Physics: around the world on a grain of sand?

With Einstein’s e=mc2, 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 \frac{60000}{40}=1500\ days to circumnavigate the earth. At 3000 calories per day, they’ll consume 1500\times3000=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\times 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

    \[e=mc^2=1.0e^{-5}\times (3.0e^{8} )^2 = 9.0e11 J\]

Let’s compare the energies:

    \[\frac{grain\ of\ sand}{walking\ around\ earth\ 7\ times}=\frac{9.0e11J}{1.3e11J}=6.8\]

Apparently, the grain of sand can send the walker round the world 6.8×7≈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.

Physics: the case of the falling penny

Likely, we’ve all heard this question posed:  Would a penny dropped from…kill you? The tutor answers.

 
Recently I was asked if a penny dropped from the Eiffel Tower could kill someone below. It’s a familiar question. Sometimes the penny (hypothetically) drops from the CN Tower or the Empire State Building.

Because of air resistance, a falling penny accelerates only a short distance before reaching “terminal velocity” – the maximum velocity it can be pulled through air by gravity. The folks at Scientific American put that distance at around 50 feet (15m). Therefore, after falling 60 feet or 6000, the penny will travel the same downward speed: about 25 miles per hour, or 40km/h.

To gain some perspective, let’s compare the falling penny to a soccer shot.

Apparently, pro shots are typically 40 to 60 miles per hour, but can reach beyond 90 mph. Therofore, I suspect that a fit amateur can deliver a 30 mile per hour kick (50km/h).

soccer ball shot at net falling penny
mass(g) 450 2.35
speed(km/h)

50 40

Some might argue that the falling penny could still be dangerous due to its harder material and smaller contact point. Scientific American says not really; the penny is round, after all, rather than tapered.

Perhaps a more meaningful question: Which would you rather be – a soccer goalie, or a person walking beneath a falling penny?

HTH:)

Other sources:

forums.bigsoccer.com

www.soccerballworld.com

Royal Canadian Mint

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