How Do You Calculate Uncertainty in Stress Measurements?

[abray10]

Homework Statement

For my physics course work i need to work out the uncertainty of stress, is there formula for this or is it just the largest value of uncertainty

for example is my area is 7.548E-08 +/- 6.452% and my force 2 +/- 25%

Homework Equations

stress= Force/area

The Attempt at a Solution

I tried putting both the uncertaintys in the equation for stess so 6.452/25% but the uncertainty becomes far to small then

 

[AdrianMay]

I suggest that you try all four extreme combinations and just see what uncertainty you get. Try that first just for fun.

Then, consider this logic: I'm going to rewrite your equation as Stress = Force*Smallness where Smallness is something I just invented equal to 1/Area.

25% is too big for this to work accurately so I'll change it to 5%.

So if Area is 2 +/- 5%, what about Smallness? Area is 1.9 -> 2.1 so Smallness is 0.526 -> 0.476 which is near enough 0.5 +/- 0.025 which is 5%

So if the percentage uncertainty in X is Y then the percentage uncertainty in 1/X is also roughly Y.

So when you divide A by B you treat the percentage uncertainties just as you would if you'd multiplied them.

If you remember, you add the uncertainties when you multiply the quantities. If you don't, do what I said up top just for fun.

As for that 25% I had to tiptoe around, well indeed, this whole way of treating uncertainties is just a fairly bad approximation, and it fails badly at numbers like 25%. If you want to know the real deal, study statistics.

Adrian.

 

[Astronuc]

See this text
http://books.google.com/books?id=giFQcZub80oC&lpg=PA61&pg=PA61#v=onepage&q&f=false

The uncertainty in area measurement is independent of applied force and it's uncertainty.

Note that σ = F/A, and one is looking for δσ based on F±δF and A±δA