Sunday, November 03, 2013

At what rate is work done by this machine?

In this video, there is an electric motor running at 200 rpm. It is connected to a series of gears each of which reduces the rotation rate by a factor of 50. After 12 such reductions, the last gear is turning at a rate of 1 rev/2.3 trillion years. Just for emphasis, this last gear is set in a block of concrete. 

So as an interesting exercise, at what rate is this machine doing work?

In a limited sense, this can be imagined as a representation of the layers of the vast and interconnected machine we call life on this planet. While there are many living things we see moving, reproducing, and living at fast rates in the world around us, there are other mechanisms and processes intimately connected with these that move very, very much slower. As a result we have evolution that we cannot see at a casual glance, but it happens nonetheless.

If the motor and gear were to run long enough, the earth would be gone when the sun explodes long before a single revolution has happened.

Food for thought.

As noted on Gizmodo, the rotation rate at each step is

  • motor: 200 rev/minute (1 rev/ 0.3 sec)
  • 1st: 4 /minute ( 1/ 15 sec)
  • 2nd: 4.8 /hour (1/ 12.5 minutes)
  • 3rd: 1/ 10.4 hours
  • 4th: 1/ 3.1 weeks
  • 5th: 1/ 2.98 years
  • 6th: 1/ 149 years
  • 7th: 1/ 7452 years
  • 8th: 1/ 372,600 years
  • 9th: 1/ 18.6 million years
  • 10th: 1/ 932 million years
  • 11th: 1/ 47 billion years
  • 12th: 1/ 2.3 trillion years
This give a new perspective on those astronomical numbers such as the size and age of the universe. It really is possible to build this table top machine that, in fact, that could have been built 100 years ago just as easily. It that has time scales built in that span the range from a bit too fast for a human to essentially infinite for our purposes.

Just because you don't see something happening, doesn't mean nothing is happening.

As one of the commenters, RichardThunderBay, at Gizmodo noted:

Estimating the size of the gears to 0.2 meters and using 2.3 trillion years as the revolution time, I calculated that for the outer edge of the gear to move the interatomic distance between atoms in iron would take the about 1000 years for it to do.