Transcript
ERROR THEORY
SESSION 1&2
PHYSICS
BILINGUAL GROUP FACULTY OF EDUCATION, UCM
ERROR THEORY
CONTENTS
▸ Introduction
▸ Types of errors
▸ Significant figures
▸ Absolute and relative errors
▸ How to estimate errors
WHY AN ERROR THEORY?INTRODUCTION
ERROR THEORY
INTRODUCTION
▸ T h e m e a s u r e m e n t o f a physical quantity can never be made with perfect accuracy. There is usually involved some error or uncertainty.
▸ You can find a large number of factors that can cause a value obtained experimentally to d e v i a t e f r o m t h e t r u e (theoretical) value.
ERROR IN A SCIENTIFIC MEASUREMENT USUALLY DOES NOT MEAN A MISTAKE.
INSTEAD, THE TERMS "ERROR" AND "UNCERTAINTY" BOTH REFER TO UNAVOIDABLE IMPRECISION IN
MEASUREMENTS.
Not all measurements have errors. If asked how many eggs there are in a dozen, one can usually give an exact number as an answer. However, if we wish to know how many atoms there are in a peace of metal, giving an exact answer is nearly impossible
ERROR THEORY
REAL LIFE EXAMPLE
https://phys.columbia.edu/~tutorial/introduction/tut_e_1_2.html
TYPES OF ERRORSERROR THEORY
ERROR THEORY
TYPES OF ERRORS▸ Systematic: They occur consistently in only one direction
each time the experiment is performed, i.e. the value of the measurement will always be greater (or lesser) than the “true” value.
▸ Random: They result from human and from accidental errors. Acidentals are related to changing experimental conditions that are beyond the control of the experimenter.
https://www.youtube.com/watch?v=j_m42zbH8FM
SIGNIFICANT FIGURESERROR THEORY
ERROR THEORY
SIGNIFICANT FIGURES
▸ Whenever you make a measurement, the number of meaningful digits that you write down implies the error in the measurement. For example if you say that the length of an object is 0.428 m, you imply an uncertainty of about 0.001 m.
▸ Accepted convention: only one uncertain digit is to be reported for a measurement. In the example if the estimated error is 0.02 m you would report a result of 0.43 ± 0.02 m, not 0.428 ± 0.02 m.
ERROR THEORY
SIGNIFICANT FIGURES
▸ Students frequently are confused about when to count a zero as a significant figure. The rule is: If the zero has a non-zero digit anywhere to its left, then the zero is significant, otherwise it is not.
▸ For example
▸ 5.00 has 3 significant figures; 0.0005 has only one,
▸ and 1.0005 has 5 significant figures.
▸ A number like 300 is not well defined. Rather one should write:
ABSOLUTE AND RELATIVE ERRORS
ERROR THEORY
ERROR THEORY
ABSOLUTE AND RELATIVE ERRORS
▸ The absolute error in a measured quantity is the uncertainty in the quantity and has the same units as the quantity itself. For example if you know a length is 0.428 m ± 0.002 m, the 0.002 m is an absolute error.
▸ The relative error is obtained by dividing the absolute error in the quantity by the quantity itself. The relative error is usually more significant than the absolute error. For instance, a 1 mm error in the diameter of a skate wheel is probably more serious than a 1 mm error in a truck tire. Note that relative errors are dimensionless. When reporting relative errors it is usual to multiply the fractional error by 100 and report it as a percentage.
https://www.youtube.com/watch?v=h--PfS3E9Ao
HOW TO ESTIMATE ERRORS?ERROR THEORY
ERROR THEORY
HOW TO ESTIMATE ERRORS
▸ Errors when reading scales
https://phys.columbia.edu/~tutorial/estimation/tut_e_2_1.html
▸ Errors of digital instruments
https://phys.columbia.edu/~tutorial/estimation/tut_e_2_2.html
‣ Time intervals using a stopwatch
https://phys.columbia.edu/~tutorial/estimation/tut_e_2_3.html
ERROR THEORYPHYSICS
BILINGUAL GROUP
FACULTY OF EDUCATION, UCM
More info:
Error Analysis Tutorial, Columbia University, NY (USA) https://phys.columbia.edu/~tutorial/
Please send your comments and suggestions regarding this presentation to juan.pena@quim.ucm.es
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