Answered: Using partial derivatives, calculate…

An Introduction to Physical Science

14th Edition

ISBN:9781305079137

Author:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres

Publisher:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres

Chapter1: Measurement

Section: Chapter Questions

Problem 9MC

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Question

Using partial derivatives, calculate the propagated uncertainty in the mass in the following case: given the centripetal force Fc = (20.0 ± 0.5) N, the angular velocity w = (29.2 ± 0.3) rad/s, and the radius R = (0.12 ± 0.01) m get the mass value,m = Fc / (w²R). Express the result in the form m = m + Δm

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THAT'S THE QUESTION ASKED, see the image for the answer.

Also have a look at the second image, the blue one.

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Explain what is the 1/m just after the equals sign at the second line of the answer. Also, explain why the answer does not use the square root just like the blue image, of if it is using it. Then, say in which case should I use the partial derivate to calculate the uncertainty.

Am = m
Δη
m
=
+
m =
m
1 roami
Δ
Fe
w²R
ω
+
ΔF +
20,0
29,2².0,12
lami
|du
Δω +
· kg = 0,195471 kg :
iam
[8m|^e] = [fr] +|al + [R] =
|ΔR] =
ƏR
· = 0,195471 kg ·
0,5 2.0,3
+
29,2
[20,0
m = (0, 20 ± 0,03) kg
+
0,011
0,12]
= 0,025193 kg

Experimental Uncertainty
σ₁ = f (0,0₁) = ±
d'
av
ad
2
av
at
+
Od
Ot
2

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