Magic mass balance


Continuing with my playground theme that I started with the merry-go-round, let's consider the seesaw. What determines whether it will be balanced? Archimedes sorted this out over 2000 years ago, using a scale and weights.

Below is a virtual scale. The mass and the arm length of the left side of the scale can be adjusted, and the right side magically adjusts to keep the scale balanced. Can you figure out the relationship between the distances and masses?

Here is the accompanying handout.