Error Propagation: x/(y-z) Uncertainty

Click For Summary
SUMMARY

The discussion focuses on error propagation in the calculation of the quantity q = x/(y-z), where x, y, and z are measured values with associated uncertainties. The participants emphasize the importance of understanding how to propagate uncertainties, particularly in the subtraction of y and z, which requires adding the squared uncertainties of both values. The final uncertainty in q is derived from the uncertainties of x and the result of (y-z). The method of propagation is confirmed to be through the use of derivatives and the combination of uncertainties.

PREREQUISITES
  • Understanding of basic calculus, specifically derivatives.
  • Familiarity with the concept of independent random uncertainties.
  • Knowledge of error propagation techniques, particularly for addition and subtraction.
  • Experience with uncertainty analysis in measurements.
NEXT STEPS
  • Study the method of error propagation for functions of multiple variables.
  • Learn about the propagation of uncertainty in subtraction and addition of independent variables.
  • Explore the use of derivatives in calculating uncertainties in complex functions.
  • Review practical examples of error propagation in scientific measurements.
USEFUL FOR

Students in physics or engineering, researchers conducting experiments with measured quantities, and anyone involved in uncertainty analysis in scientific calculations.

newbe318
Messages
12
Reaction score
0

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?
 
Physics news on Phys.org
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?
 

Similar threads

Replies
15
Views
2K
  • · Replies 4 ·
Replies
4
Views
1K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 15 ·
Replies
15
Views
4K
  • · Replies 13 ·
Replies
13
Views
2K
  • · Replies 1 ·
Replies
1
Views
4K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 9 ·
Replies
9
Views
3K
  • · Replies 2 ·
Replies
2
Views
1K