Accurate Weighing Balance
How
does a balance work?
Building our balance
Making your own balance
The challenge
We have to devise a method of weighing very small amounts of gold. A simple
balance seems the easiest route.
How does a balance work?
When the distances from the center are equal:
If you have a straight balance bar (or arm) set over a center pivot,
with an identical weight hanging off each end at the same distance from
the center, it's easy to see that the arm will be balanced.
When the distances from the center are not equal:
If you move weight A towards the center, the balance would tip upward and away from A.
If you move weight A towards the center, the arm would tip upward and away from A.
The closer that a force acts to the center of rotation (the pivot point), the less impact it has. It's like turning a wrench: if you hold it close to the head, it's much harder to turn than if you hold it by the end. This is why the balance is most accurate when the pans are hung a long way from the center.
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Building our balance
So we needed a long thin 'arm' of some kind, with two identical pans that will hold our weights to be set at the same distance from the center of the arm. The weights should be of a known value, which can be added to the other pan until the whole thing balances.
But we didn't have any known weights. All we had was a 500g (onepound) bag of sugar. We knew we had to weigh some gold, but we didn't know how much there would be. It could be twenty grams or just a few milligrams.
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Making your own balance
a) Decide whether you want to weigh tiny things or heavy things.
Weighing tiny things is harder. Keep the whole balance light, and
keep friction down to a minimum so the balance is responsive.
Weighing heavy things means making a sturdy balance that won't bend much
or break when you add the weights.
b) Choosing an arm Find
something long and thin that won't bend when you hang weights at both
ends.
The longer the arm, the more accurately you can weigh things. However, the
longer it is, the more easily it will bend when weights are put at the ends.
For weighing small things, choose a light but stiff material for the arm,
like a drinking straw or light piece of wood. For heavier things, test
out possible arms before deciding which to use. It can be hard to find
something that doesn't bend. We looked for something at least a meter
long, and eventually chose a wooden pole (the metal ones all bent too
much).
Have a small pointer
at one end of the balance (such as a piece of wire) which you can line up
against a strip of paper. Then you can draw a line to represent the balance
point onto the paper before starting to weigh something.
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c) Balancing the arm  the pivot point
Find the center of the pole by balancing it on a pivot, like a nail or a sharp knife edge, until you find the point at which the pole stays horizontal. Pivot the arm at this point.
The final pivot shouldn't have too much friction. A 'sticky' pivot means the balance isn't completely free to move as necessary, so the readings will be less accurate. Ideally you should make a hole through the center of the balance and hang it by putting a nail or pin through the middle. The balance will be held in position, which will reduce the chance of losing whatever you're weighing.
Make the hole slightly higher than the center of the arm for extra stability. Mark a lengthscale onto your balance arm, so you can easily measure off distances from the center.
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d) Making the pans
To be accurate, the pans should weigh the same.
To weigh light things, you need really light pans. We folded up square pieces of tin foil and used small pieces of wire to hang them from the arm. You could use paper and glue, or two small containers. To keep the weights the same, start off with two pieces of tin foil or paper that are the same size. Also try to use similar lengths of wire and amounts of glue.
To weigh heavy things, the pans need to be bigger. Again, try to get two pans of the same weight. You can use string or thin rope to hook them onto the balance arm, but make sure it's strong enough to hold the things you want to weigh. That sounds obvious, but it's easy to get it wrong!
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e) Obtaining known weights
Most foods come in known weights, so you could use bags of flour, sugar, salt, etc. Water could be useful, if you can measure volumes of it easily. One cubic inch of water weighs about half an ounce (or, one cubic cm of water weighs one gram).
You may want to make some weights. Start off with a known amount of something, and using your balance to find something of the same weight that's easier to handle.
We started off with the 500 grams of sugar and used our balance to find how many nails weighed the same amount. Then we counted the nails and divided by 500 grams to find out much each nail weighed. Then we found out the length of wire we needed to balance against 50 nails, which in turn told us how much the wire weighed per centimeter. With that information, we were able to cut the wire up into lengths equal to 1 gram, 0.5 gram, 0.1 gram, and so on, to give us small weights.
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f) Using your balance
To get the arm of your balance pivoted, hang your two pans at equal distances from the center. Make sure the arm is horizontal. It's worth trying to do this when the pans are at several different distances from the center.
If the pans aren't an equal weight, add small weights to one of them until they balance. Then mark where the pointer is pointing onto a clean strip of paper.
Put your unknown weight into one pan, and add weights to the other pan until you reach a balance point. Start with bigger weights and go on to smaller ones. Add up all the weights to get the final amount.
You may need to start with the pans very close to the center to make sure that the arm doesn't bend when you add the weights. Ideally, you should make your final reading with the pans hung as far as possible from the center, to get a more accurate measure.
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