# Marble Experiment

#### blastyournos

I did an experiment with several bags and in each of the bags there were different of amount of marbles. All of the marbles are the same size and the same mass. So I was wondering how can I determine the mass of each marble in the bag and determine the amount of marbles in each of the bags.

Here are our masses for each of the bags with the unknown amount of marbles:

69.81
53.85
48.10
42.67
37.77
36.64
32.79
32.60
32.22
31.16
26.24
19.21
16.02
15.59
13.50
12.55

can anyone find the lowest common denominator for these numbers?

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#### cesiumfrog

Maybe you should write a spreadsheet to plot, as a function of "marble mass estimate", the standard deviation in: your data points modulo the estimate. More data would be nice too of course.

#### blastyournos

i dont get what you mean, please either find the number yourself or be clearer about the spread sheet thing, i need it by at least the 6th, thank you.

#### einstein_a_go_go

Depends how accurate your data is....

The differences between successive weighings is the key. I would find the difference between succesive weighings (round off to 1 dp?)

and then see if the lowest difference corresponds to 1 marble (i.e. are the others multiples of this lowest amount?)

A spreadsheet would make it easier

Cheers

EaGG

#### blastyournos

i cant be sure how accurate it is cause i didnt do the weighing, but lets assume that it is very accurate cause an electronic scale was used. are you sure the succesive diference method works? this is a must hand in lab, so i cant afford to mess it up.

#### AlephZero

Homework Helper
Do you KNOW all the marbles are the same mass, or are you just assuming that? Also, were all the bags the same mass? If they were not, then can't deduce anything much from your data.

Taking differences gets rid of the mass of the bags (if they were equal), but you still can't get a unique answer to the number of marbles in each bag. For example if the marbles weighed exactly 2, a weight of 7.6 might be 3 marbles in a bag of mass 1.6, or 2 marbles in a bag of mass 3.6. There's no way to tell the difference from the numbers you have.

#### blastyournos

yes i know for a fact that all the marbles are the same mass, and the masses i gave you are the masses of the marbles in the bags without the mass of the bags ( electronic scale). and of course theres a way to get the number of marbles in each bag or else it cant be due on the first school day back. also the masses of the marbles doesnt need to be a whole number.

#### Doc Al

Mentor
and of course theres a way to get the number of marbles in each bag or else it cant be due on the first school day back.
Play around with the numbers a bit using the fact that each bag contains a whole number of marbles. What's the smallest difference in mass between bags? Is that difference due to one marble, or more than one?

#### AlephZero

Homework Helper
Here are our masses for each of the bags with the unknown amount of marbles).
...the masses i gave you are the masses of the marbles in the bags without the mass of the bags ( electronic scale).
Well, make your mind up which story we are supposed to believe. They can't both be true...

also the masses of the marbles doesnt need to be a whole number.
... and thank you for thinking that I'm so stupid I would make that assumption :uhh:

Actually I did play around with the numbers before asking the questions, and got nowhere. That's why I asked the questions.

If all the numbers are as exact as you say they are, then the mass of a marble is obviously 0.01 (precisely) because that's the only number that fits all the data :yuck:

#### blastyournos

im not sure, if the smallest diference is one marbles mass, than the heaviest bag will contain 66 marbles, that seems a bit too much considering the size of the bag isnt very big, also how would you deal with numbers like 66.5, should i round down? cause you cant really have half a marble in there, but if it isnt, then what does the half marble mean?

ok alephzero sory for not stating that the masses are without the bags in the first place. and i just think that you would say 0.01 is the only number is very dumb, im sory, cause my teacher will have to put in 7000 marbles in a bag the size of my palm.

Last edited:

#### Doc Al

Mentor
im not sure, if the smallest diference is one marbles mass, than the heaviest bag will contain 66 marbles, that seems a bit too much considering the size of the bag isnt very big,
How did you determine this? Consider this bit of data:

32.79
32.60
32.22
What would you conclude from this?

Note that the best you can do (assuming your data is good enough to get anywhere--I haven't checked) is to get a maximum value for a single marble. What you think of as one marble may actually turn out to be more than one. (For example: What if the number of marbles in each bag is always a multiple of three? How could you tell?)

#### blastyournos

ya im definitly screwed, how can this be done, plz help

#### einstein_a_go_go

Blastyournos,

There is NO definite answer! AlephZero was right in that the data is NOT. If it were (this wouldn't be physics!), then 0.01g fits, as does 0.005,0.0025,0.001 etc ad infinitum.

YOU need take the differences between the massses and then LOOk at it. SIT and LOOK and THINK. IF the smallest difference is one marble, is this consistent with the rest of the data? IF NOT, then if the smallest difference is two marbles, is this then consistent? If not, then if the smallest difference is three marbles etc....

WE cannot do this for you. (Although I did do it on a spreadsheet yesterday! Sad but true). You need to do it. It isn't too difficult. Just remember that 3.9 and 4.2 might both be solutions to 2+2 (you data is NOT exact)...

(DISCLAIMER - the figures in the above paragraph are illustrative and not intended to be a hint at the answer!

Cheers

EaGG

#### einstein_a_go_go

oooops,

please insert "exact" at the end of the first sentence above....

cheers

Cheers

EaGG

that didnt help

#### blastyournos

i cant check my data, i didnt do the weighing, and theres no possibility of half a marble.

#### dan_c_101

Here were the conditions during the lab; marbles were the same size and were the same mass and the mass of the bag itself is the same. But is there a method to find the mass of one marble, maybe rounding the masses?

#### dan_c_101

Are you kidding me, this lab must be impossible if no one on this forum can even think of a procedure to finding the mass of a marble.

#### blastyournos

this dude can, but he wont tell us