Confused with deducing uncertainties from equipment

I know that uncertainty is half the smallest division, unless both ends of something are measured (hence two times the uncertainty) with e.g. a ruler, in which case the uncertainty is +/- 1 the smallest division. I'm pretty sure none of this is wrong, but I've encountered a few questions which contradict this and I don't know where my understanding is wrong.

Link to questions and my doubts: https://imgur.com/a/ti4Z1Jo

Original post by NeoChen

I know that uncertainty is half the smallest division, unless both ends of something are measured (hence two times the uncertainty) with e.g. a ruler, in which case the uncertainty is +/- 1 the smallest division. I'm pretty sure none of this is wrong, but I've encountered a few questions which contradict this and I don't know where my understanding is wrong.

Link to questions and my doubts: https://imgur.com/a/ti4Z1Jo

Can you explain how they contradict your understanding?

Reply 2

NeoChen

OP

2

Original post by Eimmanuel

Can you explain how they contradict your understanding?

I've explained in the description of the screenshots, but if for some reason it cannot be seen, I'll copy paste it here.
Q47: Why is the uncertainty of the ohmmeter 0.1 rather than 0.05? The smallest division is 0.1, hence half the smallest division should therefore be 0.05.
Q1: So I've learnt that there is a difference in a metre rule and a metre ruler, being that the rule starts measuring directly from 0, hence uncertainty is half the smallest division. Assuming the metre rule is placed in the water and the water surface is measured (don't know how else it would be), shouldn't the uncertainty be 0.5mm?
Q39: Again using metre rule so uncertainty should be half the smallest division right?

Original post by NeoChen

I know that uncertainty is half the smallest division, unless both ends of something are measured (hence two times the uncertainty) with e.g. a ruler, in which case the uncertainty is +/- 1 the smallest division. I'm pretty sure none of this is wrong, but I've encountered a few questions which contradict this and I don't know where my understanding is wrong.

Link to questions and my doubts: https://imgur.com/a/ti4Z1Jo

Original post by NeoChen

I've explained in the description of the screenshots, but if for some reason it cannot be seen, I'll copy paste it here.

Q47: Why is the uncertainty of the ohmmeter 0.1 rather than 0.05? The smallest division is 0.1, hence half the smallest division should therefore be 0.05.

As far as I know, the estimate of uncertainty for analogue device like ruler is in general different from the estimate of uncertainty for digital device like the one shown in Q47 the ohmmeter.

Examination boards like CAIE and OCR take the uncertainty for digital devices to be the resolution of the digital device.

From OCR.

For AQA,

I would consider AQA to follow CAIE and OCR.

As for Edexcel, it takes half the resolution of the reading.

Below is an extract from Measurements and their Uncertainties - A practical guide to modern error analysis by Ifan Hughes and Thomas Hase
https://books.google.com.sg/books?id=AbEVDAAAQBAJ&pg=PA9&source=gbs_toc_r&cad=2#v=onepage&q&f=false

The precision here refers to the uncertainty that you are interested in.

Original post by NeoChen

I've explained in the description of the screenshots, but if for some reason it cannot be seen, I'll copy paste it here.

Q1: So I've learnt that there is a difference in a metre rule and a metre ruler, being that the rule starts measuring directly from 0, hence uncertainty is half the smallest division. Assuming the metre rule is placed in the water and the water surface is measured (don't know how else it would be), shouldn't the uncertainty be 0.5mm?

Q39: Again using metre rule so uncertainty should be half the smallest division right?

For Q1 and Q39, there are two measurements. For Q1, the below explanation should help but if it does not, you can post your queries.

As for Q39, there are also two readings instead of one in determining the height:
The question states, "The initial height of a ball bearing was measured using a metre rule.” This is the first reading.
The second reading is shown in the picture.
So there are two measurements or readings in measuring the height. So the uncertainty should be 1 mm similar to the explanation above.

Reply 5

NeoChen

OP

2

Original post by Eimmanuel

As far as I know, the estimate of uncertainty for analogue device like ruler is in general different from the estimate of uncertainty for digital device like the one shown in Q47 the ohmmeter.
Examination boards like CAIE and OCR take the uncertainty for digital devices to be the resolution of the digital device.

From OCR.
For AQA,

I would consider AQA to follow CAIE and OCR.
As for Edexcel, it takes half the resolution of the reading.

Below is an extract from Measurements and their Uncertainties - A practical guide to modern error analysis by Ifan Hughes and Thomas Hase
https://books.google.com.sg/books?id=AbEVDAAAQBAJ&pg=PA9&source=gbs_toc_r&cad=2#v=onepage&q&f=false

The precision here refers to the uncertainty that you are interested in.

I see. I took this question from Edexcel Physics A-level Topic 1: Working as a Physicist Revision - PMT and as you said edexcel takes half the resolution as the uncertainty. So it likely is an error with the mark scheme or PMT misplaced the question.

