How Does A Vernier Caliper Reduce Random And Systematic Error
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of the measurement device. Random errors usually result from the experimenter's inability to take the same measurement in exactly how to reduce systematic error the same way to get exact the same number. Systematic
Random Error
errors, by contrast, are reproducible inaccuracies that are consistently in the same direction. Systematic errors are
How To Reduce Random Error
often due to a problem which persists throughout the entire experiment. Note that systematic and random errors refer to problems associated with making measurements. Mistakes made
Random Error Examples Physics
in the calculations or in reading the instrument are not considered in error analysis. It is assumed that the experimenters are careful and competent! How to minimize experimental error: some examples Type of Error Example How to minimize it Random errors You measure the mass of a ring three times using the same random error calculation balance and get slightly different values: 17.46 g, 17.42 g, 17.44 g Take more data. Random errors can be evaluated through statistical analysis and can be reduced by averaging over a large number of observations. Systematic errors The cloth tape measure that you use to measure the length of an object had been stretched out from years of use. (As a result, all of your length measurements were too small.)The electronic scale you use reads 0.05 g too high for all your mass measurements (because it is improperly tared throughout your experiment). Systematic errors are difficult to detect and cannot be analyzed statistically, because all of the data is off in the same direction (either to high or too low). Spotting and correcting for systematic error takes a lot of care. How would you compensate for the incorrect results of using the stretched out tape measure? How would you correct the measurements from improperly tared scale?
the empirical resources are exhausted need we pass on to the dreamy realm of speculation." -- Edwin Hubble, The Realm of the Nebulae (1936) zero error definition Uncertainty To physicists the terms "error" or "uncertainty" do not mean "mistake". how to calculate uncertainty in physics Mistakes, such as incorrect calculations due to the improper use of a formula, can be and should be corrected. parallax error However, even mistake-free lab measurements have an inherent uncertainty or error. Consider the dartboards shown below, in which the 'grouping' of thrown darts is a proxy for our laboratory measurements. A https://www2.southeastern.edu/Academics/Faculty/rallain/plab193/labinfo/Error_Analysis/05_Random_vs_Systematic.html 'precise' measurement means the darts are close together. An 'accurate' measurement means the darts hit close to the bullseye. Notice the combinations: Measurements are precise, just not very accurate Measurements are accurate, but not precise Measurements neither precise nor accurate Measurements both precise and accurate There are several different kinds and sources of error: Actual variations in the quantity being measured, e.g. http://www2.sjs.org/friedman/PhysAPC/Errors%20and%20Uncertainties.htm the diameter of a cylindrically shaped object may actually be different in different places. The remedy for this situation is to find the average diameter by taking a number of measurements at a number of different places. Then the scatter within your measurements gives an estimate of the reliability of the average diameter you report. Note that we usually assume that our measured values lie on both sides of the 'true' value, so that averaging our measurements gets us closer to the 'truth'. Another approach, especially suited to the measurement of small quantities, is sometimes called 'stacking.' Measure the mass of a feather by massing a lot of feathers and dividing the total mass by their number. Systematic errors in the measuring device used. Suppose your sensor reports values that are consistently shifted from the expected value; averaging a large number of readings is no help for this problem. To eliminate (or at least reduce) such errors, we calibrate the measuring instrument by comparing its measurement against the value of a known standard. It is sometimes quite difficult to identify a systematic error.
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 wind. Random errors often have a Gaussian normal distribution http://www.physics.umd.edu/courses/Phys276/Hill/Information/Notes/ErrorAnalysis.html (see Fig. 2). In such cases statistical methods may be used to analyze the data. http://www.citycollegiate.com/phXch1a.htm 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 m is s/sqrt(n), where n is the number of measurements. Fig. 2. The Gaussian normal distribution. m = mean random error 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 < 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 how to reduce 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 by the wrong use of instruments are: errors in measurements of temperature due to poor thermal contact between the thermometer and the substance whose temperature is to be found, errors in measurements of solar radiation because trees or buildings shade the radiometer. The accuracy of a measurement is how close the measurement is to the true val
100 cm One meter = 1000 mm Kilogram Kilogram is the unit of mass in S.I. System. "Kilogram is defined as the mass of a platinum cylinder placed in the International Bureau of Weight and Measures in Paris." One kilogram = 1000gram Second Second is the unit of time in S.I. System. A second is defined in terms of the time period of Cs-133 atoms. i.e." one second is equal to 9,192,631,770 periods of vibrations of Cs-133 atoms." 60 seconds = one minute 3600 seconds = one hour Least Count Minimum measurement that can be made by a measuring device is known as " LEAST COUNT'. Least count (vernier callipers) = minimum measurement on main scale / total number of divisions on vernier scale . Least count (screw gauge) = minimum measurement on main scale / total number of divisions on circular scale Smaller is the magnitude of least count of a measuring instrument, more precise the measuring instrument is. A measuring instrument can not measure any thing whose dimensions are less than the magnitude of least count. Least Count of Vernier Callipers = 0.01 cm Least Count of Micrometer Screw gauge = 0.001 cm Zero Error It is a defect in a measuring device (Vernier Callipers & Screw Gauge). When jaws of a Vernier Callipers or Screw Gauge are closed, zero of main scale must coincides with the zero of vernier scale or circular scale in case of screw gauge. If they do not coincide then it is said that a zero error is present in the instrument. Types Of Zero Error Zero error may be positive or negative. A positive zero error in the instrument shows a larger measurement than the actual measurement. In order to get exact measurement, positive zero error is subtracted from the total reading. . A negative zero error in the instrument shows a smaller measurement than the actual measurement. In order to get exact measurement, negati