| MadSci Network: Physics |
The question: "We had to conduct a similar practice to Millikan's oil
drop experiment in class. This is the situation:
There are 10 bags each containing a different amount of small marbles of the
same mass. There is also one big marble of different mass to the small marble
added to each bag. Each bag is massed and that mass is given to us. Now through
techniques similar to those of Millikan, we must:
1. Determine the mass of one SMALL marble.
2. Determine the number of SMALL marbles in each bag.
Our technique was simply to find the difference between all the bags and thus
having 45 differences. This difference represents the net mass. That is, since
all the bags contain one large marble, this difference eliminates the mass of
the large marble as well as the bag since they were constants of each total
mass. This leaves the net mass of just the small marbles in each bag. Moreover
the smallest difference between the differences were found. If this difference
was divisible into all the other differences as an integer value, it was
concluded that this was the mass of a single small marble. Now how do we find
the number of small marbles in each bag? We don't have either the mass of one
big marble nor the mass of the bag. I know there are some serious flaws with
this method so feel free suggesting a more sound, error-proof method that may
involve mathematical equations and more physics concepts.
"
Frankly I do not see how to determine the number of small marbles unless you know the masses of the bag and the large marble, or, at the very least, the total mass of the bag plus large marble. The best that can be hoped for without knowing those two masses (or the total mass of the bag plus large marble) is to determine a maximum number of small marbles. This maximum number of small marbles can be determined by subtracting [n * small mass], for increments of n, from each of the bags' masses until the result is just larger than the mass of the small marble. (An alternative to this approach is to divide the total mass of each bag by the mass of the small marble; the integer part of that result represents the maximum number of small marbles.) At that point we know for sure that n can not be any larger because if n were set to n+1 then the resulting subtraction would be nonsensical since we know that the large marble is more massive than the small. But, not knowing the mass of either the bag or the large marble or the total of these two, each "n" determined for each of the ten bags is only a maximum n.
(By the way, the discussion of the preceding paragraph is not precisely correct in all cases of the masses of the bag, large marble, and small marbles. It is possible to overestimate the maximum number of small marbles if the sum of the masses of the bag and the large marble are very close to a multiple of the mass of the small marble. But the result of the maximum will be off by no more than one unit of small marble, overestimated.)
John Link, MadSci Physicist
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