Sunday, November 2, 2014

Ask Santos: Goofy Edition

Now we go from the seriousness of Ebola to something a little more goofy. Today's question comes from Kaylee.  She writes,

Since I was little and watched A Goofy Movie quite often, I always wondered what the answer would be to Goofy's question he asks Max while sleeping, trapped in their car due to the presence of Bigfoot: How many cups of sugar does it take to get to the moon? 

I'm not sure if it's even possible to calculate, or what exactly the question is specifically asking (whether it is meaning to use the sugar as fuel, or to build a bridge from sugar), but I'm just curious. Call it a question that's plagued me since childhood.

Why is it that Goofy can talk, but Pluto can't? Seriously, what mutation lead to this genetic monstrosity?
I'd hate to see the Punnett square on that one!  (Image from Wikipedia.)

As you point out, the answer to your question depends on context. Unfortunately, I've never seen A Goofy Movie (I'll have to check it out when I get a chance), so I'll need to use your interpretations:

(1) Building a bridge of sugar. There are obvious practical problems with this (e.g. structural integrity of the sugar, aligning the bridge with the constantly moving moon, not being able to breathe in space, the base of the bridge dissolving when its humid out, etc.) However, from a pure volume perspective, we might imagine building a ladder bridge that was two feet wide, half a foot thick, and long enough to reach to the moon. The moon is 240,000 miles away. If we use the equation 

volume = base*width*height, 

we can get a rough estimate of the volume of sugar ladder and use the density of sugar (1.6 grams per cubic centimeter) to find the total mass of sugar needed. By my estimate, you'd need about 60 million tons (~57 billion kilograms) of sugar to build a bridge to the moon.

(2) Using sugar as a fuel. Food is just like gasoline: both act as fuel. "Calories" are a unit of energy. Just like we talk about the miles per gallon you get out of a good car, you could talk about miles per gram of sugar you get out of a fit person. However, rather than power people, we're using the sugar energy to power a rocket. To escape Earth's gravitational pull, you need an "escape speed" of roughly 12 km/s.1 Rockets typically have a mass of around 5 million pounds, which means they'd require about 40 billion food calories to reach the moon. Carbohydrates have about 4 calories per gram, meaning you'd need about 5000 tons of sugar to reach the moon.2

Just to compare, it would take 5000 tons of sugar to power a rocket to the moon, and 60,000,000 tons to build a ladder to the moon. That's about 10,000 times more sugar required for the ladder.

Thanks for a great question, Kaylee!

Do you have a question you'd like to ask Santos? Try Tweeting him at @aarontsantos for a chance to have your question appear on Diary of Numbers.

[1] This ignores important effects like air resistance.
[2] This weighs more than the rocket itself, meaning you'd need even more energy to reach the moon. For comparison, you can get a rough idea how much rocket fuel is needed here:

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