Popular trivia - fact or fiction?

trivia/fact.or.fiction New

New entry, edited from material collected for the archive and not yet in a released version.

Problem

Popular trivia - fact or fiction?

1. If the population of China jumped up and down simultaneously it would
cause a tidal wave that would wash over most of the planet.  (Say each
person jumps 60 cm, landing on solid ground.)

2. If you put 1 grain of rice on square one, 2 grains on square 2, 4
grains on square 3, 8 on the next square and so on, doubling the amount
until you complete 64 squares, you will have enough rice to cover
England, Scotland and Wales, 3 feet deep.

-- Ivan Audouin <audouin@husc4.harvard.edu>

Show solution

1. China jumping

Say each person hit the ground going 5 m/s, that the de and reacceleration took
.01 seconds, and that each of 1 billion people weigh 100 kg. Also suppose
that the forces act in the same direction.

The force on the earth is given by F=N(2mv)/(t), i.e

 Then F=10^9 [Editor: "1^9" in the original]*2*5*100/.01=10^14. The Earth
has mass 6*10^24 kg, so the earth feels an acceleration of <10^-10 m/s^2.
This, I think, is negligible.

-- David Savitt <dsavitt@unixg.ubc.ca>

Just to add a bit to this...

From "The Flying Circus of Physics With Answers" [Editor: "With Answer" in the original] by Jearl Walker, c 1977.

"The original, purely tongue-in-cheek calculations by David Stone
indicated that such a jump by the Chinese would produce an earthquake
with a Richter scale magnitude of 4.5.  The jump would surely devastate
part of China.  But if the ground wave is resonantly amplified,
destruction elsewhere would also be possible.  To make resonance, the
Chinese would have to jump every 53 or 54 min, the time a ground wave
requires to circle the earth.  To protect itself, the target nation would
have to organize jumps whose waves would cancel the Chinese-generated
waves.  Since the target nation would have a smaller population, the
jumps would have to be from proportionally greater heights.  One writer
to "Time" magazine argued that any jumps must be with stiff knees in
order to impart the greatest energy to the waves.  The difference between
stiff- [Editor: "still-" in the original] and loose-kneed jumping is not clear to me, since the energy
imparted must be the gravitational potential energy in both cases.  But
were his argument correct, he points out that a resonant wave 'would not
be generated ... because the only weapon derived from the actions would
be the ear shattering scream from 750 million badly maimed Chinese'."

-- Jeff Shearer <jshearer@beta.tricity.wsu.edu>

2. Rice on the chessboard

This gives 2^64-1 grains of rice. Suppose each grain of rice measures 6 mm
by 1.5 mm by 1.5 mm (this seems to be what my rice is like). The total volume
is 2.49*10^11 m^3. If this is spread 1 m deep, this covers an area of
2.49*10^11 m^2, or 2.49*10^5 km^2. My atlas reports an area for the UK of
about 2.44*10^5 km^2, so this is actually pretty accurate!

-- David Savitt <dsavitt@unixg.ubc.ca>, January 1994