MathCats balance

About MathCats balance

Balance items ranging from electrons to galaxies.
Balance them, multiplying or dividing each one.

Choosing objects:
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.

Fulcrum:
Fulcrum is like a big fraction. 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.

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.

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.