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How do you calculate uncertainities in physics properly? I am starting to lose my mind!


Guest thedarkzapper

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Guest thedarkzapper

I have searched the whole internet for weeks, read IB Physics books, and looked everywhere for clues on how to calculate uncertainties in physics, but nothing helps.

So lets say this is my data:

h, m t1, s t2, s t3, 2

±0.05 ±0.05 ±0.05 ±0.05

1 0.10 1.35 1.31 1.35

2 0.15 1.72 1.70 1.71

3 0.20 1.99 1.95 2.05

Then when I look for t(ave) I find the averages go like this:

1) 1.34

2) 1.71

3) 2.00

So now when i come to calculating uncertainties what do I do. Since the measurement uncertainty stays the same when you calculate the average of a value I would assume the uncertainties are ±0.05. However, no, that is not what IB wants, basically they want to calculate the uncertainties in the following way: (max.value - min.value)/2. When I do this, I get:

1) 0.02

2) 0.01

3)0.05

The first and second uncertainties are lower than the measurment uncertainity. What do I do now which uncertainty do I use???

t^2

1)1.80

2)2.92

3)4.00

Continuing with other calculations…. We now have to calculate the uncertainties for t^2 and we do it in the following way or so Pearson says:

1) [(t+0.02)^2 - (t-0.02)^2] /2= [(1.34+0.02)^2 - (1.34-0.02)^2] /2= 0.05

2) 0.03

3) 0.20

Using t^2 and h we find g. I know that when you divide or multiply that you convert all uncertainties to percentage uncertainties and add them up. But, my teacher showed us that for g we calculate the uncertainty by finding the residual. The residuals are calculate in the following way:

1) g(ave)-g1= 1.11

2)0.32

3)0.79

The largest residual is the error.

g residual

1 g1 19.02 1.11

2 g2 17.59 0.32

3 g3 17.12 0.79

g(ave) 17.91 1.11

(I know the results are far off but that is because the data is fake)

At this point I don't know what is happening anymore or what the error is and then I have to find the line with the max gradient by adding the residual to the average result and the line with min gradient by subtracting the residual from the average result.

I mean I don't know what the IB expects from us just to miraculously know what they are asking for. I am extremely upset because of this and I hope someone can explain in great detail how to calculate uncertainties properly. I

am not submitting my labs untill I figure this out.

Thanks in advance :)

Edited by thedarkzapper
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It's worth keeping in mind that the method of uncertainties used by the IB is very much simplified and as a result, there's often ambiguous cases, Generally speaking it's ok provided you outline your reasoning for selecting the uncertainties, provided your arguments are logical.

The two uncertainties in an example of this ambiguity - in this case I would take the larger of the two. I don't think they will mark you down for continuing with the uncertainty calculated from the max-min/2 formula though, even if the former is more 'correct.' Using the uncertainty from the apparatus without any reasoning however will probably be seen as incorrect, so make sure you clearly state what you are doing.

For calculating g, I think it'll be better to calculate the uncertainties of t^2 (using percentage uncertainties), then plot it against h to find g. Uncertainties would follow by applying the (max-min)/2 formula, which is probably what the IB expects you to do. I don't think the residual method your teacher explained is correct, since it doesn't use the idea of uncertainties. It might be 'more correct' in a general sense (ie: how it's actually done in university, etc) but it's not what the IB is looking for.

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Guest thedarkzapper

Thank you so much. IB sometimes drives me mad especially physics. For example, chemistry is so simple I can write a 20page lab report without a problem but in physics everything is messed up.

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