UNC - UNC Uncertainty revised Learning Objectives During...

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1 Uncertainty UNC Uncertainty revised October 18, 2004 Learning Objectives: During this lab, you will learn how to 1. estimate the uncertainty in a directly measured quantity. 2. estimate the uncertainty in a quantity that is calculated from quantities that are uncertain. 3. use Origin to perform calculations, make graphs, and perform linear regression. 4. look at a graph with data and a model and determine if the data support the model. ( You will turn in two worksheets and two graphs for this lab. The worksheets (UNC Worksheet and Error Analysis and Propagation Exercise) are included in Appendix IX of the lab manual. The material for this lab is due one week from the date of your lab at 6:00 PM. ) A. Introduction The purpose of this laboratory is to accustom you to recording measurements. You will measure mass, time, length, and force. Besides learning some basic measure- ment techniques, you must realize that all measurements possess some uncertainty in their values. When you make a measurement ( x ), you must estimate the absolute uncer- tainty ( δ x ) in your measurement. This quan- tity is based upon how well you think that you could make the measurement. The abso- lute uncertainty may be a function of the quality of the measuring instrument, the nature of the quantity being measured, the ability of the individual making the meas- urement, and the conditions under which the measurement is made. Too often we assume that the absolute uncertainty is based solely on the resolution of the measuring instru- ment. The resolution is the smallest gradua- tion on a scale or the last decimal place in a digital readout. The absolute uncertainty often depends on several of the factors above. There is no prescribed formula of how to calculate the absolute uncertainty for a measured quantity. For this reason, it is necessary for you to discuss how you determine the absolute uncertainty of a measurement in the Procedure paragraph of a laboratory report. Taking the measured value and the absolute uncertainty together, you report the measurement interval ( x ± x ). This symbol x ± x represents the interval in which we have confidence the measured value lies. Remember to always report the absolute uncertainty ( x ) together with your best estimate of the measured value ( x ). There are rounding rules that guide us in reporting the number of digits in the answer. For example, we would not report a number such as 2.1789345 meters if we were really only sure of the reading to within 0.01 meters. Instead, we would report the value as 2.18 ± 0.01 meters, i.e., we estimate that the value lies somewhere between 2.17 and 2.19 meters. In Physics laboratories, we will adopt the simple rule that the absolute uncertainty of a measurement is reported to only one, or at most two, significant figure(s), and the measurement is then rounded to the same decimal place as its absolute uncertainty.

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UNC - UNC Uncertainty revised Learning Objectives During...

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