement necessary to make physical observations and how to handle measurements associated with the errors. The procedures outlined illustrate the difference between basic physical quantities (e.g. mass, length and time) and derived quantities (e.g. volume, area and density). The units used to describe these quantities are also introduced, and appreciation of the methods and accuracy by which these quantities can be measured. For this experiment it is assumed that the uncertainties are independent and random. Note: For Independent and random Uncertainties we use: Measurements are stated as: (z z) units ; where z is the absolute error in the measurement z. Two principles to follow while writing the uncertainty are: (1) Express the uncertainty to one significant figure only and (2) Express the value of the measurement to the same accuracy as the uncertainty. THE EXPERIMENT 1- Experimental Apparatus: The apparatus for this experiment consists of: meter rule, electronic balance, Vernier caliper, micrometer gauge, and a variety of objects for measurement such as thin wires and metal cylinders. Diploma in ILT,ES,FT/S-1/Y-09/PKD. Page 1 of 6 Diploma in ILT,ES,FT/Applied Physics-G5601/Lab Expt.//SGS 2- Experimental Requirements/Procedure: Task 1 – Direct Computation Involving Errors Given the two lengths that you have measured as: L1 = 8.4 0.2 cm and L2 = 4.7 0.1cm Determine the total length (L1 + L2) and state correct value of uncertainty using the addition & subtraction rule of error propagation. Determine the square of length (L1)2 and state correct value of uncertainty using the power rule of error propagation. Determine the product of lengths [π × (L1 × L2)] and state correct value of uncertainty using the multiplicative and division rule of error propagation. Determine the quotient of lengths (L1 / L2) and state correct value of uncertainty using the multiplicative and division rule of error propagation. Task 2 – Applied Computation Involving Errors Given below the diameter (d), height (h) and the mass (m) of the copper metal cylinder respectively: d (4.3 0.1) cm h (10.1 0.1) cm m (1298.7 0.2) g Determine the volume of the cylinder and state it with its correct value of uncertainty. Determine the density of the cylinder and state it with its correct value of uncertainty. Determine the % error in your experimental result, provided that the density of copper is 8.92 g / cm 3 at 20C . Task 3 – Statistical Method of Error Analysis The following replicate weightings were obtained: 29.8, 30.2, 28.6 and 29.7 mg. Compute the mean, standard deviation and standard error in the mean. State the best value of the weighting with its required uncertainty. Explain the significance of the values and its uncertainty you just stated above. Task 4 – Computation of % Difference in Results Suppose you have measured the diameter of wire using two different instruments namely; micrometer and vernier caliper. The diameters are as follows: Using micrometer: d (2.13 0.01) mm Using vernier caliper d (0.21 0.01) cm Compute the % difference between the two results. Diploma in ILT,ES,FT/S-1/Y-09/PKD. Page 2 of 6 Diploma in ILT,ES,FT/Applied Physics-G5601/Lab Expt.//SGS Task 5 – Instrument Familiarization Familiarize yourselves with the measuring instruments such as meter rule, vernier caliper, micrometer and electronic balance. Check for the zero error of the instruments such as vernier caliper and micrometer. Determine the uncertainties of the instruments and record them. Take a reading of diameter of copper wire using vernier caliper and micrometer. Record the diameter of wire with its required uncertainty after zero error correction. You should have a 2 readings; one from vernier caliper and other from micrometer. Zero error of: Vernier Caliper cm Micrometer mm Uncertainties of: Metre Rule cm Vernier Caliper cm Micrometer mm Micrometer Readings Venier Caliper Readings D1 ( ) mm D1 ( ) cm Task 6 – Graphing How can one estimate the uncertainty of a slope on a graph? If one has more than a few points on a graph, one should calculate the uncertainty in the slope as follows. In the picture below, the data points are shown by small, filled, black circles; each datum has error bars to indicate the uncertainty in each measurement. It appears that current is measured to ±2.5 milliamps and voltage to about ±0.1 volts. The hollow triangles represent points used to calculate slopes. Notice how I picked points near the ends of the lines to calculate the slopes! 1. Draw the "best" line through all the points, taking into account the error bars. Measure the slope of this line. 2. Draw the "min" line -- the one with as small a slope as you think reasonable (taking into account error bars), while still doing a fair job of representing all the data. Measure the slope of this line. 3. Draw the "max" line -- the one with as large a slope as you think reasonable (taking into account error bars), while still doing a fair job of representing all the data. Measure the slope of this line. 4. Calculate the uncertainty in the slope as one-half of the difference between max and min slopes. Diploma in ILT,ES,FT/S-1/Y-09/PKD. Page 3 of 6 Diploma in ILT,ES,FT/Applied Physics-G5601/Lab Expt.//SGS Graphing a) The data’s shown in Table 1.0 are for the speed of an object as a function of time. Table 1.0 Speed (± 0.06 m/s) Time (s) Draw a graph of speed against time. Label axis 0.48 1 carefully and include error bars. 0.84 2 0.94 3 1.05 4 Evaluate the slope and its uncertainty. 1.40 5 1.60 6 1.69 7 1.89 8 2.21 9 Use the undermentioned materials to compare your experimental results Percent Difference and Errors a) If you have measured the same quantity more than one-way, one can calculate the percent difference between the two results. This is defined as: b) If a "true" or reference value is known for the measured quantity, one can calculate the percent error or percentage discrepancy for the experimental result, thus: Diploma in ILT,ES,FT/S-1/Y-09/PKD. Page 4 of 6 Diploma in ILT,ES,FT/Applied Physics-G5601/Lab Expt.//SGS Diploma in ILT,ES,FT/S-1/Y-09/PKD. Page 5 of 6 Diploma in ILT,ES,FT/Applied Physics-G5601/Lab Expt.//SGS Diploma in ILT,ES,FT/S-1/Y-09/PKD. Page 6 of 6