Experimental Error In Physics
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of this type result in measured values that are consistently too high or consistently too low. Systematic errors may be of four kinds: 1. Instrumental. For example, a poorly calibrated instrument such as a thermometer that reads 102 oC human error in physics when immersed in boiling water and 2 oC when immersed in ice water at
Lab Error Examples
atmospheric pressure. Such a thermometer would result in measured values that are consistently too high. 2. Observational. For example, parallax in experimental error equation reading a meter scale. 3. Environmental. For example, an electrical power ìbrown outî that causes measured currents to be consistently too low. 4. Theoretical. Due to simplification of the model system or approximations in the equations
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describing it. For example, if your theory says that the temperature of the surrounding will not affect the readings taken when it actually does, then this factor will introduce a source of error. Random Errors Random errors are positive and negative fluctuations that cause about one-half of the measurements to be too high and one-half to be too low. Sources of random errors cannot always be identified. Possible sources of random systematic error physics errors are as follows: 1. Observational. For example, errors in judgment of an observer when reading the scale of a measuring device to the smallest division. 2. Environmental. For example, unpredictable fluctuations in line voltage, temperature, or mechanical vibrations of equipment. Random errors, unlike systematic errors, can often be quantified by statistical analysis, therefore, the effects of random errors on the quantity or physical law under investigation can often be determined. Example to distinguish between systematic and random errors is suppose that you use a stop watch to measure the time required for ten oscillations of a pendulum. One source of error will be your reaction time in starting and stopping the watch. During one measurement you may start early and stop late; on the next you may reverse these errors. These are random errors if both situations are equally likely. Repeated measurements produce a series of times that are all slightly different. They vary in random vary about an average value. If a systematic error is also included for example, your stop watch is not starting from zero, then your measurements will vary, not about the average value, but about a displaced value. Blunders A final source of error, called a blunder, is an outright mistake. A person may reco
and Graphs phy124:error_and_uncertainty Table of Contents Uncertainty, Error and Graphs Uncertainty in measurements An inspirational message from 1600 for care in experimentation Notation Error Absolute Error Relative Error Random Error Systematic Error Propagation of Errors Obtaining Values from Graphs An experiment with the simple pendulum:
Type Of Error In Physics Experiment
Things one would measure Estimate of error in the length of the string Error
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in the period Making a plot of our data Uncertainty, Error and Graphs Uncertainty in measurements In physics, as in every standard deviation physics other experimental science, one cannot make any measurement without having some degree of uncertainty. A proper experiment must report for each measured quantity both a “best” value and an uncertainty. Thus it is necessary http://www.physics.nmsu.edu/research/lab110g/html/ERRORS.html to learn the techniques for estimating them. Although there are powerful formal tools for this, simple methods will suffice in this course. To a large extent, we emphasize a “common sense” approach based on asking ourselves just how much any measured quantity in our experiments could be “off”. One could say that we occasionally use the concept of “best” value and its “uncertainty” in everyday speech, perhaps without even knowing http://skipper.physics.sunysb.edu/~physlab/doku.php?id=phy124:error_and_uncertainty it. Suppose a friend with a car at Stony Brook needs to pick up someone at JFK airport and doesn't know how far away it is or how long it will take to get there. You might have made this drive yourself (the “experiment”) and “measured” the distance and time, so you might respond, “Oh, it's 50 miles give or take a few, and it will take you one and a half hours give or take a half-hour or so, unless the traffic is awful, and then who knows?” What you'll learn to do in this course is to make such statements in a more precise form about real experimental data that you will collect and analyze. Semantics: It is better (and easier) to do physics when everyone taking part has the same meaning for each word being used. Words often confused, even by practicing scientists, are “uncertainty” and “error”. We hope that these remarks will help to avoid sloppiness when discussing and reporting experimental uncertainties and the inevitable excuse, “Oh, you know what I mean (or meant).” that attends such sloppiness. We rarely carry out an experiment by measuring only one quantity. Typically we measure two or more quantities and then “fold” them together in
of causes of random errors are: electronic noise in the circuit of an electrical instrument, irregular changes in the heat loss rate from a solar collector due to changes in the http://www.physics.umd.edu/courses/Phys276/Hill/Information/Notes/ErrorAnalysis.html wind. Random errors often have a Gaussian normal distribution (see Fig. 2). In such cases statistical methods may be used to analyze the data. The mean m of a number of measurements of the same quantity is the best estimate of that quantity, and the standard deviation s of the measurements shows the accuracy of the estimate. The standard error of the estimate experimental error m is s/sqrt(n), where n is the number of measurements. Fig. 2. The Gaussian normal distribution. m = mean of measurements. s = standard deviation of measurements. 68% of the measurements lie in the interval m - s < x < m + s; 95% lie within m - 2s < x < m + 2s; and 99.7% lie within m - 3s < error in physics x < m + 3s. The precision of a measurement is how close a number of measurements of the same quantity agree with each other. The precision is limited by the random errors. It may usually be determined by repeating the measurements. Systematic Errors Systematic errors in experimental observations usually come from the measuring instruments. They may occur because: there is something wrong with the instrument or its data handling system, or because the instrument is wrongly used by the experimenter. Two types of systematic error can occur with instruments having a linear response: Offset or zero setting error in which the instrument does not read zero when the quantity to be measured is zero. Multiplier or scale factor error in which the instrument consistently reads changes in the quantity to be measured greater or less than the actual changes. These errors are shown in Fig. 1. Systematic errors also occur with non-linear instruments when the calibration of the instrument is not known correctly. Fig. 1. Systematic errors in a linear instrument (full line). Broken line shows response of an ideal instrument without error. Examples of systematic errors caused