And what happened then?

Well, in Who-ville they say

That the Grinch’s small heart

Grew three sizes that day.

And then the true meaning

Of Christmas came through

And the Grinch found the strength

Of ten Grinches, plus two– Dr. Seuss’s How the Grinch Stole Christmas

It’s nearly Christmas, so SteelyKid keeps demanding to watch the two classic Christmas specials we have recorded, Dr. Seuss’s How the Grinch Stole Christmas and Rudolph the Red-Nosed Reindeer. Watching these over and over again, my thoughts naturally turn to physics, and what sort of physics you could do with these shows.

The most obvious possibility is suggested by the lines above. As you no doubt remember if you’ve seen the cartoon, the Grinch steals all the Christmas trappings from the Whos down in Who-ville, loads it on a sled, and drives it ten thousand feet up the side of Mt. Crumpet, to dump it. When he hears the Whos singing their Christmas song even without their material goods, he has a change of heart, and saves the sled from falling off the cliff, using his new-found strength:

So, just how strong *is* the Grinch, to lift all that?

The actual lifting shot is from a funny angle, so it’s hard to work with, but there’s a cleaner shot while he’s driving up the mountain:

Now, the Grinch positively towers over Cindy Lou Who (who is no more than two), so let’s say he’s my height, roughly 2m tall. He’s approximately 52 pixels high in the original screen capture of that image, which works out to about 0.04m/pixel. Using that as the scale, the sack he’s standing on is 6.6m high, and the sled full of loot is 9.6m long. It’s hard to estimate the depth of the sled, but let’s say it’s roughly 4.5 m deep, a bit less than half as wide as it is long.

Treating the sacks as a giant rectangular solid, then, we would have a volume of 285 cubic meters of stuff. To convert this into a mass, we need an estimate of the density; the simple and easy density figure to remember is that water has a density of 1 g/cm^{3}, or 1000 kg/m^{3}. So, at the density of water, the Grinch’s sled has a mass of 285,000 kg.

Of course, water’s pretty heavy, and a lot of what’s in those sacks is considerable lighter, so let’s guess and average density of about a third that of water, and call it 100,000 kg total. Since he’s lifting that with the strength of twelve Grinches, that means a single Grinch could lift 8,333 kg. That’s around 32 times the clean and jerk lift world record, so you do *not* want to mess with a Grinch.

(Of course, the one in that relationship that you *really* don’t want to mess with is the Grinch’s faithful dog, Max, who pulls that whole sled ten thousand feet up the side of Mt. Crumpet, all by himself… Max rules.)

Given this, we can also answer a second question, namely, just how much do the Whos like Christmas? It says that “Every Who down in Who-ville liked Christmas a lot,” but that’s not very quantitative. Given the video evidence, though, we can quantify this. The population of Who-ville, the tall *and* the small, is exactly 33 Whos, as we can see when they’re singing:

With 100,000 kg of Christmas trappings for all of Who-ville, that works out to 3,030 kg of Christmas gear for each and every Who. So, when they say they like Christmas a lot, they mean they like it a *lot*.

So, there’s your incredibly dorky analysis for this Christmas. Fah-who foraze, da-who doraze, and all that.