As you know from kindergarten, some things float while other things sink. You may also know that oil, which is insoluble (cannot be dissolved) in water, floats on top of water. What you might not know is how to find out whether something will sink or float. We will discuss that in this long chapter.
DensityEdit
First, let's learn a new word: 'mass'. 'Mass' means how much of matter there is. This is not the same as 'volume'. Do you remember that there are always spaces between particles? 'Mass' does not include the spaces between the particles, while 'volume' does. Mass is measured in the units kilogram, gram and milligram.
Imagine you are in an enclosed room, say your bedroom. You are the only one inside the empty, airless room. Therefore, you are the only thing with mass in it. If your room is 1.5m × 2m × 2.5m, and your mass is 30kg, then there are 30kg in every 1.5m × 2m × 2.5m = 7.5 m^{3}. Then, in every average cubic metre, there would be 30 kg ÷ 7.5 m^{3} = 4 kg.
Remember that in your room, there are (on average) 4 kg in every cubic meter. That is also the density in there: density is the amount of matter in a specific space; the volume is usually represented by an invisible '1'. What are the units of density then? The units of density are always constructed by the unit of the mass, a forwardslash, and then the unit of the volume. By now you may have deduced that the method of finding density is mass over volume. This formula is very important, so we will put it here:
Note: You can also swap them around like you do in maths to find the mass or volume when you have the density.
Floating and sinkingEdit
What does all that have to do with floating or sinking? Here's an old riddle: which one is heavier, 1kg of lead or 1kg of feathers? Yes, that's right, they are the same. But what if you put the lead and feathers into a pond? Will they both sink?
Actually, no. While their mass may be the same (1kg), the volume of lead is a lot smaller than that of feathers. As there is the same mass stuffed in a smaller space, it must be denser. The density of water is 1 g/cm^{3}, so if the density of the lead is more than 1g/cm^{3}, it has to sink. On the contrary, the feathers' density is probably less than 1g/cm^{3}, which makes them float.
In other words, whether an object will float or sink in a certain liquid (or gas) depends on their density with relation to the density of the liquid. An example is the diagram on the right.
Unfortunately, we need a bit of math here. The following is a table of the name, mass and volume of some liquids and solids. If all these things are put into a measuring cylinder (or any container for that matter), and nothing dissolves, what will be the order of their altitude, from top to bottom?
Name  Volume  Mass  Density 

Solid W  0.000 001m^{3}  5g  
Solid X  5.4cm^{3}  1.8g  
Solid Y  300mm^{3}  1.6g  
Solid Z  5cm^{3}  0.01kg  
Liquid A  24cm^{3}  96g  
Liquid B  24cm^{3}  12g  
Water 


Next, we need to know their densities. Remember to change the units. Note that we use division rather than fractions here. We will round off to three significant figures here.
Name  Volume  Mass  Density 

Solid W  0.000 001m^{3} = 1cm^{3}  5g  5g ÷ 1cm^{3} = 5g/cm^{3} 
Solid X  5.4cm^{3}  1.8g  1.8g ÷ 5.4cm^{3} ≈ 0.33g/cm^{3} 
Solid Y  300mm^{3} = 0.3cm^{3}  1.6g  1.6g ÷ 0.3cm^{3} ≈ 5.33g/cm^{3} 
Solid Z  5cm^{3}  0.01kg = 10g  10g ÷ 5cm^{3} = 2g/cm^{3} 
Liquid A  24cm^{3}  96g  96g ÷ 24cm^{3} = 4g/cm^{3} 
Liquid B  24cm^{3}  12g  12g ÷ 24cm^{3} = 0.5g/cm^{3} 
Water 


1g/cm^{3} 
Then, we arrange them in the correct, ascending order.
5g/cm^{3}, 0.33g/cm^{3}, 5.33g/cm^{3}, 2g/cm^{3}, 4g/cm^{3}, 0.5cm^{3}, 1cm^{3}
0.33g/cm^{3} < 0.5cm^{3} < 1cm^{3} < 2g/cm^{3} < 4g/cm^{3} < 5g/cm^{3} < 5.33g/cm^{3}
Solid X < Liquid B < Water < Solid Z < Liquid A < Solid W < Solid Y
Since Solids W and Y are both on the bottom, they are on the same level—they both sink in liquid A. So, the correct order is as follows:
 Solid X
 Liquid B
 Water
 Solid Z
 Liquid A
 Solid W and Solid Y
You can refer to the diagram on the left, which shows a container with all the solids and liquids in it.
Balloons, ships and submarinesEdit
Let's get to a topic with no sums: how vehicles work.
BalloonsEdit
Once upon a time, when aeroplanes were yet to be invented, the only way to soar through the skies was to ride in a hotair balloon. A hot air balloon is just like those you ride in amusement parks. They work the same way: using the differences in density to hurl the balloon up.
How exactly? Look at the diagram on the right. Did you know that a hotair balloon has to be heated before it flies? This is because the particles inside the balloon are just as dense as the particles outside the balloon at the beginning. However, as soon as the particles are heated, they move more vigorously, and as they bump into each other more often, they become less dense. As less dense things float, the balloon will rise.
ShipsEdit
Many ships are made of steel. Steel is very heavy and dense. Its overall density is approximately 7.85g/cm^{3}. The density of water, however, is much lower, at 1g/cm^{3}. Therefore, it is difficult for steel ships to float if they are made only of steel.
So, how exactly do those ships manage to float? You see, the density of air is very, very low. If there is a large amount of air inside the ship, the total density of the ship will decrease greatly. As long as the density is under 1g/cm^{3}, the ship will float.
SubmarinesEdit
Submarines work in a way that is similar to the ship, except the overall density of the ship can be altered at will so that the submarine sinks or floats as desired. Look at the diagram below. A tank called a ballast tank takes up a significant part of the submarine's area. Note that it does not have to be position like that in the diagram; it can be anywhere the shipbuilder wants it to be. The ballast tank fills up with sea water when the submarine needs to be submerged. When it needs to surface again, the sea water is pumped out of the ballast tank with the air in another tank.
QuizEdit
 Explain why a hotair balloon cannot rise up if there is no fire.
 Evaluate the following.
Matter  Mass  Volume  Density 

Solid P  15  3  a 
Solid R  100  b  4 
Liquid H  c  15  6 
Answers:
 It is because the fire makes the air particles inside the balloon vibrate more vigorously, thus decreasing the density of air inside the balloon, so that it floats.
 a) 5; b) 25; c) 90