Math Cats Balance
Click to know my weight
Click here to get alternate fulcrum
Click  to know my weight

Help and Ideas

Choosing objects:

choosing how many objects
balance the objects
finding actual weights
alternate fulcrum
jumping cats
AOL users
You can choose from a wide range of objects to place on this scale - from electrons to galaxies! Click the arrow next to "thin cat" and scroll up and down the object lists to see all the choices.
Choosing how many objects:
Scroll through the number menus to choose a multiple and a power of ten. For instance, if you choose the number 4 and next to it the number 100,000, the balance will place 400,000 objects on that side of the scale. You will still only see one object, but the scale is weighing 400,000 of them. You can choose fractions, too. If you choose the number 2 and next to it the fraction 1/100, the balance will place 2/100ths of an object on the scale. That is the same as 1/50th of an object.
top .

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.)
top .
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).
top .
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.
top .
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.)

Jumping cats:
Explore what happens when you place one or more jumping cats on the scale. Do the jumping cats ever become stable? When?
What is mass?
The mass of an object is a measure of the amount of material it contains. An object's mass determines its weight when there is gravity. In a weightless environment an object has no weight - but it always has mass.

(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.)


Photo Credits

Math Cats Balance © copyright 2003 -  by Wendy Petti of Math Cats & Maurici Carbó Jordi of nummòlt.  All rights reserved.