Determining Mass & Amount of Marbles in Bags

In summary: N marbles in a bag, then the mass of a marble is 0.01*(N). So if there are 3 marbles in a bag, then the mass of a marble is 0.003. That's about the size of a marble.In summary, the experimenter weighed several bags of marbles and found that the difference in mass between bags is the key to determining how many marbles are in each bag.
  • #1
blastyournos
10
0
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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  • #2
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.
 
  • #3
i don't 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.
 
  • #4
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
 
  • #5
i can't be sure how accurate it is cause i didnt do the weighing, but let's 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 can't afford to mess it up.
 
  • #6
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.
 
  • #7
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 there's a way to get the number of marbles in each bag or else it can't be due on the first school day back. also the masses of the marbles doesn't need to be a whole number.
 
  • #8
blastyournos said:
and of course there's a way to get the number of marbles in each bag or else it can't 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?
 
  • #9
blastyournos said:
Here are our masses for each of the bags with the unknown amount of marbles).

blastyournos said:
...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...

blastyournos said:
also the masses of the marbles doesn't 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:
 
  • #10
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 isn't very big, also how would you deal with numbers like 66.5, should i round down? cause you can't 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, I am sory, cause my teacher will have to put in 7000 marbles in a bag the size of my palm.
 
Last edited:
  • #11
blastyournos said:
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 isn't very big,
How did you determine this? Consider this bit of data:

blastyournos said:
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?)
 
  • #12
ya I am definately screwed, how can this be done, please help
 
  • #13
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
 
  • #14
oooops,

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

cheers
 
  • #15
Also, I forgot to add: having just checked my spreadsheet again, check your data again...or admit the possibility of a "half marble"!

Cheers

EaGG
 
  • #16
that didnt help
 
  • #17
i can't check my data, i didnt do the weighing, and there's no possibility of half a marble.
 
  • #18
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?
 
  • #19
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.
 
  • #20
this dude can, but he won't tell us
 

What is the purpose of determining the mass and amount of marbles in bags?

Determining the mass and amount of marbles in bags is important for various reasons. It helps in calculating the cost and quantity of marbles needed for a project. It also allows for quality control and ensures that the correct amount of marbles are included in each bag.

What is the process for determining the mass and amount of marbles in bags?

The process involves weighing a sample of marbles from the bag using a scale. The average mass of the marbles in the sample is then calculated. This average is multiplied by the total number of marbles in the bag to determine the total mass of marbles.

How does the size and shape of marbles affect the mass and amount in a bag?

The size and shape of marbles can greatly affect the mass and amount in a bag. Larger marbles will have a greater mass and therefore, fewer will fit in a bag compared to smaller marbles. Similarly, irregularly shaped marbles may take up more space in the bag and result in a lower total amount.

What factors can affect the accuracy of determining the mass and amount of marbles in bags?

Some factors that can affect the accuracy of determining the mass and amount of marbles in bags include human error during the weighing process, variations in the size and shape of marbles, and the presence of impurities or debris in the bag. It is important to carefully select a representative sample and to use precise measuring equipment.

What are some common applications of determining the mass and amount of marbles in bags?

Determining the mass and amount of marbles in bags is commonly used in construction and landscaping projects that require a specific amount of marbles. It is also important for manufacturers to ensure that their product packaging accurately reflects the contents of the bag. Additionally, this process is used in scientific experiments and studies involving marbles.

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