1. 2009
Nov
28

## Buoyancy, part 2

Following up on my calculation of the lifting power of helium balloons, it’s time to see how the same argument applies to ping-pong balls being used to raise a sunken ship.

Raising a ship with ping-pong balls is, in fact, nearly the same situation as raising a child with helium balloons. All you have to do is replace the air with water, the helium with air, the rubber balloons with plastic balls, and the child and harness with a boat (though preferably not in that order). The physical principle at work (Archimedes’ Principle) is exactly the same, and so the same equation I used last time is equally applicable here: the buoyant force on an object (ping-pong ball) immersed in a fluid (water) is equal to the weight of the water displaced by the fluid,

$$F = \rho g V$$

Let’s see what this says about how many ping-pong balls it would take to raise the Mythtanic II, which weighs about $$\unit{3500}{\pound}$$ according to the show. We can start by figuring out how much mass it takes to balance out the buoyant force on a single ping-pong ball, using \(-m_\text{load} - m_\text{ball} + \rho V …

2. 2009
Nov
25

## Buoyancy, part 1

Finally, time to get back to covering some old (by now) Mythbusters episodes. I’ll start with the bonus episode aired a few weeks ago, “Ping-Pong Rescue” — an oldie but a goodie in which the Mythbusters try to raise a boat with ping-pong balls and lift a child off the ground with balloons.

This episode was all about buoyancy, the physical description of how stuff floats. Buoyancy goes all the way back to one of the scientific world’s earliest experts, Archimedes. According to legend, he had been tasked with figuring out whether a crown, given as a gift to the king of Athens, was composed of pure gold or of other, less valuable materials with merely a gold coating. The straightforward way would have been to melt the crown down in order to make an accurate measurement of its volume and thus determine its density, but the king, for some reason, didn’t want his crown damaged and so melting it was out of the question.

The bright idea that Archimedes eventually came up with was — we think — based on a principle that now bears his name (Archimedes’ Principle): that the buoyant force on an object immersed in water …