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# Help with uncertainties? watch

1. I just have a couple of questions about combining uncertainties.

If I am measuring the diameter of a circle and have an uncertainty of +/- 0.00001 m, then is the uncertainty just half of that if I want the radius?

And what happens when I use the radius to find the area of the circle (i know there is something about percentage error having to be multiplied by the index (2 in this case), but we have been told not to work in percentages, so what happens then?)

If you have an uncertainty in the mass of +/- 0.0001 kg, then is the
uncertainty in the force generated by that mass the same? (+/- 0.0001 N)

And what happens when you have two measurements with different uncertainties and you want to divide them e.g. force / area to find stress?

Thank you so much in advance!
2. If you have been told not to work in %ages then I guess your teacher wants you to use fractional errors instead.
They work the same as % errors.

100 ± 1 is either a 1% error or a fractional error of 0.01 (one hundredth)
The rules for combining errors using with %ages are identical to those using fractional errors.
Add the fractional uncertainties when you multiply or divide.
Multiply it by the index (eg 2 for squared))

The absolute uncertainty in the calculated radius is half the uncertainty in the diameter.
(The % or fractional uncertainty is the same)
3. (Original post by Stonebridge)
If you have been told not to work in %ages then I guess your teacher wants you to use fractional errors instead.
They work the same as % errors.

100 ± 1 is either a 1% error or a fractional error of 0.01 (one hundredth)
The rules for combining errors using with %ages are identical to those using fractional errors.
Add the fractional uncertainties when you multiply or divide.
Multiply it by the index (eg 2 for squared))

The absolute uncertainty in the calculated radius is half the uncertainty in the diameter.
(The % or fractional uncertainty is the same)
thanks for your answer. he told us to work in absolute uncertainties. should've probably mentioned that. sorry :/
oh, wait, i think i've realised what i'm meant to do.
when calculating the stress, i would use the maximum force and minimum area, and then the minimum force and maximum area to find the absolute uncertainty.
4. (Original post by TeslaCoil)
thanks for your answer. he told us to work in absolute uncertainties. should've probably mentioned that. sorry :/
oh, wait, i think i've realised what i'm meant to do.
when calculating the stress, i would use the maximum force and minimum area, and then the minimum force and maximum area to find the absolute uncertainty.
Yes you can also do it that way.

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