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How tf do you do uncertainties?

The table below shows the measurements recorded by a student for a solid metal sphere.
The absolute uncertainties in the mass of the sphere and in its radius are also shown.

mass: 100 ± 6 g
radius: 1.60 ± 0.08 cm

What is the percentage uncertainty in the density of the sphere?
A 1%
B 11%
C 16%
D 21%

How on Earth do you do this? I don't understand uncertainties at all and none of the online resources have helped..

Reply 1

Parallex

Total percentage uncertainty is found by adding the percentage uncertainties of all the measurements used to find the density.

For a spherical object:

\rho = \dfrac{Mass}{4/3 \pi r^3}

Percentage uncertainty is the absolute uncertainty/mean value so you can calculate the percentage uncertainties for the mass and radius of the object with the date you've been given.

Note that when calculating density, you're cubing the radius of the object. This means the percentage uncertainty of the radius is going to be multiplied by 3 when calculating the total % uncertainty.

Reply 2

jbman690

wait so 11%???

(edited 7 years ago)

Reply 3

RiahDawson

Original post by Parallex

Total percentage uncertainty is found by adding the percentage uncertainties of all the measurements used to find the density.

For a spherical object:

\rho = \dfrac{Mass}{4/3 \pi r^3}

The answer is 21 right?

Reply 4

Parallex

Original post by jbman690

You need to change the unit of the radius to metres first right?

Nope because this is percentage uncertainty. Changing the units to SI units only changes the absolute uncertainty value whereas the percentage uncertainties are unchanged.

^ Yeah, looks like 21.

Reply 5

jbman690

can someone give the rules for uncertainties, i'm basically an illiterate when it comes to them.

Reply 6

RiahDawson

Original post by jbman690

can someone give the rules for uncertainties, i'm basically an illiterate when it comes to them.

You add the uncertainties if its + - / or x
If its to the power of then you multiply.

Reply 7

jbman690

thanks, any predictions for the aqa paper 2 coming up?

Reply 8

xBeautifulMind

Original post by Parallex

Total percentage uncertainty is found by adding the percentage uncertainties of all the measurements used to find the density.

For a spherical object:

\rho = \dfrac{Mass}{4/3 \pi r^3}

I still can't get 21 as the answer :\ Or anything related to 21

Reply 9

Parallex

Original post by Jessika300599

I still can't get 21 as the answer :\ Or anything related to 21

mass: 100 ± 6 g
radius: 1.60 ± 0.08 cm

Percentage uncertainties of these values: absolute uncertainty/mean value
Mass = 6% (6/100)*100
Radius = 5% (0.08/160)*100

For the mass, you have a percentage uncertainty of 6%. For the volume, however, the radius is cubed. The radius has a percentage uncertainty of 5%, so the effective percentage error in the volume of the sphere is 15%.

When multiplying or dividing percentage errors, you sum together the errors to find the total % error. r^3 is just r*r*r which has a percentage uncertainty of

(5\% + 5\% + 5\%) = 15\%

Total percentage error =

6\%(mass) + 15\%(volume) = 21\%.

Reply 10

xgirl17

i just tried the question and didn't get anything so i looked it up and bro your title is a whole mood 😭😭

Reply 11

strugglesWmaths.

Original post by Parallex

mass: 100 ± 6 g
radius: 1.60 ± 0.08 cm

Percentage uncertainties of these values: absolute uncertainty/mean value
Mass = 6% (6/100)*100
Radius = 5% (0.08/160)*100

is just r*r*r which has a percentage uncertainty of

(5\% + 5\% + 5\%) = 15\%

Total percentage error =

6\%(mass) + 15\%(volume) = 21\%.

thanks, really needed this!

Reply 12

Stonebridge

Original post by strugglesWmaths.

thanks, really needed this!

This post (and some of the follow up questions) might also be of use.

It summarises the rules for combining uncertainties.

https://www.thestudentroom.co.uk/showthread.php?t=2661762