Find error in w:
(1) w = x + 2y - 3z = 14
(2) w = 2t - 3e = -115
(3) w = x * 2y * 3z = 600
(4)w = 2x/2y = x/y = 2
(5) w = 1/8 (1/y) + ¾ (z/x) + ¼ (y/x) = 0.3
(6) w = 2 (y/z) - 3(x/z) = -10
(7) w=ycost = 4.92
(8) w = t2/sin t = v1 / v2 = 575.877
(9) w = tan t / tan e = 0.1763
(10)w = x3 / cos e = v1/v2 = 1414.2136
(11) w = ln x = 2.303
(12) w=ln (x/3y2) = -2.0149
(13) w = 3 x-2 + 5 y-3
(14)w = (x3 + 3y/z2) ½ = 31.682
Following is the text part of the solution. Please see the attached file for complete solution. Equations, diagrams, graphs and special characters will not appear correctly here.
For all the calculations I have used the following general rules for calculating the propagation of error.
w = x +/- y, dw = dx +/- dy
w = xy or x/y, dw/w = dx/x + dy/y
w= xmyn , dw/w = |m| dx/x + |n| dy/y
w = f(x,y), dw = |f/x| dx + |f/y| dy
w = x + 2y - 3z = 14
dw = dx + 2dy + 3dz = 3.6
% error = dw/w *100 = 25.7%
w = 2t - 3e = -115
dw = 2dt + 3de = 14
% error = dw/w *100 = 12.2%
w = x * ...
I have calculated the error in 14 different functions, which involves sine, cosine, ln and tan functions. I consider this problem set to be a great practice problem set for students who are taking physics/Engineering laboratory.
Problems Involving Propagation of Measurement Error
Please see attachment for problems with appropriate symbol notations.
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