Which is heavier?

In the story of Archimedes and the Crown we saw how Archimedes was able to catch a gold thief by weighing King Hiero's crown. So how do you do that?

Copyright 1997, Doug Craigen
All rights reserved.

You've already learned a lot about how to weigh things. You learned it at the playground. Have you ever played on a teetertotter (see-saw)? You know that if two kids sit on it, and one is much bigger and heavier, that one sits on the ground while the other one stays up high. If they are the same size, then the teetertotter balances. This means that neither side moves up or down except when the kids push it that way. Now lets find a brick, and we'll say "This weighs a pound". We now have a new word - pound. Anything else that balances with this brick on a teetertotter weighs a pound too. So we can find lots of other one pound bricks, stones, sticks and other things by checking which ones balance with our brick that we call a pound. If we find something that balances with two of our one pound bricks, it weighs two pounds. If we find something that balances with three of our one pound bricks, it weighs three pounds. If we find two things which balance with each other, and together balance with a one pound brick, they each weigh half a pound.

There's one other thing you might have learned from teetertotters - two different size kids can balance if the heavier one sits closer to the middle. (This is the start of understanding something called leverage that Archimedes studied too - something I'll write more about later.) So when you want to weigh things by balancing them, it is important to make sure that they are both the same distance from the middle. One way to do this is instead of putting them on top, you hang them underneath in a pan. Then you can make sure the strings holding the pans are each the same distance from the middle.