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Intermediate Lab A

by: Yvonne McKenzie

Intermediate Lab A PHYSICS 440

Yvonne McKenzie
GPA 3.62


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Class Notes
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This 6 page Class Notes was uploaded by Yvonne McKenzie on Friday October 30, 2015. The Class Notes belongs to PHYSICS 440 at University of Massachusetts taught by Staff in Fall. Since its upload, it has received 21 views. For similar materials see /class/232314/physics-440-university-of-massachusetts in Physics 2 at University of Massachusetts.

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Date Created: 10/30/15
Achermann 112007 ErrorDiscussionppt Umass Amherst Physics 440 Error propagation f fX f a 6f 5 6x 5xgtf7 x x m ltf7c x a ltfx mlgt ltff J 5x gt21 0 6x 7 6x 7 Example f x sinbx Q Ziax nx H sinbxx 1bcosbx 0x x x n 0f nax Ha 0 Relative error f ax x n x Error propagation f fxyz use fxyfltmi X 5x 6y 5y 05j5j x y and uncorrelated variables lt5x5ygt 0 Example f xy a a a 47 Example g F absolute relative 2 2 2 2 2 4 2 4 2 039 039 039 0 7 07227z3 039 212 T T g l T of data points m p m m 8 3 o o o o o o I I I I I I o I fx2 gt 0300 2039Xx X o f x2 o o axX 10019927 0101 csf 199799555 0201 0 q 39r H1u ooo 0 afor a function of a variable o o o 9 o moodo I I I I I I I 20 4o 60 so 100 120 140 160 180 value of data points l xltxgt 100 O x2ltx2gt I 80 39 391 quot39 60 I O 5 40 M630 0 I g 950 1 20 Ch O 0 CD 39 Q6 ISOiota o W I I I I I I I 04 06 08 10 12 14 16 valuemean afor a function of two variables x ly If xy mean 9927 3 024 3009 2 2 Std dev 100121 099662 10556 ny gt Off OxX tiy2 Slderr 003166 003152 0338 100 o x GXltXgt 10019927 0 I y cyltygt 09973024 o f xy cgltfgt 10556301 I l cXltxgt2 cyltygt2 03452 E 09 cltfgt2 03512 a 4 g 10 8 E I mm m I cmmmm 3 o elm cm moo I modem 00 0 on o 1 I I Y I I TW39 I flx39 l 0 10 20 30 40 50 60 70 Systematic error vs random errors Systematic errors Reproducible inaccuracies that shift the result consistently in one direction Example Wrong calibrated instrument Often one can correct results for systematic errors Random errors Statistical fluctuation of measured data due to randomness in the measured process or in the measurement device Random errors can be reduced through averaging X X X Bad accuracy Good precision Good accuracy Bad precision Reporting results significant figures 13 WWW39E WLg i39mi it p it H i0 Good or bad G 667x1011 1 5gtlt1O13 Nm2kg2 G 667 i 005gtlt1011 Nm2kg392 G 6673 i 0010gtlt1011 Nm2kg392 G 667 i 0001 gtlt1011 Nm2kg2 G 66726 i 005gtlt1011 Nm2kg392


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