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# AS Physics - Uncertainty? watch

1. Ah, can someone help me with this question please?

Basically the question is about stress, strain, and Young Modulus. One of the questions says "What was the uncertainty in the diameter of the lace? What was the percentage uncertainty in the area?"

In the question you are given five diameters {1.02, 0.99, 1.04, 1.03, and 1.05}. I worked out the average, and then worked out the area using the average diameter {I calculated the average as 1.026mm, and the area as 8.27x10-7m2}. I don't know what it means by "uncertainty" and "percentage uncertainty"? Can anyone explain this to me?

The question includes a table of values for load {N}, extension {mm}, stress, and strain, and I plotted a stress-strain graph.
2. It is referring to http://en.wikipedia.org/wiki/Measurement_uncertainty I'd guess standard uncertainty. In which case it's the standard deviation of those values.

Have you done the propagation of errors?
3. (Original post by Hanvyj)
It is referring to http://en.wikipedia.org/wiki/Measurement_uncertainty I'd guess standard uncertainty. In which case it's the standard deviation of those values.

Have you done the propagation of errors?
No we haven't done anything on uncertainty or propagation of errors :/ I'm not really sure what I'd write as an answer?
4. Anything?? This is really urgent, I have to hand this in tomorrow and I don't want to hand in unfinished homework that I couldn't do :/
5. I suggest you ask your teacher why they are assigning homework for stuff that isn't covered. Can you work out a standard deviation? It's statistics not physics really...

Error/uncertainty Propagation: Basically, you have a reading like '1m' with an error of 0.2m. If you add two of those values together, you follow certain rules for calculating the 'final' uncertainty in your reading. I'm not going to straight up tell you the answer.

Take a look at these:

http://courses.washington.edu/phys43...errors_UCh.pdf
http://www.rit.edu/~w-uphysi/uncerta...tiespart2.html

and see how you get along
6. (Original post by Hanvyj)
I suggest you ask your teacher why they are assigning homework for stuff that isn't covered. Can you work out a standard deviation? It's statistics not physics really...

Error/uncertainty Propagation: Basically, you have a reading like '1m' with an error of 0.2m. If you add two of those values together, you follow certain rules for calculating the 'final' uncertainty in your reading. I'm not going to straight up tell you the answer.

Take a look at these:

http://courses.washington.edu/phys43...errors_UCh.pdf
http://www.rit.edu/~w-uphysi/uncerta...tiespart2.html

and see how you get along
I've never seen any of the stuff on those sites before :/ I missed a physics lesson because I had a biology field trip, so they might've done something then but I can't imagine it was anything like that. That looks way too complicated for a two mark question..
7. You have a minimum value of 0.99mm and a maximum value of 1.05mm. The range is 1.05-0.99 = 0.06mm. If you half this, you get a spread of 0.03mm. You can use this as your uncertainty (there are more complex methods of estimating uncertainty, but at AS this will suffice). You can then work out what 0.03mm is as a percentage of 1.026mm. For the area, you should convert everything into meters first, and then calculate the uncertainty. You will have to double the % unc. for area however as to calculate it it is A=(pi)r^2 (it's easier if you think about uncertainties as if you had a square - you'd have length*width, so you'd have the uncertainty in both dimensions. The same applies to a circle).

Hope this helps, quote me if there's something I haven't explained very well or if you don't understand anything.
8. (Original post by ChrissM)
You have a minimum value of 0.99mm and a maximum value of 1.05mm. The range is 1.05-0.99 = 0.06mm. If you half this, you get a spread of 0.03mm. You can use this as your uncertainty (there are more complex methods of estimating uncertainty, but at AS this will suffice). You can then work out what 0.03mm is as a percentage of 1.026mm. For the area, you should convert everything into meters first, and then calculate the uncertainty. You will have to double the % unc. for area however as to calculate it it is A=(pi)r^2 (it's easier if you think about uncertainties as if you had a square - you'd have length*width, so you'd have the uncertainty in both dimensions. The same applies to a circle).

Hope this helps, quote me if there's something I haven't explained very well or if you don't understand anything.
Why do you half the 0.06mm?
9. (Original post by lulagreenleaf)
Why do you half the 0.06mm?
This is the range of your values. When you half it you get +/- 0.03mm.

EDIT: So you can say the diameter is 1.026mm+/-0.03mm. Also, when calculating the uncertainty for area, you should actually halve the uncertainty in the diameter as you will have calculated the area using the radius.
10. (Original post by lulagreenleaf)
I've never seen any of the stuff on those sites before :/ I missed a physics lesson because I had a biology field trip, so they might've done something then but I can't imagine it was anything like that. That looks way too complicated for a two mark question..
This might be simpler, though it's not how I learned it.

http://web.uvic.ca/~jalexndr/192UncertRules.pdf

Multiplying by a constant just plains multiplies the error. So:
( 2 +/- 0.5 ) * 4

= (2x4) +/- (0.5 x 4)

= 8 +/- 0.2

If you were adding two lengths of say, 2m +/- 0.05, then your final length is

= (2+2) +/- (0.5 + 0.5)

= 4 +/- 0.1

If you are multiplying, you add their relative uncertainty. So a square of 2m +/- 0.05

= square of 2m +/- 2.5%

= (2x2) +/- (2.5% + 2.5%)

= 4 +/- 5%

= 4 +/- 0.2

You can use those rules. That's my interpretation of the internet anyway - I haven't done this for years and I'm sure I did it in a different way! This may not be correct.

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