Error Propagation for F=4*pi^2*r*m/T^2

In summary: The uncertainty in F/uncertainty in r is the value that you get after evaluating the partial derivative expression.In summary, when dealing with error propagation in a formula like F=4*pi^2*r*m/T^2, you need to consider the uncertainties associated with each variable (r, m, and T). If a variable has no uncertainty, it does not contribute to the final error. To calculate the error in F, you can use the partial derivative method, treating the other variables as constants and substituting in known values. The final expression will be the partial derivative of F with respect to r, squared, multiplied by the square of the uncertainty in r.
  • #1
badtwistoffate
81
0
I know there is a formulas for doing error propagation with separate formulas for when dealing with powers, multiplying/dividing, and adding/subtraction.
What about if I have the formula F=4*pi^2*r*m / T^2...?
Also should i do error propagation for the varibles in the formula r (radius), and T(Period).
 
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  • #2
If the variables in your formula r,m and T each have an associated uncertainty then you take into account their affect on the final result F.
I'm pretty useless with the Latex and it is just easier and faster to do it in word so I've explained what I've done in the attached document instead.
I'm sorry if I've explained stuff you already know, but like I said, I don't really have an idea of what you know already so I thought I'd cover all bases.
 

Attachments

  • Equation 1.doc
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  • #3
why can't i download it?
 
  • #4
Yeah sorry forgot about the pending approval thing so you can't see it until a mod approves it, but yeah I can just send it to you if you want.
 
Last edited:
  • #6
done.

If you don't really follow it then just come back here to discuss it and I will try and clarify it...or someone else will.
 
  • #7
Um with eqn 2, in the square root, After the (uncertainty in f / uncertainty in m) squared, is that then times the standard deviation of m squared? Also in ours m, has no uncertainty so we just leave that term out of eqn 1?
 
  • #8
Yeah if it has no error associated with its value then it doesn't contribute to the error in the final value.
The [tex]\sigma_m[/tex] is just the uncertainty associated with the value m.
However, since you are given the value of m and it doesn't have an uncertainty then you will just leave it out of the expression. Remember that you only include the expressions that have an associated uncertainty.
 
  • #9
Also, could you try explaining this part again? So for the partial derivative (uncertainty in F/uncertainty in r ) we treat the variables m and T as constants while differentiating F with respect to r. so the partial derivative is just the equation without r? And we sub this into the partial derivative spot? Do we sub those numbers in too?
 
  • #10
To answer your question about the partial derivative, yes it will just become the equation without r in it. Once you have the partial derivative expression you substitute in your known values for T and m into the expression. Then square the expression and multiply by the square of the uncertainty in r. By the way the partial derivative symbol that I used isn't uncertainty in F/uncertainty in r. It is essentially dF/dr...the symbol just tells you that it is the partial derivative.
 

1. What is error propagation?

Error propagation is the process of calculating the uncertainty or error in a final result when it is dependent on multiple variables that also have uncertainties.

2. How is error propagation calculated for the equation F=4*pi^2*r*m/T^2?

To calculate error propagation for this equation, you would first calculate the partial derivatives of each variable (F, r, m, and T), then plug them into the equation: √( (δF/δr)^2 * (δr)^2 + (δF/δm)^2 * (δm)^2 + (δF/δT)^2 * (δT)^2 ).

3. What are the sources of error in the equation F=4*pi^2*r*m/T^2?

The sources of error in this equation could include uncertainties in the measurements of r (radius), m (mass), and T (period), as well as potential rounding errors in the calculation of 4*pi^2.

4. Can error propagation be used to improve the accuracy of a measurement?

Yes, error propagation can be used to identify the sources of error in a measurement and provide a more accurate estimation of the final result by accounting for these uncertainties.

5. How does error propagation differ from standard error or standard deviation?

Error propagation takes into account the uncertainties of multiple variables in a final result, while standard error or standard deviation measures the variability or spread of a set of data points. Error propagation is used to calculate the uncertainty in a single result, while standard error or standard deviation is used to analyze a set of data.

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