Lab 1.5 - Error Propagation

Lab 1.5 - Error Propagation - ERRORS AND ERROR PROPAGATION...

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1 ERRORS AND ERROR PROPAGATION INTRODUCTION: Laboratory experiments involve taking measurements and using those measurements in an equation to calculate an experimental result. It is also necessary to know how to estimate the uncertainty, or error, in physical measurements and to know how to use those uncertainties to calculate the error in the experimental result. TYPES OF EXPERIMENTAL ERRORS Experimental errors can generally be classified into three types: personal, systematic, and random. Personal Errors These errors arise from personal bias of carelessness in reading an instrument, in recording data, or in calculations, and parallax in reading a meter. Of these, only parallax errors can be estimated and used in error propagation. Effort should be made to eliminate experimental errors. (When looking at non-digital meter, there is a small distance between the needle and the scale. As a result, the reading will change as the observer’s eye position changes from side to side. This apparent change in reading, due to the change in position of the observer’s eye, is called parallax.) Systematic Errors Errors of this type result in measured values which are consistently to high or to low. Conditions which lead to systematic errors are as follows: 1. An improperly calibrated instrument such as a thermometer which consistently reads 99ºC in boiling water instead of 100ºC. 2. A meter, micrometer, vernier caliper, or other instrument which was not properly zeroed or for which the zero correction factor was not considered. 3. Theoretical errors due to a simplified mathematical model for the system which consistently gives a calculated value different from the calculated value predicted from a more accurate mathematical model. Random Errors Random errors result from unknown and unpredictable variations in experimental measurements. Possible sources of random errors are:
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2 1. Observational-e.g. , errors when reading the scale of a measuring device to the smallest division. 2. Environmental- unpredictable fluctuations in readings beyond the experimenters control. Such errors can be determined statistically or can be estimated by the experimenter. STATISTICAL DETERMINATION OF RANDOM ERRORS When there are many measurements of the same quantity, the average or mean value is defined by ! = = N i i x N x 1 _ 1 where i x is the i th measured value and N is the total number of measurements. There are two ways to statistically calculate the uncertainty in the measured value. One
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Lab 1.5 - Error Propagation - ERRORS AND ERROR PROPAGATION...

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