Maciej asked:

How much wood would a woodchuck chuck? Assume for purposes of this question that a woodchuck could chuck wood. Make sure to show your work.

My answer:

The Woodchuck, more commonly known as a groundhog, is a burrowing animal, and does not normally (up)chuck wood. The groundhog can, however, chuck dirt, and can displace 1 m³ or 320 kg of dirt when digging a burrow.

A woodchuck has a finite amount of possible chucking that it is capable of in one year. As the typical groundhog chucks dirt during it's traditional activity of underground burrowing, we will assume that the amount of wood that the groundhog is capable of chucking will be limited by the difference in density of wood (0.31 grams per cubic centimeter) and that of dirt (1.2 grams per cubic centimeter).

So if you want to assume a Woodchuck is limited by area of the volume, and not affected by it's density, then a woodchuck would move 1 m³ or 80 kg of wood per year. If you believed the gating issue was density and not area, then a woodchuck could potentially move 4 m³ or 1280 kg of wood per year.

A woodchuck hibernates for roughly eight months per year, leaving the animal about 120 days during which it can burrow and chuck. That would allow for about 10.7 kg of wood chucking per day.

edit: Mr.D of Mosedale suggested that I did not prove that a woodchuck has a finite amount of chucking per year, but I merely made an assertion. This is true- Phil of Puxatawney, Pennsylvania does not actually hibernate because he is kept indoors year round. Therefore, Phil (and other non-hibernating ground-rats) has a chucking potential of roughly 12 m³ or 3900 kg of wood per year.

another edit: I found out via the interweb that woodchucks in captivity can live up to 10 years. so that's about 120 m³ or 39,000 kg of wood for lifetime captivity chucking potential.