Error Propagation: x/(y-z) Uncertainty

AI Thread Summary
To find the uncertainty in the quantity q = x/(y-z), the discussion emphasizes the need to apply error propagation methods, particularly for the subtraction in the denominator (y-z). The uncertainties for x, y, and z are independent and random, requiring the use of derivatives to assess how each contributes to the overall uncertainty in q. Specifically, when subtracting y and z, the uncertainties must be combined by adding their squares and taking the square root to find the new uncertainty. The conversation reveals that many participants are struggling with the initial steps of the problem and the application of these principles. Understanding how to propagate errors in both addition and subtraction is crucial for accurately calculating the uncertainty in q.
newbe318
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Homework Statement


Suppose you measure three numbers as follows:

Homework Equations


x= 200. +-2.
y= 50. +-2.
z= 40. +-2.

where the three uncertainties are independent and random. Use step-by-step propagation to find the quantity
q= x/(y-z) with its uncertainty.

The Attempt at a Solution


I do not know what to do. The only thing I am thinking of doing is taking the derivatives of the func., q= x/(y-z), with respect to x, y, and z, ... and ... that's it. I'm stuck. Help, please?
 
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newbe318 said:

Homework Statement


Suppose you measure three numbers as follows:

Homework Equations


x= 200. +-2.
y= 50. +-2.
z= 40. +-2.

where the three uncertainties are independent and random. Use step-by-step propagation to find the quantity
q= x/(y-z) with its uncertainty.

The Attempt at a Solution


I do not know what to do. The only thing I am thinking of doing is taking the derivatives of the func., q= x/(y-z), with respect to x, y, and z, ... and ... that's it. I'm stuck. Help, please?

How is error propagated in the (y-z) part? That will produce some new uncertainty a, which you then propagate for x/a. How far have you actually gotten?
 
I didn't get very far.
I skipped that problem and continued with my other homework problems.
 
newbe318 said:
I didn't get very far.
I skipped that problem and continued with my other homework problems.

Do you know how error is propagated in subtraction?
 
You add them?
 
newbe318 said:
You add them?

You add the sum of the uncertainties squared, then take the square root. Is it apparent why?

So what's the uncertainty of a?
 
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