Chapter 9

Archimedes' Principle

This guy is important!

Demos to Prepare:
Archimedes' Principle:
Gold sample
Iron Ball
Overflow can
Hydrometers
Spring Balance
Weigh Air Ball
Decigram Balance
Centigram Balance
Mercury
Beaker, 500 ml
Boat & Rock
Quicksand!

Archimedes solves the Problem of the King's Crown:

So King Hiero of Syracuse ordered his goldsmith to make him a new crown. The gold was weighed out and given to the goldsmith.

When the goldsmith presented the king with the finished crown, the crown was weighed. The weight matched the original weight of the gold.

The king suspected that the crown was not pure gold, so he asked Archimedes to figure out how to test it. The story goes that when Archimedes lowered himself into his bath, the tub overflowed and this inspired him to discover the solution to the crown problem.

With much excitement, Archimedes leapt from the tub, omitting his toga, and streaked down the street to the palace crying, "Eureka, eureka!".

Thus was discovered Archimedes' Principle: An immersed body is buoyed up by a force equal to the weight of the displaced fluid.

To test the crown, Archimedes weighed it in air and again when suspended under water. The loss of weight in water is called the Buoyant Force and is the weight of the displaced water.

For example: If the crown weighs 1000 grams in air and 900 grams under water, the buoyant force is 100 grams. Because the density of water is 1.0g/cm3, cm3 can be substituted for grams to get the volume of the crown.

Density = mass/volume, so this density is 1000g/100 cm3 or 10 g/cm3. This is a long way from 19 g/cm3, the density of gold!

So the goldsmith alloyed the gold with a cheaper metal and kept the extra gold for himself.

So just what is the difference in the alloyed crown such that it has the correct weight? The size. The alloyed crown must be larger.

[Perhaps it was the bad fit that alerted the king to the fakery].

The crown is buoyed up by the weight of the displaced water.

Ah, so, Mr. Goldsmith, so the crown is NOT pure gold?!

The density of liquids can be determined by the Hydrometer method.

Divers’ Helmet Crush video:

Where the pressure in the suit must balance the
pressure of the water. P = hd, Total force = PA

At 100 meters deep, the pressure is 10 kg/cm2 and
the total force on a human body is over 100 tonnes.

Killer Quicksand density is measured, Video:

A mixture of different density substances, Video:

This is for insurance purposes. Different densities of sea water
will determining how deeply a ship will submerge in different
densities of water due to temperature and salinity concentrations.

Can Ping Pong balls raise a sunken ship by Archimedes' Principle? Video:

The limit is about 25 meters deep where the pressure will crush the ping pong balls!

The burning of the Hindenburg. Video:

Exploding Hydrogen produced by Alkali Metals plus water! Video:

Three thousand party balloons are needed to lift a 40 kg child, Video:

An 11 kilolgram Lead Balloon and Archimedes Principle: Video

The flames are buoyed up by Archimedes' Principle.

Because the density of air is 1gram/liter, the buoyant force of air is 1 gram per each liter of displaced air.
Methane Bubbles are buoyed up by Archimedes' Principle, Video:

Dangerous Methane Combustion Video:

Sulfur Hexafluoride, a very High Density gas = 4 grams/liter!

Helium is a Low Density Gas = 0.2 grams/liter. Video:

Here Endeth Archimedes