This week I am investigating how GEARS allow us to visibly express ratios. They aren't just numbers written on paper in math class. We use them to do work (turn, lift, etc.). In the last few days we've looked at watches, but today I want to examine gears that are doing heavier work. Here's an example:
The gears on the left are the same size, and represent a ratio of 1:1. The gears on the right are different sizes, representing the ratio of 2:1. You have to turn the smaller gear twice to get the larger one to turn once - but in the process you are gaining "mechanical advantage" or strength.
In a car's transmission, the gears touch all the time. Transmissions are very complicated mechanisms. The active pairs of gears are brought into use by a shift lever that locks each set of gears to the shafts upon which they rotate.
When I was the age that our Excel Math students are now, ropes and pulleys were a handy way to lift a train set up into the rafters of my garage. The number and size of the pulleys was determined by how many we had on hand, not by any math analysis.
If you have read this blog for a long time, you might remember the posting on non-circular gears.
As I said at the beginning, a set of gears is a way to represent a math ratio. If you can read this linked article without falling asleep, you might want to become an engineer!