The Student Room Group

Percentage uncertainty

Im getting really confused over some questions relating to this. (yet the practical exam is only in a few days..)


What is the uncertainty in reading of a ruler? +-0.5mm or +- 1mm



In this practical book it states the uncertainty of a rule is +- 1mm
(From what I understand its because its to the nearest 0.5 of a mm at either end. ie where the object starts and ends)
But this has confused me...

In a past practical paper they talk of measuring the diameter of a ball using blocks and a ruler.

Such that:

Block | Ball | Block

Meter rule here


And in the question they ask to estimate the percentage uncertainty in measuring the diameter of a 2cm ball.

Some people ive talked to about it say its



(0.5 x 2)
-------- X 100 = 5%
20



Which I can see the logic behind...

But back to the practical book they say in a question of similar nature to calcuate the percentage uncertainity where the readings have uncertainity +- 1mm. And the blocks touch the ball at 168mm and 204mm

Block | Ball | Block

Meter rule here




(1 X 2)
------- x 100 = 6% (which is the answer).
(204-168)




You can probably see where this is going....

With this knowledge it led to confusion over the practical paper question...
If each measurement is +-1mm
Then



(1 x 2)
-------- X 100 = 10%
20



This answer has been achieved by using the figure in the book, so am I taking the figures in the book too literally? Because if so... they ust be using some weird ruler with 2mm divsions or something :s-smilie:

Im confused about it...

Help please you physics genious' :biggrin:
Well, I think you maybe are trying to do things a little too by the book. Error analysis is a hand wavey thing at best. What you estimate the error to be is to an extent down to you, since it is not an exact science and therefore in an exam I would think they would accept any method which made use of thought and the principles - ie not plucking a value out of midair.

If it was me, I would say that if the smallest increment on the ruler is 1mm then the error is half that ie 0.5mm, and you then pick up this error for each measurement you take. However, me saying that I can tell 1/2 an increment is fairly arbitrary and I could just as well argue that I can't tell to better than 1mm (depending on your eyesight! :p:). As long as you argue it well it doesn't really matter. I would say all of the methods you outline are acceptable.
Reply 2
Yeah the practical papers seem to be that...

I think I was too focused on what the book stated... as you have mentioned.
I just thought physics would be a little more consistant: they say its +-1mm at the start of the book then they say in the question with a metre rule its +-1mm For each reading.

I'm pretty sure I understand it now:

+- 0.5 mm for each reading
therefore +-1mm for a length.

Conclusion:
Questions are subjective arent they: They can say anything...

So that value for percentage uncertainty is based on what Data they give you, not on what you have learnt.

( I confuse my self alot... haha)
Livethefire
Yeah the practical papers seem to be that...

I think I was too focused on what the book stated... as you have mentioned.
I just thought physics would be a little more consistant: they say its +-1mm at the start of the book then they say in the question with a metre rule its +-1mm For each reading.

I'm pretty sure I understand it now:

+- 0.5 mm for each reading
therefore +-1mm for a length.

Conclusion:
Questions are subjective arent they: They can say anything...

So that value for percentage uncertainty is based on what Data they give you, not on what you have learnt.

( I confuse my self alot... haha)

well, physics is consistent, but error analysis is not really "physics" in the pure sense of the word. It's not something you can learn rigidly. It's open to interpretation and is therefore more suited to applying principles rather than any form of book learning. When it comes to errors its really more about common sense than anything else.
Reply 4
haha "common sense". :P

SO much for me trying to do physics at Uni whenever Im confusing myself on comon sence questions!

Thanks for your help.
Livethefire
haha "common sense". :P

SO much for me trying to do physics at Uni whenever Im confusing myself on comon sence questions!

Thanks for your help.

errors is very different to other stuff you do though, although I guess you have to understand and apply common sense later at uni. No problem, good luck with the exam.
Reply 6
The way my teacher told me how to calculate percentage uncertainty is as follows. You measure say a box. If its length is 3.55 centimetres, the limits are that the upper bound is 3.555 and the lower bound is 3.545. Therefore the absolute error is 0.005, hence the percentage uncertainty is 0.005/3.55*100=0.14%. It makes sense also saying that the estimated uncertainty is half the smallest scale division because if you imagine any two lines on a ruler, sometimes the object you are measuring lies in between the two so that is the uncertainty.
Yet again, percentage uncertainty depends on what you're measuring and how you're measuring.
What is the absolute uncertainty of a voltmeter that goes up at 0.001V? I thought its 0.0005 but the mark scheme specifically says that it is wrong. WHY!!! Someone please help here!!!
Reply 8
3173 radioactive
What is the absolute uncertainty of a voltmeter that goes up at 0.001V? I thought its 0.0005 but the mark scheme specifically says that it is wrong. WHY!!! Someone please help here!!!


if its digital i believe it should be that. if its analogue then it is 0.001 V error.
How much your ruler is accurate to depend on what you are measuring

For example, using a tape measure to measure the width of a room usually only accurate to 5cm, as the tape measure may get slack, etc. Despite that the tape measure has 1mm graduation.

Same with a stopwatch as it is usually accurate to 0.01s but the reaction time of us means using stopwatch we only accurate to about 0.1-0.2 s
Reply 10
yifan's heroes, I don't think you could just say that we take 0.1 - 0.2 seconds for timing the reaction. It should be mathematical. My teacher said that we must find half the spread of values. That would be the timing. It varies from person to person.
Reply 11
You have to understand that such a small value isn't right. It's like micrometer screw gauge it measues to 0.01mm, would that mean the error value is 0.005mm. Well you can't really say that because nothing is built to that sort of scale, it's impossible, so you have to use some sense to decide what the error should be. In this case I would be inclined to say 0.05mm.
Reply 12
VMB
You have to understand that such a small value isn't right. It's like micrometer screw gauge it measues to 0.01mm, would that mean the error value is 0.005mm. Well you can't really say that because nothing is built to that sort of scale, it's impossible

Err...it's not impossible. A micrometer screw gauge measures to 0.01mm - that's what it does. That's what it actually does. The error most certainly is 0.005mm.
Reply 13
Mohit_C
yifan's heroes, I don't think you could just say that we take 0.1 - 0.2 seconds for timing the reaction. It should be mathematical. My teacher said that we must find half the spread of values. That would be the timing. It varies from person to person.

Yes, the error should come from the distribution of reaction times.

It doesn't matter whether it takes about 0.2s or about 0.8s for you to react - if you're timing something, you press the start button and the stop button, so you start the clock x1x_1 seconds after the 'real' start, and you stop the clock x2x_2 seconds after the 'real' stop.

Say each of these reactions is around xx seconds, but deviates by an amount Δxi\Delta x_i for the ith reaction.

Then, the error on your measurement will be:

x2x1=(x+Δx2)(x+Δx1)x_2 - x_1 = (x+\Delta x_2) - (x+\Delta x_1)
=Δx2Δx1= \Delta x_2 - \Delta x_1

In other words, the absolute value of the reaction time is not important - it's the degree to which the reaction time strays from the mean reaction time.

What you're interested in is how different the reaction time when you stopped it was to the reaction time when you started it. I'd say, if you're reaction time is 0.2s, it will probably not deviate by much more than 0.05s either way.

But as Mohit_C says, it's best just to do lots of repeat readings and find the spread of the results. Since the deviation from mean reaction time is a random variable, it will average to zero given enough readings.