# With Einstein’s e=mc^{2}, the tutor investigates an old claim.

When I was a kid, a friend of mine told me you can travel around the earth, not just once, but seven times, on the energy contained in a grain of sand. For years I’ve wondered if it’s true.

Today, I’ll work the numbers for* walking* around the earth seven times.

Let’s assume the moderate pace of 4km/h, ten hours per day. Let’s also assume a diet of 3000 calories per day.

The circumference of the earth is 40 024km. We’ll call it 40 000km for easy figures. Let’s imagine the route isn’t direct, so is 50% longer: 60 000km.

At 4km/h, ten hours per day, our walker covers 40km per day. They’ll take 60000/40=1500 days to circumnavigate the earth. At 3000 calories per day, they’ll consume 1500*3000=4 500 000 or 4.5e6 calories to support one round trip. Multiplying that by 7, we arrive at 31 500 000 or 3.15e7 calories.

To my knowledge, the nutritionist’s calorie is 4186 J. Therefore, the walker, by consuming 3.15e7 calories, consumes 3.15e7*4186J=1.3e11J.

Let’s take a look at the grain of sand. There is tremendous possible size variation from grain to grain; I imagine quite a coarse one, maybe 100 grains to a gram. Therefore, my grain of sand is 0.01g=0.00001kg=1.0e-5kg. Its energy content is

e=mc^2=1.0e-5*(3.0e8)^2 =9.0e11J

Let’s compare the energies:

9.011e11/1.3e11 = 6.9

Apparently, the grain of sand can send the walker round the world 6.9×7≈48 times.

Coming soon: driving around the earth?

HTH:)

Source:

Serway, Raymond A. __Physics for Scientists and Engineers with Modern Physics__. Toronto: Saunders College Publishing, 1986.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.