Here's a rather interesting problem in fluid mechanics.
A hollow weightless infinitely thin spherical shell (yes, this IS an ideal problem)
is evacuated and tied with a string to the earth's surface, where the gravitational acceleration is g. Of course, there will be an upward tension in the string of m*g, where m is the mass of the displaced air.
The string is then cut. Assuming the air is an ideal gas, what is the INITIAL
upward acceleration of the sphere? Some would say g, but this is wrong,
since it doesn't account for the acceleration of the air adjacent to the
The problem was reportedly given to Feynman, and, after working on it for a
number of hours, came up with the answer. I won't tell you now what he got, but will leave it for those who might want to try to solve it. I don't know how Feynman did it, but will post his answer later on.