Error Propagation: x/(y-z) Uncertainty

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Homework Help Overview

The discussion revolves around error propagation in the context of measuring three quantities: x, y, and z, with associated uncertainties. The specific focus is on calculating the uncertainty of the derived quantity q = x/(y-z).

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants express uncertainty about how to proceed with the problem, particularly in taking derivatives for error propagation. Questions arise regarding the propagation of error in the subtraction of y and z, and how that affects the overall uncertainty in q.

Discussion Status

The discussion reflects a lack of progress on the problem, with some participants indicating they have moved on to other homework. However, there is an exploration of the method for propagating error in subtraction, with some guidance offered on combining uncertainties.

Contextual Notes

Participants note that the uncertainties are independent and random, and there is a specific emphasis on using step-by-step propagation methods. The discussion highlights a need for clarity on the rules of error propagation, particularly in the context of subtraction and division.

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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