2012-03-09

Goofy physics


Source: "Goofy" - Wikipedia

For years, I've pondered a question presented by Goofy in the film "A Goofy Movie" [IMDB]:
"How many cups of sugar does it take to get to the Moon?"
Having just watching the film with my kids tonight, I decided to finally calculate the answer.
Disregarding the effects of atmospheric drag and the gravity of the Sun, I can focus solely on the physics involving the gravity of the Earth and Moon ["Escape velocity" - Wikipedia]:
- A "cup of sugar" has the potential to release 3.18 MJ of energy
- The velocity required to break free of Earth (VeE) is 11.2 km/s
- The velocity gained by an object falling to the Moon (VeM) is 2.4 km/s
- My mass (Mi) is approximately 77 kg 1
Using an understanding of (simplified) rocket science [minutephysics - YouTube], we can learn the basic equation needed to calculate how much energy is needed to travel to the Moon:
Energy in Joules = (.5*Mi)*((VeE)²-(VeM)²)
(38.5)*(11.2²-2.4²) = 4.61x109 J = 4610 MJ
Now we know that I, as some sort of bizarre human-rocket, would need 4610 MJ of energy to travel to the Moon. We already found that 3.18 MJ of energy is in each cup of sugar.
4610 MJ / 3.18 MJ = 1450
This means that it would require the energy of 1450 cups of sugar for me to travel to the Moon. Don't worry, the hard part will be figuring out how I can fly.

1 As a point of reference, the Saturn V rocket which launched Apollo 11 was 3,039,000 kg [Saturn V - Wikipedia].
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