How to balance the objects:
Experiment with the number of objects to place on the balance. For instance, you may find that the mass of 2 thin cats is a bit less than the mass of one fat cat. The numbers on the balance show "5" and "6." So how can we balance thin cats with fat cats? You might try multiplying each side by the number shown on the opposite side of the balance. Will 2 x 6 thin cats balance with 5 fat cats? Yes, 12 thin cats do balance with 5 fat cats.

When you are comparing two objects of very different mass, you might multiply one object by a large number and multiply the other side by a fraction.

Not every pairing of objects can be balanced if the difference in their mass is too vast. Even 14 billion electrons do not come close to balancing with one billionth of a thin cat. (When the objects are very far out of balance, the scale will show a gray background. It cannot show all the powers of 10.)
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Finding actual weights:
It is possible to balance one type of object with a variety of other objects without ever learning their actual weights. But if you like, you can find the actual weight of an object. There are two ways:

   1) Click on the object and a small window will pop up announcing its weight. Choose the unit of measurement you want from the menu.
   2) It is more of an exploration if you place an object (or multiples of it) on one side of the balance scale and place weights on the other side until it balances. You can find different units of measurement when you scroll up to the top of the objects menu.

You might find that the actual weights of the objects do not exactly confirm your explorations. Take the example above: we have balanced 12 thin cats with 5 fat cats. If we divide 12 by 5 we get 2.4 ... this means that one fat cat balances with 2.4 thin cats. When we click on each picture to learn their actual weights, what do we find?

   
(You may click the menu bar to choose the unit of measurement you like; this example uses kilograms.)

If we divide 5 kilograms by 2 kilograms we get 2.5 ... this means that one fat cat balances with 2.5 thin cats. But on the scale, we found that one fat cat balances with 2.4 thin cats. How can this be?

The explanation is that this scale has a tolerance for slight differences in weight. Objects which are almost (but not quite) equal in weight will appear to balance. We've built in this tolerance so that it is easier to find the equilibrium (to get the two sides to balance).
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Magnification:
Many of the objects are shown in a blue circular frame with a yellow symbol in the bottom left corner. The symbol shows what kind of magnification was used to view the object.

* The very tiniest objects such as electrons show a question mark in the corner because they cannot be viewed with any magnification.

* Other microscopic objects are seen through an electron microscope or a regular microscope.

* Small objects which can be seen with the naked eye, such as an ant or a fly, are seen here through a magnifying glass.

* Objects such as cats do not need magnification.

* Objects in space - the moon, planets, comet, sun, and so on - are seen through telescopes.
One symbol is for a visual telescope. Another symbol is for a radio telescope, but it represents all of the telescopes used for observing wavelengths that are longer and shorter than visible light: radio, infrared, x-ray, and gamma ray. The Milky Way galaxy is shown on the balance scale through a gamma ray telescope. But here is an example of how it appears in different wave lengths:

The neutron star is shown through an x-ray telescope. A black hole cannot be viewed directly so we've tried to simulate objects falling into a black hole.
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Alternate fulcrum:
Click on the center fulcrum between the two objects to see an alternate fulcrum - another way to visualize how the objects balance. Click again to return to the "normal" fulcrum. Each fulcrum is like a big fraction. The normal fulcrum uses decimal "steps." The alternate fulcrum uses rational steps. On the rational fulcrum, the blue point and line show the ratio of the left side to the right side of the balance.

(Compare the rational fulcrum to the "normal" one. When both sides are balanced, the blue line is centered.)

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(AOL users: The Math Cats Balance may not always work properly with the AOL browser. If the balance does not work properly, open another browser (Internet Explorer or Netscape) for exploring this project.)

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