|Feb26-12, 07:31 AM||#1|
Uncertainties for Stress
1. The problem statement, all variables and given/known data
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%
2. Relevant equations
3. 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
|Feb26-12, 08:56 AM||#2|
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.
|Feb26-12, 09:37 AM||#3|
See this text
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
|area, force, stress, uncertainty|
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