# lab_2 - LAB 2 Experimental Uncertainty and Error Analysis...

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Experimental Uncertainty and Error Analysis Introduction: In the physical sciences as well as in engineering, we depend on accurate measurements of real-world objects to test our theories and to design the things we build. In this lab we will study the accuracy of measurements and how this accuracy affects things we calculate from measured values. All measurements are subject to "experimental uncertainty", sometimes called "experimental error". These terms do not refer to any kind of "mistake" or “blunder” 1 in making measurements. It is simply an observed fact that when repeated, independent measurements are made on a physical system, the measured values will not generally all be exactly the same. (We will see this happen in this lab.) To make progress in experimental science and engineering, it is important to strive to reduce these measurement errors, and to be able to calculate the effect they will have when we use measured values to calculate desired quantities and results. The mathematics of error analysis, or error propagation, gives us a systematic way to determine from our data itself, how confident we should be of our results; that is, how far from the "correct" or "actual" value our results are likely to be. In this lab the whole class will work as a large group, each person measuring the diameter and the mass of a metal object. We will study the spreads of the measured values and relate them to characteristics of the measurement tools. We will see graphically how certain mathematical quantities such as mean (or average) value and standard deviation can be used to describe the set of measured values. Next we will calculate the volume and density of the object from our measurements, and observe the spreads of these "derived quantities". Mathematical formulae of error propagation which should predict the spreads in the derived quantity, will be checked against the observed spreads. Figure 1. S teel ball, triple beam balance , a ruler and a Vernier Caliper. Metal calipers are sharp. Use with CUATION. Vernier Micrometer s are also shown and often used to make precise measurements. Equipment: 1. Vernier Caliper. 2. Triple-beam balance. 3. Steel ball (one for entire class). Theory: This experiment is somewhat different as the theory is mathematical, though we will approach it from a physical point of view. The theory we shall discuss will be spread throughout the Procedure and Analysis sections. 1 In fact, we tacitly assume all human blunder has been removed from the experiment. LAB# 2

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(Hint: Fill in the open circles in front of the procedure steps to help you perform the experiment) Procedure: In this part of this lab we will study the measurement process itself. That is, the fact that each and every measurement ever made has some uncertainty. There is no such thing as a “Perfect Measurement”. You can see one aspect of this inability to make a perfect measurement quite easily. What if a measurement comes out between the finest markings on your measurement scale? What value would you assign to this measurement?
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## This note was uploaded on 02/29/2012 for the course PHYS 227 taught by Professor Rabe during the Fall '08 term at Rutgers.

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lab_2 - LAB 2 Experimental Uncertainty and Error Analysis...

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