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# Chalenging Percentage uncertainty question: ATTEMPTED! Please check. watch

1. A student wants to measure the density of the sugar mix used to make aniseed balls. He measure the diameters of 5 diffrent balls with a micrometer skrew gauge and obtains the following results: 10.2, 10.7,10.1,10.3,10.5 mm

He weighs 10 balls and obtains 11.16

(a) What is the mean diameter and it's uncertainty

Pretty simple - add up the readings and divide it by 5 to get the mean diameter which I got to be 10.4mm (1dp) Therefore
10.4 +- 0.005??? (is that correct)

b) What is the percentage uncertainty in the diameter, and in radius.

so I did: (0.005) / 10.4 = 0.048% (in diameter)
: 0.0005/5.2 = 0.0096% (in radius) (is that correct?)

c) What is the volume of one ball? give your answer in mm^3 and in cm^3???

Have no idea how to do this??

d) if the balance reads +-0.01g, what is the percentage uncertainty in the total mass. and in mass of 1 ball.

I know how to calc percentage unceratainty of the total mass but not the uncertainty of one mass.

so.... I got (0.01/11.2) x 100= 0.0896...%

c) what is the density of the sweet give your answer in gcm^-3 and in kg m^-3???

No idea???

EDIT: new solution posted. Please check.

2. (A) if you're measuring to 1dp then your uncertainty would be +- 0.1, unless half the range is bigger.
If in your readings the highest value was say, 10.2 and lowest 9.2, the range would be 0.4. You half that and then the uncertianty which would be 0.2 which is bigger so that's what you use.
Where are you getting 0.005 from?
(b) calculation looks correct but wrong numbers.
(c) use gcse maths for volume of a sphere.
Density is mass/volume for the last one.

When you do one mass you just take the mass of 1 ball and use it to divide 0.01 then x100. You should get a smaller number than for total mass.
Hope it helps, I've just been doing this in physics as well (just not same question).
3. The diameter is 10.4 ± 0.3mm if the mean is 10.4 and the highest value was 10.7 and the lowest 10.1
This is actually the maximum uncertainty.

The % uncertainty is 100 x 0.3/10.4
That is, the uncertainty expressed as a % of the mean value.
Volume? You must know the formula for the volume of a sphere in terms of its radius. (Half the diameter measured)
Radius in mm give mm cubed
Radius in cm gives cm cubed

I'm not sure what you mean when you say the student weighed 10 balls and "obtains 11.16"
What is the unit of that and is it the mean value?
4. (Original post by Millyshyn)
(A) if you're measuring to 1dp then your uncertainty would be +- 0.1, unless half the range is bigger.
If in your readings the highest value was say, 10.2 and lowers 9.2, the range would be 0.4. You half that and then the uncertianty which would be 0.2 which is bigger so that's what you use.
Where are you getting 0.005 from?
(b) calculations looks correct but wrong numbers.
(c) use gcse maths for volume of a sphere.
Density is mass/volume for the last one.
Wait wait wait, okay say if I don't round it up to 1 dp and use the full value will I use +- 0.005 as the uncertainty???
5. (Original post by Stonebridge)
The diameter is 10.4 ± 0.3mm if the mean is 10.4 and the highest value was 10.7 and the lowest 10.1
This is actually the maximum uncertainty.

The % uncertainty is 100 x 0.3/10.4
That is, the uncertainty expressed as a % of the mean value.
Volume? You must know the formula for the volume of a sphere in terms of its radius. (Half the diameter measured)
Radius in mm give mm cubed
Radius in cm gives cm cubed

I'm not sure what you mean when you say the student weighed 10 balls and "obtains 11.16"
What is the unit of that and is it the mean value?

it's in grams and I don't know thats all it says
6. (Original post by Stonebridge)
The diameter is 10.4 ± 0.3mm if the mean is 10.4 and the highest value was 10.7 and the lowest 10.1
This is actually the maximum uncertainty.

