In the Beginning
Archimedes was a mathematician in ancient greece. He lived in Syracruse. He was very well known and was very wise the arts of how things worked; he was blessed by the gods. He was also a cousin to the king. They call him when they need advice on matters of technical warfare and business and other matters normal people may have found daunting. The smiths those days were known to be cheats. When they are given gold to work out molds for jewelry they might add some silver and keep some of the costlier gold to sell later for more profit. Well, you see the king gave some gold to this goldsmith to forge out a crown for him. Maybe the old one was now looking dull in his parades or he just wants a new look. Anyways that goldsmith brought back the crown and the king may have been told one or two things because he became suspicious that goldsmith played him and added silver to it. How does one figure out what was done in this kind of thing. You call Archimedes. So he called for his cousin and told him the story and asked him to help him figure out if it was crown of pure gold. Archimedes thought or may have thought it was a bigger problem than a mathematician could handle but he took the job. He ye didnt know what to do. One day in his house when he called for bath and it was filled for him, he entered the tub and some water fell out. He suddenly screamed 'eureka!!!!' which means 'I found it!!!' and he ran half naked to the king's presence and told them he knew what to do. The goldsmith was said to have lost his head as a result. What made them find that goldsmith guilty and what did Archimedes find out about in the tub?
The Tighter Packing
Substances called elements are made of atoms. Substances called compounds are made of molecules. Some substances are a mixture of two or more other sustances. Water may seem sometimes to be heavier than sand or vice versa. One good way to find out which is heavier is to have equal sized buckets and put water in one and sand in the other. When you weigh them you will that time find out which is heavier.
You can try the same experiment with iron and copper. Find one each of these substance both having the same volume and weigh them. To your suprise oil may be lighter than water. The subject being looked at here is density. What is density? Density is the amount of mass in a given unit volume of a type of matter.
It is different for different substances. Irpn has a higher density than wood. Water has a higher density than plastic.
Why Ships don't Sink
Ships dont sink. Why? Sometimes a fluid has more density than a solid has. When thats the case you will see the solid floating on a liquid. So whenever you see anything floating on water that thing has less density than water. Things that are denser will sink. So the size won't matter. A coin will sink but a ship won't because it is less dense than water. I mean the ship isn't as dense as water is. But how?
Remember that some object are mixtures or combinations of more than one substance. When looking for that density you take all thats in the combination into account. If you throw a coin into water it sinks but if you put a coin inside an empty coke can you will find that that combination won't sink. That is because the density of the combination is less than water. So what about a ship? With that big hulk it isn't going to sink? How? A ship is a combo of metal and large spaces filled with air.
How to Staying Afloat or Falling Deep
There are some rules that thing floating or sinking follow. A thing floating will displace it's own mass in liquid. The volume displaced will be the volume of the portion under the liquid. A thing sunk will displace it's own volume in liquid. The mass of liquid will be calculable from the density of the liquid.
The liquid displace is the amount of liquid that gives way so that the solid might take that space. If you enter a tub with water in it you will notice it goes up in the tub. That is because you pushed some water away as you entered the tub. It is possible to know this volume. You can do so by putting water in a cup until it just reaches the brim. You can put that cup in a larger bowl that is empty. If you put in a small object into the cup at this point gently the water will flow out until that flowing into the bowl is matched in volume to the volume of the object. You can now use a measuring cylinder to find the volume of the liquid in the bowl. That measured volume is equal to the volume of the object. You can measure out the mass also using a mass balance. In order to build a ship you have to make sure it contains enough spaces to displace enough water to balance it's weight before it sinks in too deep. Once the water displaced is lighter than the ship the ship will start and continue to sink until it hits the bottom of the sea.
Relative Business
Water is used as some kind of standard. 1gram of pure water is exactly 1cm3. Consequently 1000kg of water is exactly 1m3. Now the density of other substances is usually measured as a relation to how their absolute densities relate to that of water. If the density of an object is 1200kg/m3, then its relative density is 1.2. Relative density has no units. It is a dimensionless number. There are tables for relative densities in textbooks. Looking at it, you can quickly tell which objects can sink and which can float in water.
Floating Films
Sometimes you see an oil floating on water. These oils are immiscible with water meaning it won't mix well with water. When they both are in a slim like a coke bottle container you will find the water seeming like it fell to the bottom.
Special Cases
Solutions. Sometimes an object that is a solid might sink then disolve. These cases involve like some chemistry. It usually means the water molecules break the bonds between the molecules of the solid or may be more attached to the solids molecules than the molecules are attached to one another. Like in sugar. Sugar molecules are more attached to water molecules than water molecules are attached to each other. This causes the sugar to dissolve into the water. Solutions spread throughout the solvent so we don't talk about densities here.
Chemical Reactions
Two chemicals in an equilibrium reaction usually don't leave you a subject of relative density to talk about. Except if one reactant is solid and the other is a fluid.
Close Calls
When the densities of two liquids are almost equal or they mix you might have a problem in experiment.
Archimedes' Verdict
Archimedes realized that if the goldsmith used only gold for the crown, then pure gold that's equal in size or volume to that crown would come out having the same weight as the crown. If the goldsmith had added Silver or something else the weight of the crown would come out different from that of pure gold of the same size or volume. Archimedes had probably found volumes before using water so he realized all he had to do was find the volume of the irregular shaped crown and compare it weight to that of pure gold or collection of gold of the same volume.
Questions
An object subject into water until it had 20m3 under the water. What is the mass of the object?
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