How can uncertainties be calculated for equations and variables?

In summary: Then look at how those compare. In summary, the uncertainty in Y is very large, and may be due to incorrect calculations.
  • #1
dagg3r
67
0
Hi guys, i am trying to work out the uncertainty of this equation

Y = (AC-CX)/(B+X)
and i am needed to work out the uncertainty in Y.

values for these are:
Y=2.18 UNCERTAINTY UNKNOWN
A=29m Uncertainty in A denoted (Sa)=3mm
B=710mm Uncertainty in B denoted(Sb)=3mm
C=5.85mm Uncertainty in C denoted(Sc)=0.2mm
D=0.150mm Uncertainty in D denoted (Sd)=0.005mm
X=18.68m Uncertainty in X denoted (Sx)=0.005mm

using these values i used the formula:

Sy/Y = (Sc/C)+ S[(A-x)(B+x)]/[(A-x)(B+x)]
Sy/Y = (0.2/5.85) + (0.1099555934/0.3723445134)
Sy= 0.7182971382

i obtained an uncertainty of 0.7 it is very large hence i think i may have done something wrong in my calculations.

to obtain S[(A-x)(B+x)]
i did
[S(A-x)/(a-x)] + [S(B+x)/(B+x)]
=[(3mm+.005)/(29-18.68)] + [(3mm+.005)/(710+18.68)]
=0.1099555934

so can anyone please check this thanks!

also another simple question
Y= (AC-CX)/(B+X)
how do i derive for B, keeping everything else constant?
eg if i were to derive with respect to C, whilst keeping everything else constant i would get
: [A-X/(B+X)] ... so how do i derive with respect to B while keeping everything else constant since it is in the denomitor...

THANKS ALL
 
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  • #2
First question: Looks to me like your arithmetic is just wrong!
0.2/5.85= 0.034188... and 0.1099555934/0.3723445134= 0.29530606591642170268376325203836. Their sum is about 0.329, not 0.7.


As for the derivative of Y= (AC-CX)/(B+X) with respect to B, use the quotient formula:
[tex]\frac{\partial Y}{\partial B}= \frac{(0)(B+X)- (AC-CX)(1)}{(B+X)^2}= \frac{CX- AC}{(B+X)^2}[/tex].
 
  • #3
Sy/Y = (0.2/5.85) + (0.1099555934/0.3723445134)
yes you are correct the sum is 0.329
but i had
Sy= 0.7182971382

which is the sum multiplyed by Y
so
0.329*2.18=0.7182971382
which is the uncertainty in Y... but i don't know if its right or not the way i went about it all.

so is their another way of working out uncertainty?
 
Last edited:
  • #4
Well, one thing you could do is this: calculate each of the given number plus[\b] their "uncertainty" and minus. Use those to see what is the largest and smallest values Y could have.
 

1. What is the purpose of calculating uncertainties in scientific measurements?

Calculating uncertainties allows scientists to determine the level of confidence in their results. This is essential in ensuring the accuracy and reliability of scientific data and conclusions.

2. How are uncertainties typically calculated?

Uncertainties are often calculated using statistical methods based on the precision and accuracy of the measurement tools used. This can include methods such as standard deviation, error propagation, and confidence intervals.

3. What is the difference between precision and accuracy in uncertainty calculations?

Precision refers to the degree of consistency and reproducibility in a measurement, while accuracy refers to how close a measurement is to the true value. Uncertainty calculations take both precision and accuracy into account to determine the reliability of a measurement.

4. How do uncertainties impact scientific conclusions?

Uncertainties can affect the significance and validity of scientific conclusions. Higher uncertainties can decrease the confidence in results and may require further analysis or experimentation to reach a more definitive conclusion.

5. Can uncertainties be completely eliminated?

No, uncertainties are inherent in any scientific measurement. However, through careful experimentation and analysis, uncertainties can be minimized to increase the reliability and accuracy of results.

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