Determining Mass of Individual Objects in Bags - Oil, Candy, Millikan?

In summary, the conversation discussed the need to design a procedure to determine the mass of an individual object inside a bag filled with identical objects. Suggestions such as using the Euclidian algorithm and Millikan's oil drop experiment were mentioned, but it was noted that the problem can be solved by finding the smallest difference between the masses of multiple bags containing the same items and using a method like least squares or lattice reduction to account for errors.
  • #1
zeja7
1
0
hello everyone,

we have to design a procedure to determine the mass of an individual object inside a bag which is filled with many of these identical objects ( one kind)

For ex. Bag 1; mass = 435.6, filled with candy- find mass of individual candy.
we have:

10 bags of one candy
10 bags of pennies
10 bags of paper clips
we are to design a procedure to find the masses of the individual which is sort of like millikans experiment with the oil drop.

Some one suggested Euclidian Algorithm, but not sure where that fits in.

Any help if greatly appreciated-

THank you!
 
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  • #2
From what I remember from chemistry class in high school, Millikan's oil drop experiment was to prove the existence of atoms by showing that each drop of oil was a factor of the weight of a single atom.

I'm not sure I completely understand the problem: why not just take one piece of candy out and weigh it and repeat for each thing in the bag?

It is impossible to determine the weight of an individual object inside of a bag without having the measurements of at least 3 bags all containing the same items.

However, if you have 3 different bags filled with arbitrary (known) amounts of the same three items, it's easy to calculate the weight of each item if you know the total weight of each of the three bags. Simply set up 3 equations and simultaneously solve using substitution or elimination.

Edit: I'm unfamiliar with the Euclidian algorithm, so I can't help you out there.
 
  • #3
DyslexicHobo said:
Millikan's oil drop experiment was to prove the existence of atoms by showing that each drop of oil was a factor of the weight of a single atom.

No, it was to measure charge of electron.

I'm not sure I completely understand the problem: why not just take one piece of candy out and weigh it and repeat for each thing in the bag?

That's exactly where the problem lies - you can't take one object. You are given bags and they always contain INTEGER number of identical objects, but you don't know how many.

Not only mass of each bag is a multiply of the mass of the objects inside, also differences between bags masses are multiplies of the same value. Just look for the smallest one.

--
methods
 
  • #4
Anyone have an answer to this?
 
  • #5
Borek said:
Not only mass of each bag is a multiply of the mass of the objects inside, also differences between bags masses are multiplies of the same value. Just look for the smallest one.

This is the answer.
 
  • #6
But what about accounting for errors? For example, three bags weight 5, 10, and 14. We could say the mass of one object is 4 (smallest difference) or 1 (gcd). However they are both wrong, it should be 5.
 
  • #7
Errors make the thing more complicate, still the correct approach is to find the smallest difference then use some method like least squares to fine tune the value.
 
  • #8
Lattice reduction is probably the thing to do if the errors are significant enough and you can't just eyeball when to stop the Euclidean algorithm.
 

1. How do you determine the mass of individual objects in bags?

To determine the mass of individual objects in bags, you must first weigh the entire bag using a scale. Then, you must carefully remove the objects from the bag and weigh the empty bag again. The difference between the two weights is the mass of the objects in the bag.

2. What types of objects can be measured using this method?

This method can be used to measure the mass of any solid objects that can fit inside a bag, such as oil, candy, and Millikan oil droplets.

3. Why is it important to determine the mass of individual objects?

Determining the mass of individual objects is important for many reasons. For example, it can help scientists understand the distribution of different components within a mixture, or provide information about the density and composition of a substance.

4. How does the Millikan oil drop method work?

The Millikan oil drop method involves measuring the mass of individual oil droplets using an electric field. By measuring the mass and charge of the droplets, scientists can calculate the charge of an electron.

5. Are there any limitations to this method?

While this method is useful for determining the mass of individual objects in bags, it does have some limitations. For example, it may not work well for objects that are very small or light, or for objects that are not evenly distributed within the bag.

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