![]() A possible explanation is given by considering the “wrapping method in detail. Partial answer to question 3: Another interesting observation is that the “wrapping method” results all predict a value for π that is too high. The average value of π was derived from the diameter (d) and circumference (C) measurements using the relationship: □□ = □□ □□ (3) The error was propagated using Gaussian error propagation as outlined in the supplementary handout: □□□□ = □□ ∙ �� □□□□ □□ � 2 + �□□□□ □□ � 2 (4) 5 measurements increases the errors as expected and all observations for π are consistent. The precision of the measurements was analyzed using the standard formulas for error analysis: 1) The average value, ?̅?□, of a set of N data points was determined from: 2) The standard deviation (precision), σ, for the same set of values was determined from: □□ = � 1 □□−1 ∑ (□□□□ − ?̅?□)2□□□□=1 (2) All average values and the standard deviations (precision) for the raw data were calculated using these formulas. I think this second method is more accurate and precise than the first method. 2) A method that avoids the problem of slipping is to wrap the paper around the cylinder. Due to slipping in particular for the lighter cylinders I expect a comparatively low accuracy and precision of this method. I aligned the cylinder parallel to the edge of a sheet of paper and started rolling the cylinder for one complete revolution. For the measurement of the circumference I used two methods: 1) I added a thin clearly visible marking on one of faces perpendicular to the cylinder axis. In order to obtain better precision I repeated each measurement 10 times. On the Vernier Caliper the smallest difference between markings is 0.01 cm which I assume to be equal to the precision. ![]() Therefore I assume that the precision of a value is half the distance between the closest markings: 0.05 cm. Data analysis: Random errors: Reading errors on measuring devices: The circumference was determined using a meter stick with millimeter markings. 2 Transcripts of the raw measurement data are added in Table A1 – A2 at the end of this document. Method 2: Wrap a piece of g around the cylinder and obtain the circumference.Method 1: Roll the cylinder on a piece of paper and measure the distance traveled by a marking on the cylinder after one complete revolution.Method 1: Ruler/meter stick with millimeter markings.Experimental setup and procedure: Measurement of the diameter (d): Hypothesis: the accuracy and precision of the determination of π increases for larger cylinders and are obtained by measuring the diameter with a Vernier Caliper and the circumference by wrapping paper around the cylinder. Since π is known with arbitrary accuracy it is a good example that allows me to evaluate accuracy and precision of my measurements simultaneously. The experiment consisted of determining π from the measurement of the diameter and circumference of cylinders with different diameters. Goal of this lab: Learn about the relationship between measurement and error analysis, how to calculate precision errors and the appropriate use of the terms accuracy and precision. But we may also ask how consistent our observations are all by themselves, in this case we are interested in precision. When we compare our observations to the measurements of other scientists or to literature values we ask how accurate our obervations are. For the interpretation of our observations it is crucial that we understand the magnitude and origin of errors. An example is the repeated measurement of the length of a piece of paper. Random errors may be due to reading errors that are sometimes too large, sometimes too small, but appear random. The former is often related to the equipment, for example the needle on a pressure gauge does not go to zero but is slightly off, or we are not looking head down on a scale, or the aero mark of a meter stick is not correctly aligned. To be more specific we distinguish systematic and random errors. Examples are sloppy experimentation, limitations of the equipment, inappropriate equipment… The understanding of the magnitude and origin of these limitations is essential for the discussion of the observations in the context of current knowledge. ![]() Experiment 1: Measuring and Error Analysis Introduction: Observations generally have limitations that originate from a variety of sources. Download Experiment 1: Measuring and Error Analysis - Sample Lab Report | PHYS 217 and more Physics Lab Reports in PDF only on Docsity!1 Sample lab report PHYS 217 Lab Fall 2008 Lab report: Boris Kiefer 08/20/08 Lab group: Boris Kiefer and John Doe.
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