Measurement Uncertainty: How do I calculate it?

[Olbor]

Homework Statement

Hey guys! I'm new here, so firstly- hello!
I've a exercise to from Metrology.

Evaluate measurement uncertainty for the following measurement:
1. Measurement quantity: length of a bar L = 500 mm
2. Material of the measuring object: steel
3. Temperature range in the measuring room: 14 to 26 °C
4. Measurement instrument: Micrometer; digital (resolution 0,001 mm)
- Uncertainty of calibration: U = 2 µ m + 4 × 10-6 × L
5. Temperature difference between the measurement object and the measurement instrument: T = 2 °C

Homework Equations

I'm not sure which are good, this is why I'm writing here.

The Attempt at a Solution

I have problem because I'm now on exchange, and this is my first time with Metrology. I didn't had any lectures, practice and etc. In internet I found a lot of things about that, but with another excercise I don't know how to use this data. I'm waiting for any help!

 

[BvU]

Hello Olbor, and welcome to PF.
When in PF, do as the PFers do, i.e. use the template in a way that is helpful for self and for potential helpers. I can kind of reconstruct what you need, but I can't fathom what part of that you're missing. I don't really help you by coughing up the final answer, because that way you have missed the learning opportunity and also the small satisfaction of having done something by yourself and with success.

Long story, short summary: what is the problem you are struggling with, what do you have in your kit of tools and how can I help you ? To get started, let me throw some questions back at you:

1. Is the 500 the hypothetical outcome of an imagined measurement ? If so, fine. Not very realistic (500.432 or something would be). Never mind.
2, 3. If they tell you that it's steel and give you a temperature range, what do you think they want you to do with those tidbits of circumstantial information ? You must have some idea !?
4. Corroborates my comment on 1. The outcome of the measurement must be expressed in at least 6 digits: 500.000 being just a "lucky" one in a thousand (well, thousand: in fact the exercise wants you to come up with some number, probably other than 1000 ...). There is a U and an exepression for U. Do you need help to calculate U = 4 μm ? I should think not.

Where do you need help, then ?

Where I need some guidance is: What do you have available as relevant equations and what is it you propose to do (or hopefully already have done) for this exercise and where do you think steps are becoming a little less believable ?

 

[Olbor]

Hello Olbor, and welcome to PF.
When in PF, do as the PFers do, i.e. use the template in a way that is helpful for self and for potential helpers. I can kind of reconstruct what you need, but I can't fathom what part of that you're missing. I don't really help you by coughing up the final answer, because that way you have missed the learning opportunity and also the small satisfaction of having done something by yourself and with success.

Long story, short summary: what is the problem you are struggling with, what do you have in your kit of tools and how can I help you ? To get started, let me throw some questions back at you:

1. Is the 500 the hypothetical outcome of an imagined measurement ? If so, fine. Not very realistic (500.432 or something would be). Never mind.
2, 3. If they tell you that it's steel and give you a temperature range, what do you think they want you to do with those tidbits of circumstantial information ? You must have some idea !?
4. Corroborates my comment on 1. The outcome of the measurement must be expressed in at least 6 digits: 500.000 being just a "lucky" one in a thousand (well, thousand: in fact the exercise wants you to come up with some number, probably other than 1000 ...). There is a U and an exepression for U. Do you need help to calculate U = 4 μm ? I should think not.

Where do you need help, then ?

Where I need some guidance is: What do you have available as relevant equations and what is it you propose to do (or hopefully already have done) for this exercise and where do you think steps are becoming a little less believable ?

This is everything what I got, I put all information from task here. My problem is that I never had metrology, and now I didnt had any lectures etc so I'm totally noob in that :)

 

[BvU]

Well, I never had metrology either, so we're even there. You have a very lengthy quote in your post 3. Did you also read it and notice there were some questions in there that have nothing to do with the subject you never studied? So please stop whining and answer them as best you can. I'm sure that will - finally - enable me to help you instead of telling you to stop crying .

 

[bloby]

I will give a try.
From 4 1 and 2 it's a measurement of the length of a bar of steel. Fro 1 the measurement is done and it read 500 mm on the digital screen of the device. Now the true length of the bar is not known. What can disturb the measurement? There are facts about the device, the temperature and the matter of the bar. The length of the bar changes with temperature. I guess you have to find which information is relevant and which is not.

 

[BvU]

Is Olbor the same person as bloby ?

Anyway: dear Olbor, after carefully re-reading your post, I now interpret your

2. I'm not sure which are good, this is why I'm writing here

in a more constructive way: You do have made up a list (can't be all that long) of relevant equations. Good. List them and add for each of them a short comment why you are so unsure it's good. I will provide some guidance if there is something to hold on to.
One giveaway: the expression for U is relevant. Did you already manage to make good use of it?

 

[bloby]

Is Olbor the same person as bloby ?

Anyway: dear Olbor, after carefully re-reading your post, I now interpret your in a more constructive way: You do have made up a list (can't be all that long) of relevant equations. Good. List them and add for each of them a short comment why you are so unsure it's good. I will provide some guidance if there is something to hold on to.
One giveaway: the expression for U is relevant. Did you already manage to make good use of it?

No, no I just wrote how I would start with a problem like that without lectures or practice...

 

[BvU]

@bloby: hehe, that's what I did in d<r>/dt and since then I knew the $\ne$ .

@Olbo: sorry for my seemingly obstinate approach. It's me. And you (by quoting a 20 line reply I composed with good intentions and then ignoring every word of it). So far we've wasted around $200 worth of free tuition that could have been put to good use (in this thread or elsewhere).

Now, shall we get on and take a first step: http://ipl.physics.harvard.edu/wp-uploads/2013/03/PS3_Error_Propagation_sp13.pdf. Or http://www.rit.edu/~w-uphysi/uncertainties/Uncertaintiespart2.html#propagation.

What would you report if you could ignore all temperature stuff ?