I 'm probably too old for that, and I’m
sure that you already have some knowledge
about me and my famous Eureka. But let me
explain to you the whole story. So this is
me Archimedes and that’s my friend Heiro,
the king. Everything started when he asked
me to build the biggest boat in the World
: the Syracusia with a hot bath, 8 towers,
a library and a gym. The problem was so hard
that one day after a long night of resultless
work, I decided to take a hot bath but was
so tired that it nearly overflowed. and when
I went inside, half of my bath overflowed.
Eureka !
And that is how I realized that an object,
let’s imagine a ball, floating in a bucket
of water. The ball is pushed down by a force
equal to its weight, which is equal to its
mass times the acceleration due to the earth
gravity g approximately equal to 10. But what
is the force pushing the ball up? As the ball
is displacing a certain volume of water, a
force is buoying the ball as if the water
wanted to return to it’s original place:
This force is equal to the weight of displaced
water, that’s to say the density times the
volume times g. And that’s what we called
the law of buoyancy or Archimedes' Principle.
Hence it was easy to help my friend, his two
thousand tons boat will be pushed down by
a force equal to his weight that's to say at his mass times g what gives us a force of 2*10^7 Newtons. Then, if his
boat is displacing a volume equivalent to
2000t of water, the buoyancy force would be
equal to two times ten to the power of seven
too and his boat will barely float. But if
now we just make the keel bigger and therefore
displacing a volume equivalent to 4 thousand
tons of water, the buoyancy force will be bigger and the boat will float and my
friend Heiro would be happy !
