Problems with propagation of error

In summary, the conversation is about a person seeking help with understanding and solving problems related to propagation of error in equations involving multiplication, division, addition, subtraction, and powers. They are looking for clarification on their approach and whether it is correct or incorrect. The expert advises them to review the basics of error propagation and neglect constant values in the formula. They also suggest checking a resource for deriving error propagation for any given formula. The expert also gives feedback on the person's attempts at solving two specific questions, suggesting they do not need to use the square and square root and to transfer a minus sign to the whole expression.
  • #1
bobey
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  • #2
bobey said:
I have problem regarding the propagation of error since the equations involving mixtures of multiplication, division, addition, subtraction, and powers. Please help me to clarify whether my attempts are right or wrong.

https://www.physicsforums.com/attachments/333https://www.physicsforums.com/attachments/334
https://www.physicsforums.com/attachments/332View attachment 331

Hi bobey, :)

I think you should review how to calculate the propagation of errors. One of the basic things that you should remember is to neglect the constant values of the formulas when deriving the error propagation formula. For example take your Question 1.

\[D=-\frac{L}{4m}\]

Now, the error propagation formula would be,

\[\frac{\Delta D}{D}=\sqrt{\left(\frac{\Delta L}{L}\right)^2+\left(\frac{\Delta m}{m}\right)^2}\]

Even if you have the formula, \(\displaystyle D=\frac{L}{m}\) you get the same error propagation formula above. The constant \(-\frac{1}{4}\) have no significance.

Read http://www.fas.harvard.edu/~scphys/nsta/error_propagation.pdf and this to find out how to derive the error propagation for any given formula.

Kind Regards,
Sudharaka.
 
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  • #3
Sudharaka said:
Hi bobey, :)

I think you should review how to calculate the propagation of errors. One of the basic things that you should remember is to neglect the constant values of the formulas when deriving the error propagation formula. For example take your Question 1.

\[D=-\frac{L}{4m}\]

Now, the error propagation formula would be,

\[\frac{\Delta D}{D}=\sqrt{\frac{\Delta L}{L}+\frac{\Delta m}{m}}\]

I would check this if I were you.

CB
 
  • #4
Problems with propagation of error for multiple variables

please help by telling me whether my approach to solve the problems are right or wrong. please refer to the ATTACHMENT for the questions and my approaches...

your help is highly appreciated!

question 1
View attachment 336
question 2
View attachment 337
 

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  • #5
Re: Problems with propagation of error for multiple variables

bobey said:
please help by telling me whether my approach to solve the problems are right or wrong. please refer to the ATTACHMENT for the questions and my approaches...

your help is highly appreciated!

question 1
View attachment 336

For this one you should not need the square and square root, they cancel, and anyway you only use a root sum of squares composition of errors when there is more than one variable involved.

CB
 
  • #6
Re: Problems with propagation of error for multiple variables

bobey said:
please help by telling me whether my approach to solve the problems are right or wrong. please refer to the ATTACHMENT for the questions and my approaches...

your help is highly appreciated!

question 1
View attachment 336
question 2
View attachment 337

For the second the same comment as for the first, otherwise OK (except you should transfer the minus sign attached to the 2 to the whole expression.

CB
 

FAQ: Problems with propagation of error

What is propagation of error?

Propagation of error, also known as error propagation or error analysis, is a method used to quantify how uncertainties in measured quantities affect the uncertainty in a calculated quantity.

Why is propagation of error important?

Propagation of error is important because it allows scientists to understand and account for uncertainties in their measurements and calculations. It also helps to determine the overall accuracy of an experiment or study.

What are the sources of error in propagation of error?

There are two main sources of error in propagation of error: random error and systematic error. Random error is caused by chance and is unpredictable, while systematic error is caused by a flaw in the experimental setup or equipment and can be corrected for.

How is propagation of error calculated?

Propagation of error is calculated using the law of propagation of uncertainty, which states that the uncertainty in a calculated quantity is equal to the square root of the sum of the squares of the uncertainties in the measured quantities involved in the calculation.

What are some ways to minimize error in propagation of error?

To minimize error in propagation of error, scientists can use more precise measurement tools, increase the number of measurements taken, and reduce sources of systematic error. It is also important to accurately record and analyze data to reduce human error.

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