Friday, November 13, 2009
Balloon Boy and the Spherical Cow (FPOTW)
Sorry, no balloon boy here, at least in the popular media sense... sorry.
Rather than my usual Fermi problem, today I would like to present a physics thought experiment.
Real life physics is not a textbook exercise. This is because reality rarely gives you all the variables. It is up to you, as a scientist, a physicist and as a critical thinker to determine what is germane to the solution of a real life problem.
A common joke among physicists is as follows:
One day a physicist was asked by a friend of his, a dairy farmer, to help design a better milking machine for her business. The physicist readily agreed, and asked for a couple of days to think about it, after which he would present his results and design to his friend.
Sure enough, a couple of days later the physicist come over to the farm with his laptop and a beautiful power-point presentation titled: "Explorations towards a better milking machine."
After setting up the projector and gathering his notes, the physicist presents his findings:
"After much though and calculation, I have come up with a workable solution to the cow milking problem. First, let us assume that the cow is a sphere of radius r, homogeneously filled with milk..."
Although the following problem is not meant to be solved exactly, it can be explored to any depth you wish, by any method you choose! You can solve a simple rule of thumb Fermi type problem, and have plenty left to explore by adding an udder to a spherical cow. ;)
The situation is thus:
A helium balloon as shown above is at neutral buoyancy a distance above the ground. Attached a given distance below the basket is a bucket. In the basket is an identical bucket filled to the brim with b-b's. In the bottom of the basket is a hole.
At time t=0 the b-b's are poured through the hole at a given rate, where they fall straight down and into the bucket hung below.
Describe the subsequent motion of the balloon.
Ask yourself if the color of the spots on the "spherical cow" have an effect on the solution?