I actually made this novelty gadget once as a kid, after learning about turning moments in a school physics lesson. It's essentially a money box that can automatically measure how much money it contains. Here's a diagram:
You simply place your coins into the different bins on the right, one bin for each denomination. The higher the value/weight ratio of the coin, the further from the pivot is its bin. (E.g. in the UK, the pound coins would go way over on the right, far from the pivot, while the 1p and 2p coins would go in a bin close to the pivot.) The whole thing is adjusted to read zero when all of the bins are empty, of course.
The total turning moment of all of the coins is balanced by the sliding counterweight on the left, with a suitably calibrated scale. Balance it, and read off the total value of the coins.
That's it.