Reply 6

cultivated-exhib

2

Original post by Eimmanuel

As far as I know, the estimate of uncertainty for analogue device like ruler is in general different from the estimate of uncertainty for digital device like the one shown in Q47 the ohmmeter.
Examination boards like CAIE and OCR take the uncertainty for digital devices to be the resolution of the digital device.

From OCR.
For AQA,

I would consider AQA to follow CAIE and OCR.
As for Edexcel, it takes half the resolution of the reading.

Below is an extract from Measurements and their Uncertainties - A practical guide to modern error analysis by Ifan Hughes and Thomas Hase
https://books.google.com.sg/books?id=AbEVDAAAQBAJ&pg=PA9&source=gbs_toc_r&cad=2#v=onepage&q&f=false

The precision here refers to the uncertainty that you are interested in.

I see, so it must be an error with the mark scheme or with PMT as I took the question from Edexcel Physics A-level Topic 1: Working as a Physicist Revision - PMT

Reply 7

cultivated-exhib

2

Original post by Eimmanuel

For Q1 and Q39, there are two measurements. For Q1, the below explanation should help but if it does not, you can post your queries.

As for Q39, there are also two readings instead of one in determining the height:
The question states, "The initial height of a ball bearing was measured using a metre rule.” This is the first reading.
The second reading is shown in the picture.
So there are two measurements or readings in measuring the height. So the uncertainty should be 1 mm similar to the explanation above.

I might be wrong but for Q1 that image makes no sense to me. We are measuring the depth of the water, not the height of the tray. Furthermore, doing the latter would still remove the first area of uncertainty the mark scheme uses a metre rule, and not ruler (and because they are both placed on the same uniform surface (assuming here but still). I guess you could argue that there is an uncertainty as to when the water actually starts due to the separation between the water and the the start of the rule due to the tray, but tbh I still don't understand why you would measure it like that. Just place the metre rule in the water, on top of the tray surface, and that would remove the initial uncertainty, and the water surface would be easier to measure rather than from the outside. I don't know if I explained myself but hopefully you can see my point of view.

As for Q39, the experiment is to determine the acceleration of free fall. I'm pretty sure they are measuring the height the ball displaces, so what would be the point of a second measurement? And if there was, I'm sure they would mention it, rather than putting the picture right below "The initial height of a ball bearing was measured using a metre rule.”.

Original post by NeoChen

I see. I took this question from Edexcel Physics A-level Topic 1: Working as a Physicist Revision - PMT and as you said edexcel takes half the resolution as the uncertainty. So it likely is an error with the mark scheme or PMT misplaced the question.

Original post by cultivated-exhib

I see, so it must be an error with the mark scheme or with PMT as I took the question from Edexcel Physics A-level Topic 1: Working as a Physicist Revision - PMT

There is no error in the mark scheme imo and PMT did not misplace the question or mark scheme.
For Q47, if you see the MS, there is a column labelled as Additional Guidance, which states the following:
MP1 accept use of 0.05 giving 0.3%.
This (0.05) is the uncertainty for the Ohmmeter.

If you go to the Edexcel official website to view the report, you will see the following:
“This question assesses candidates’ ability to calculate and combine uncertainties. In this case it was acceptable for candidates to calculate the percentage uncertainty in the resistance reading by taking the full range or just half the range. However, in future examination series the half range value is expected to be used in calculating the percentage uncertainty. This is clarified in an updated section in Appendix 10 of the specification.”

Underling and the words in red are from me, NOT from the original report. If you are doing Edexcel physics, I recommend that you familiarise yourself with Appendix 10 of the specification from the website.

Original post by cultivated-exhib

I might be wrong but for Q1 that image makes no sense to me. We are measuring the depth of the water, not the height of the tray. Furthermore, doing the latter would still remove the first area of uncertainty the mark scheme uses a metre rule, and not ruler (and because they are both placed on the same uniform surface (assuming here but still). I guess you could argue that there is an uncertainty as to when the water actually starts due to the separation between the water and the the start of the rule due to the tray, but tbh I still don't understand why you would measure it like that. Just place the metre rule in the water, on top of the tray surface, and that would remove the initial uncertainty, and the water surface would be easier to measure rather than from the outside. I don't know if I explained myself but hopefully you can see my point of view.

....

I am sorry to say your reasoning is equally senseless or the logic is flawed.
If we can remove uncertainty as we like, I don’t see the point of teaching uncertainty in measurement. The teaching and learning of physics will be soooooooooooo much easier. 😊

If you look at post #5 or reply 5, it says
“When measuring length, two uncertainties must be included: the uncertainty of the placement of the zero of the ruler and the uncertainty of the point the measurement is taken from.”
The phrase “two uncertainties must be included”, the inclusion of the word “must” is telling you it is non-negotiable or as you like.
Although the statement refers to the ruler, it applies to rule, too.

By your flaw reasoning, if we use the zero marking of the rule and there is no uncertainty in zero marking, then why is there uncertainty in other marking of the rule?
No manufacturer in the world ever claim that they are able to make a true zero marking in the rule without uncertainty. If you can make such a rule, all schools will purchase from you.

Confused with deducing uncertainties from equipment

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