Error Propagation Problems
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or more quantities, each with their individual uncertainties, and then combine the information from these quantities in order to come up with a final result of our experiment. How can you state your answer for the combined result of these measurements and their uncertainties scientifically? The answer to this fairly common question depends on error propagation example how the individual measurements are combined in the result. We will treat each case separately: Addition error propagation division of measured quantities If you have measured values for the quantities X, Y, and Z, with uncertainties dX, dY, and dZ, and your final result, R, error propagation physics is the sum or difference of these quantities, then the uncertainty dR is: Here the upper equation is an approximation that can also serve as an upper bound for the error. Please note that the rule is the same for addition
Error Propagation Calculus
and subtraction of quantities. Example: Suppose we have measured the starting position as x1 = 9.3+-0.2 m and the finishing position as x2 = 14.4+-0.3 m. Then the displacement is: Dx = x2-x1 = 14.4 m - 9.3 m = 5.1 m and the error in the displacement is: (0.22 + 0.32)1/2 m = 0.36 m Multiplication of measured quantities In the same way as for sums and differences, we can also state the result for the case of multiplication and division: Again the upper error propagation khan academy line is an approximation and the lower line is the exact result for independent random uncertainties in the individual variables. And again please note that for the purpose of error calculation there is no difference between multiplication and division. Example: We have measured a displacement of x = 5.1+-0.4 m during a time of t = 0.4+-0.1 s. What is the average velocity and the error in the average velocity? v = x / t = 5.1 m / 0.4 s = 12.75 m/s and the uncertainty in the velocity is: dv = |v| [ (dx/x)2 + (dt/t)2 ]1/2 = 12.75 m/s [(0.4/5.1)2 + (0.1/0.4)2]1/2 = 3.34 m/s Multiplication with a constant What if you have measured the uncertainty in an observable X, and you need to multiply it with a constant that is known exactly? What is the error then? This is easy: just multiply the error in X with the absolute value of the constant, and this will give you the error in R: If you compare this to the above rule for multiplication of two quantities, you see that this is just the special case of that rule for the uncertainty in c, dc = 0. Example: If an object is realeased from rest and is in free fall, and if you measure the velocity of this object at some point to be v = - 3.8+-0.3 m/s, how long has it been in free fall? Answer: we can calculate the time as (g = 9.81 m/s2
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Error Propagation Chemistry
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Error Propagation Log
Alle entfernenBeenden Wird geladen... Wiedergabeliste Warteschlange __count__/__total__ Differentials: Propagated Error AllThingsMath AbonnierenAbonniertAbo beenden337337 Wird geladen... Wird geladen... Wird verarbeitet... Hinzufügen Möchtest http://lectureonline.cl.msu.edu/~mmp/labs/error/e2.htm du dieses Video später noch einmal ansehen? Wenn du bei YouTube angemeldet bist, kannst du dieses Video zu einer Playlist hinzufügen. Anmelden Teilen Mehr Melden Möchtest du dieses Video melden? Melde dich an, um unangemessene Inhalte zu melden. Anmelden Transkript Statistik 9.363 Aufrufe https://www.youtube.com/watch?v=6u-ldWJKN7A 39 Dieses Video gefällt dir? Melde dich bei YouTube an, damit dein Feedback gezählt wird. Anmelden 40 2 Dieses Video gefällt dir nicht? Melde dich bei YouTube an, damit dein Feedback gezählt wird. Anmelden 3 Wird geladen... Wird geladen... Transkript Das interaktive Transkript konnte nicht geladen werden. Wird geladen... Wird geladen... Die Bewertungsfunktion ist nach Ausleihen des Videos verfügbar. Diese Funktion ist zurzeit nicht verfügbar. Bitte versuche es später erneut. Hochgeladen am 02.10.2011An Example of propagated error. Kategorie Bildung Lizenz Standard-YouTube-Lizenz Mehr anzeigen Weniger anzeigen Wird geladen... Autoplay Wenn Autoplay aktiviert ist, wird die Wiedergabe automatisch mit einem der aktuellen Videovorschläge fortgesetzt. Nächstes Video Differentials: Intro - Dauer: 6:45 AllThingsMath 919 Aufrufe 6:45 Propagation of Errors - Dauer: 7:04 paulcolor 29.438 Aufrufe 7:04 Propagation of Uncertaint
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