The % uncertainty is 100 x 0.3/10.4
That is, the uncertainty expressed as a % of the mean value.
Volume? You must know the formula for the volume of a sphere in terms of its radius. (Half the diameter measured)
Radius in mm give mm cubed
Radius in cm gives cm cubed

I'm not sure what you mean when you say the student weighed 10 balls and "obtains 11.16"
What is the unit of that and is it the mean value?

http://www.pearsonschoolsandfecolleg...1Topic2EAT.pdf

question is on this link P95
7. Anyone
8. 10 balls weigh 11.16 g so what does one weigh?
If the uncertainty/precision in the measurement is 0.01 g what % is that?
The % uncertainty in the mass of one ball will be the same.

Have you done the theory of how to deal with % errors?
9. (Original post by Stonebridge)
10 balls weigh 11.16 g so what does one weigh?
If the uncertainty/precision in the measurement is 0.01 g what % is that?
The % uncertainty in the mass of one ball will be the same.

Have you done the theory of how to deal with % errors?
No, but I guess 1 ball will weigh 1.116g

0.001g/1.116 x 100
10. Yes so the mass of one ball will be 1.116g with an uncertainty of 0.001 if the mass of 10 was 11.16 with uncertainty 0.01g

If you haven't done the theory of how to deal with % uncertainties in class, why are you expected to be able to do questions on this?
You really need this theory in order to do the next bit.

I'm on my iPad at the moment so can't post a sheet with some notes for you on this. I can do this tomorrow morning if you want.

Edit: Here's the sheet. It will tell you about % errors and how to combine them (part c) when you use a value with % error in a formula.
Ask here if there's anything you don't understand.

11. (Original post by Wasuppdude)
Wait wait wait, okay say if I don't round it up to 1 dp and use the full value will I use +- 0.005 as the uncertainty???
Yeah if the value is to 2 dps. and even then if the range is bigger than 0.01 then you should use half the range as the uncertainty.
12. (Original post by Stonebridge)
Yes so the mass of one ball will be 1.116g with an uncertainty of 0.001 if the mass of 10 was 11.16 with uncertainty 0.01g

If you haven't done the theory of how to deal with % uncertainties in class, why are you expected to be able to do questions on this?
You really need this theory in order to do the next bit.

I'm on my iPad at the moment so can't post a sheet with some notes for you on this. I can do this tomorrow morning if you want.

Edit: Here's the sheet. It will tell you about % errors and how to combine them (part c) when you use a value with % error in a formula.
Ask here if there's anything you don't understand.

Right okay. Can you please check if this is right then.

For part a)
i) Mean diameter = (10.2 + 10.7 + 10.1 + 10.5 ) = 10.4mm
Uncertainty = (10.7 - 10.1) = 0.6/2 = 0.3. 10.4 +- 0.3

ii) Percentage uncertainty for diameter = (0.3)/ 10.4 x 100 = 2.88%
Percentage uncertainty for radius = 0.3/5.2 x 100 ?? ( not sure what the scale resolution is 0.03?)

iii) Volume = 4/3 pi Radius cubed = 4/3 x pi x (5.2mm)^3 = 588.98 mm cubed
0.58898 cm cubed

For part b)

% uncertainty in total mass = 0.01/11.16 x 100 = 0.0896...% = 0.09%
% uncertainty for one ball (mass) = 0.001/1.116 x 100 = 0.896...= 0.9%

For part c )

D= mass/ volume = 1.116g/ 0.58898cm^3 =1.89 g/cm^3 and 1890 kg/m^3

d) uncertainty of density would be... ???
Attached Images

14. (Original post by Stonebridge)
Yes so the mass of one ball will be 1.116g with an uncertainty of 0.001 if the mass of 10 was 11.16 with uncertainty 0.01g

If you haven't done the theory of how to deal with % uncertainties in class, why are you expected to be able to do questions on this?
You really need this theory in order to do the next bit.

I'm on my iPad at the moment so can't post a sheet with some notes for you on this. I can do this tomorrow morning if you want.

Edit: Here's the sheet. It will tell you about % errors and how to combine them (part c) when you use a value with % error in a formula.
Ask here if there's anything you don't understand.

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