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

[zeja7]

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!

 

[DyslexicHobo]

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.

 

[Borek]

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.

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methods

 

[mhz]

Anyone have an answer to this?

 

[Borek]

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.

 

[mhz]

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.

 

[Borek]

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.

 

[Hurkyl]

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.