Error Physics Lab
Contents |
without proper error analysis, no valid physics lab error analysis scientific conclusions can be drawn. In fact, as the picture
Physics Lab Error Propagation
below illustrates, bad things can happen if error analysis is ignored. Since there is no way sources of error in experiments to avoid error analysis, it is best to learn how to do it right. After going through this tutorial not only will you know how to do it right, you might even find error sources of error in a chemistry lab analysis easy! The tutorial is organized in five chapters. Contents Basic Ideas How to Estimate Errors How to Report Errors Doing Calculations with Errors Random vs. Systematic Errors Chapter 1 introduces error in the scientific sense of the word and motivates error analysis. Chapter 2 explains how to estimate errors when taking measurements. Chapter 3 discusses significant digits and relative error. Chapter 4 deals with error propagation in calculations. Chapter 5 explains the difference between two types of error. The derailment at Gare Montparnasse, Paris, 1895. Next Page >> Home - Credits - Feedback © Columbia University
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,
Types Of Errors In Experiments
a poorly calibrated instrument such as a thermometer that reads 102 oC sources of error in physics when immersed in boiling water and 2 oC when immersed in ice water at atmospheric pressure. Such a
Examples Of Experimental Errors
thermometer would result in measured values that are consistently too high. 2. Observational. For example, parallax in reading a meter scale. 3. Environmental. For example, an electrical power ìbrown https://phys.columbia.edu/~tutorial/ outî that causes measured currents to be consistently too low. 4. Theoretical. Due to simplification of the model system or approximations in the equations 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 http://www.physics.nmsu.edu/research/lab110g/html/ERRORS.html 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 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 eq
sources. The process of evaluating this uncertainty associated with a measurement result is often called uncertainty analysis or error analysis. The complete statement of a measured value should include an estimate of the level of confidence associated http://user.physics.unc.edu/~deardorf/uncertainty/UNCguide.html with the value. Properly reporting an experimental result along with its uncertainty allows other people to make judgements about the quality of the experiment, and it facilitates meaningful comparisons with other similar values or a theoretical prediction. Without an uncertainty estimate, it is impossible to answer the basic scientific question: "Does my result agree with a theoretical prediction or results from other experiments?" This question is fundamental for deciding if a scientific hypothesis is confirmed of error or refuted. When we make a measurement, we generally assume that some exact or true value exists based on how we define what is being measured. While we may never know this true value exactly, we attempt to find this ideal quantity to the best of our ability with the time and resources available. As we make measurements by different methods, or even when making multiple measurements using the same method, we may obtain slightly different sources of error results. So how do we report our findings for our best estimate of this elusive true value? The most common way to show the range of values that we believe includes the true value is: measurement = best estimate ± uncertainty Let’s take an example. Suppose you want to find the mass of a gold ring that you would like to sell to a friend. You do not want to jeopardize your friendship, so you want to get an accurate mass of the ring in order to charge a fair market price. By simply examining the ring in your hand, you estimate the mass to be between 10 and 20 grams, but this is not a very precise estimate. After some searching, you find an electronic balance which gives a mass reading of 17.43 grams. While this measurement is much more precise than the original estimate, how do you know that it is accurate, and how confident are you that this measurement represents the true value of the ring’s mass? Since the digital display of the balance is limited to 2 decimal places, you could report the mass as m = 17.43 ± 0.01 g. Suppose you use the same electronic balance and obtain several more readings: 17.46 g, 17.42 g, 17.44 g, so that the average mass appears to be in the range of 17.44