How To Use Error Bars To Calculate Uncertainty
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graphs | What to plot? | Examples ] Error and Uncertainty All readings, data, results or other numerical quantities taken from the real world by direct measurement or otherwise are subject to how to calculate absolute uncertainty physics uncertainty. This is a consequence of not being able to measure anything exactly. Uncertainty how to calculate uncertainty from a graph cannot be avoided but it can be reduced by using 'better' apparatus. The uncertainty on a measurement has to do with uncertainty physics a level the precision or resolution of the measuring instrument. When results are analysed it is important to consider the affects of uncertainty in subsequent calculations involving the measured quantities. If you are unlucky (or careless) then a level physics uncertainty questions your results will also be subject to errors. Errors are mistakes in the readings that, had the experiment been done differently, been avoided. It is perfectly possible to take a measurement accurately and erroneously! Unfortunately it is not always possible to know when you are making an error (otherwise you wouldn't make it!) and so godd experimental technique has to able to guard against the affect of errors Types of
A Level Physics Uncertainty Worksheet
Error: Human Error: Errors introduced by basic incompetence, mistakes in using the apparatus etc. Reduced by repeating the experiment several times and comparing results to those of other similar experiments, by ensuring results seem reasonable Systematic Error: Error introduced by poor calibration or zero point setting of instruments such as meters - this may cause instrumentation to always 'under read' or 'over read' a value by a fixed amount. Reduced by plotting graphs, the relationships between two quantities often depends on the way in which they change rather than their absolute values. A systematic error would manifest itself as an intercept on the y-axis other than that expected. In the A Level course this is most commonly experienced with micrometers (that don't read zero when nothing is between the jaws) and electrical meters that may not rest at zero Equipment Error: Error introduced by the mis-functioning of equipment. The only real check is to see if the results seem reasonable and 'make sense' ... take time to stop and think about what the instruments are telling you ... does it seem okay? Parallax Error: Error introduced by reading scales from the wrong angle i.e. any angle other than at right angles! Some meters have mirrors to help a
the picture below, the data points are shown by small, filled, black circles; each datum has error
Percentage Uncertainty Definition
bars to indicate the uncertainty in each measurement. It appears that uncertainty physics definition current is measured to +/- 2.5 milliamps, and voltage to about +/- 0.1 volts. The hollow triangles uncertainty in gradient excel represent points used to calculate slopes. Notice how I picked points near the ends of the lines to calculate the slopes! Draw the "best" line through all the points, http://pfnicholls.com/physics/Uncertainty.html taking into account the error bars. Measure the slope of this line. Draw the "min" line -- the one with as small a slope as you think reasonable (taking into account error bars), while still doing a fair job of representing all the data. Measure the slope of this line. Draw the "max" line -- the one with http://spiff.rit.edu/classes/phys369/workshops/w2c/slope_uncert.html as large a slope as you think reasonable (taking into account error bars), while still doing a fair job of representing all the data. Measure the slope of this line. Calculate the uncertainty in the slope as one-half of the difference between max and min slopes. In the example above, I find 147 mA - 107 mA mA "best" slope = ------------------ = 7.27 ---- 10 V - 4.5 V V 145 mA - 115 mA mA "min" slope = ------------------ = 5.45 ---- 10.5 V - 5.0 V V 152 mA - 106 mA mA "max" slope = ------------------ = 9.20 ---- 10 V - 5.0 V V mA Uncertainty in slope is 0.5 * (9.20 - 5.45) = 1.875 ---- V There are at most two significant digits in the slope, based on the uncertainty. So, I would say the graph shows mA slope = 7.3 +/- 1.9 ---- V Last modified 7/31/2007 by MWR. Copyright © Michael Richmond. This work is licensed under a Creative Commons License.
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 http://skipper.physics.sunysb.edu/~physlab/doku.php?id=phy124:error_and_uncertainty Graphs An experiment with the simple pendulum: Things one would measure Estimate of error in the length of the string Error in the period Making a plot of our data Uncertainty, Error and Graphs Uncertainty in measurements In physics, as in every other experimental science, one cannot make any measurement without having some degree of uncertainty. A proper experiment must report for how to each measured quantity both a “best” value and an uncertainty. Thus it is necessary 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”. to calculate uncertainty One could say that we occasionally use the concept of “best” value and its “uncertainty” in everyday speech, perhaps without even knowing 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 discuss