A long time ago, there was an ancient Greek king named Hieron. As kings often do, he ordered his
goldsmith to make a golden crown. The goldsmith created one, but the king had his doubts about
the purity of the gold that had been used. To confirm his suspicions, he sought the help of
a local scientist and inventor, and tasked him with verifying whether the crown was pure gold.
The scientist obviously couldn’t perform scientific experiments on the crown
like it was any other object; it was an extremely valuable ornament,
and one to which the king was personally attached. Clearly, this wasn’t an easy problem to solve.
Mulling over this problematic situation, the scientist stepped into a bathtub
for a good thing. At that point, with his mind already buzzing, he made a critical
observation. He noticed that water spilled over the edge of the bathtub as he got in,
and that the more his body sunk into the water, the more water was displaced.
Realizing that he had just found a solution to his crown problem,
he leaped out of the bathtub and dashed through the streets of Syracuse shouting “Eureka,
Eureka!”, which in Greek means: “I have it!”. This scientist’s name was Archimedes,
and the discovery he made while sitting in that bathtub is known as Archimedes’ principle.
More specifically, the Archimedes principle states that if an object is submerged in a fluid,
then the buoyant force acting on it is equal to the weight of the fluid displaced by that object.
But wait a minute, what does ‘buoyant force’ really mean?
You’ve likely observed that when you jump into a swimming pool, you pop back to the surface a
few moments later, as if the water was “throwing you back”. After getting into a swimming pool,
you’ve probably also noticed that your body feels lighter.
This happens because any object, once submerged in water, experiences an upward force from the water.
This force is known as the buoyant force, and this phenomenon is referred to as buoyancy.
Buoyant force exists because pressure increases as an object goes deeper in a fluid, which, in
this case, is water. Due to this, the force from the pressure exerted in the downward direction
on the top of the object is LESS than the force from pressure exerted in the upward direction
on the bottom of the object. Put simply, an object experiences a buoyant force because the more
submerged part—or the bottom part of the object—is always deeper in the fluid than the upper part.
It is the force that opposes the weight of the body by ‘pushing’ it in the upward direction.
Mathematically, the buoyant force is represented like this:
Buoyant force (Fb ) = ρ x g x V Where v is the volume of the displaced
fluid, p (pronounced “rho”) represents density This expression can be rearranged to be
written like this: (Fb ) = W f
Translated into English, this equation states that the buoyant force on an object
is equal to the weight of the fluid displaced by the object.
That’s exactly what the Archimedes principle is all about!
When Archmiedes got into the bathtub, he realized that as more of his body was submerged in water,
the more water spilled over the bathtub’s edge.
He realized that there must be a clear relationship between his weight and the
weight of the water displaced by his submerged body. This was a groundbreaking idea, and one
that could be applied to solve the problem of determining the purity of gold in Hieron’s crown.
Since a crown is an irregularly shaped object, its volume cannot be measured as easily as you
might measure the volume of a cylinder or cube. Furthermore, it was the king’s crown,
which meant that Archmiedes had to test it without damaging it in any way.
From his own bathtub, he realized that if he put the crown in a water-filled container,
it would also cause water to spill out the sides. The key, here, was that a crown made
of pure gold would spill a different volume of water than one that wasn’t pure gold.
Why? Because Density = mass / volume
Quite simply, this means that the higher the density of a substance, the lower its volume.
Archimedes knew that gold was more dense than silver,
or any other metal the goldsmith could have used to make the crown. Therefore, a crown made of pure
gold would displace less water than a crown that wasn’t pure gold and had added metal impurities.
Overwhelmed by this sudden realization, Archimedes leaped from the tub and dashed
through the streets of the city to the king’s palace, shouting the now famous word “Eureka”,
briefly forgetting that he had no clothes on! Archimedes’ principle applies to all fluids, and
is therefore a vital tool for many disciplines, as it provides an accurate and convenient method of
measuring the volume of irregular objects, such as a crown, a rock or even much larger objects.
It is frequently used in the designing of ships and submarines—two essential components of any
nation’s naval forces. It is because of the Archimedes principle that we know how to design
a safe and efficient hot air balloon, and how to test the purity of different substances.
In short, you’ll find this principle in use almost everywhere, from engineering
and biology to geology and medicine. The man who first postulated the
principle—Archimedes—was an extraordinary scientist and mathematician.
Not only did he solve the king’s problem concerning the crown’s purity, but he is also
known to have designed a ‘death ray’ by reflecting sun rays off gigantic glasses at the ships of
invading enemy forces and setting them on fire! Archimedes was a truly exceptional mathematician
and inventor of his time, providing the world with remarkable ideas and theories
that remain an important subject of scientific research and analysis to this day.