Error Propagation Unit Conversion
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uncertainty of an answer obtained from a calculation. Every time data are measured, there is an uncertainty associated with that measurement. (Refer to guide error propagation example to Measurement and Uncertainty.) If these measurements used in your calculation have
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some uncertainty associated with them, then the final answer will, of course, have some level of uncertainty. error propagation physics For instance, in lab you might measure an object's position at different times in order to find the object's average velocity. Since both distance and time measurements have uncertainties error propagation calculus associated with them, those uncertainties follow the numbers throughout the calculations and eventually affect your final answer for the velocity of that object. How would you determine the uncertainty in your calculated values? In lab, graphs are often used where LoggerPro software calculates uncertainties in slope and intercept values for you. In other classes, like chemistry, there are particular
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ways to calculate uncertainties. In fact, since uncertainty calculations are based on statistics, there are as many different ways to determine uncertainties as there are statistical methods. The error propagation methods presented in this guide are a set of general rules that will be consistently used for all levels of physics classes in this department. In the following examples: q is the result of a mathematical operation δ is the uncertainty associated with a measurement. For example, if you have a measurement that looks like this: m = 20.4 kg ±0.2 kg Thenq = 20.4 kg and δm = 0.2 kg First Step: Make sure that your units are consistent Make sure that you are using SI units and that they are consistent. If you are converting between unit systems, then you are probably multiplying your value by a constant. Please see the following rule on how to use constants. Logger Pro If you are using a curve fit generated by Logger Pro, please use the uncertainty associated with the parameters that L
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science is here! Error propagation in calculations Jul 24, 2011 #1 jakerue This is an issue I am running into at the beginning of my physics course. 1. The http://physics.appstate.edu/undergraduate-programs/laboratory/resources/error-propagation problem statement, all variables and given/known data Given distance and time in minutes, calculate the time in hours (part of a larger average velocity question) and graph over 170minutes. Include error bars in the graph 2. Relevant equations So if tm = 10.0 +/- 0.1min and I use min -> hr conversion as 1hr/60min = 0.0167 th = 10.0min https://www.physicsforums.com/threads/error-propagation-in-calculations.516670/ * 0.0167 hrs/min = 0.167 min 3. The attempt at a solution The error in min is +/- 0.1 min. Now if I am using 0.0167hrs/min as an exact constant factor I should use z=k*x and [itex]\Delta[/itex]z= k [itex]\Delta[/itex]x So I will use hours = 0.0167 * minutes and my [itex]\Delta[/itex]hours = 0.0167 * 0.1min making the [itex]\Delta[/itex]hours = 0.00167hours. By sig fig this value is 0.002 hours correct? At 10 minutes th = 0.167 +/- 0.002hrs at 120 minutes th = 2.00 hrs +/- 0.002 hrs I think I am right but I want to make sure my answer is correct and that this error holds true for all values of minutes from 0-170min. Thanks for any help, most appreciated. JakeRue jakerue, Jul 24, 2011 Phys.org - latest science and technology news stories on Phys.org •Game over? Computer beats human champ in ancient Chinese game •Simplifying solar cells with a new mix of materials •Imaged 'jets' reveal cerium's post-shock inner strength Jul 24, 2011 #2 Delphi51 Homework Helper Looks good, JakeRue. Certai
absolute error. Absolute error is the actual value of the error in physical units. For example, let's say you managed to measure the length of your dog L to be 85 cm with a precision 3 cm. https://phys.columbia.edu/~tutorial/reporting/tut_e_3_2.html You already know the convention for reporting your result with an absolute error Suppose you also regularly monitor the mass of your dog. Your last reading for the dog's mass M, with absolute error included, is Which measurement is more precise? Or in other words, which one has a smaller error? Clearly, we cannot directly compare errors with different units, like 3 cm and 1 kg, just as we cannot directly compare apples and oranges. However, there should be error propagation a way to compare the precision of different measurements. Enter the relative or percentage error. Let's start with the definition of relative error Let's try it on our dog example. For the length we should divide 3 cm by 85 cm. We get 0.04 after rounding to one significant digit. For the mass we should divide 1 kg by 20 kg and get 0.05. Note that in both cases the physical units cancel in the ratio. Thus, relative error error propagation unit is just a number; it does not have physical units associated with it. Moreover, it's not just some number; if you multiply it by 100, it tells you your error as a percent. Our measurement of the dog's length has a 4% error; whereas our measurement of the dog's mass has a 5% error. Well, now we can make a direct comparison. We conclude that the length measurement is more precise. Finally, let us see what the convention is for reporting relative error. For our dog example, we can write down the results as follows The first way of writing is the familiar result with absolute error, and the second and third ways are equally acceptable ways of writing the result with relative error. (Writing the result in the parentheses form might seem a little bit awkward, but it will turn out to be useful later.) Note that no matter how you write your result, the information in both cases is the same. Moreover, you should be able to convert one way of writing into another. You know already how to convert absolute error to relative error. To convert relative error to absolute error, simply multiply the relative error by the measured value. For example, we recover 1 kg by multiplying 0.05 by 20 kg. Thus, relative error is useful for comparing the precision of different measurements. It also makes error propagation calculations much simpler, as you wi