How much of an iceberg sticks out of the water?
You will find here that the answer depends on the density of the iceberg.
Most of us have heard the expression, 'that is just the tip of the iceberg', which is used to say that there is more, a lot more to come. The saying comes from the commonly held notion that 10% of an iceberg sticks out of the water. Is this right?
You can see part of this iceberg above the water and another part below the water. How much is sticking out?
An iceberg, like every one else on earth, receives a force that pulls it down. This force is called weight and is due to the gravitational attraction with the earth. When you step into a pool, your weight pulls you down to the bottom. Lucky for us that is not al what happens when you go for a swim.
Think of a pool that is filled to the rim. Water will leave the pool as you enter it. Imagine you could collect and measure all the water you pushed out of the pool. You would then find your own volume, assuming you fully submerged yourself without making waves nor splashing!
Let us take all that water and put it on a scale. You will find that it has a certain weight. Here is the key, if the weight of the water is equal or more than your own weight, then you float; if the weight of the water is less than your own weight, you sink. It turns out some humans float and some very dense ones, like me, will sink to the bottom; it all depends on our density.
Diagram for the Archimedes principle. A person inside a water container displaces its own volume of water. The drawing shows a case in which the weight of the volume of water (buoyancy force) is less than the person's weight. The person sinks in this case.
Archimedes principle states that an object submerged in a fluid (gas or liquid) receives a force upwards (buoyancy force) that is equal to the weight of the volume of the fluid displaced by the object. Objects float when this force is equal or greater than their own weight, and sink otherwise.
Let us go back to the icebergs. We need to calculate the weight of an iceberg and compare it to the buoyancy force that it receives from the water. Or we could ask a penguin to let us know how much iceberg is under the water
Could we recruit a penguin to let us know how much of the iceberg is below the water?
A quick note: Weight and mass are not the same thing. Weight is the gravitational force that a mass receives, while mass is the amount of stuff an object is made of. You can change your weight without changing the mass by changing the gravitational attraction. The best weight loosing program would be to go to the moon! You can eat as much as you want and your weight will go down while your mass goes up. For practical purposes here, gravitational force is not going to change, so we will use grams as a unit of weight, just like we do with our weighting scales.
Can you find a small chunk of ice 10 cm on each side?
Imagine a small chunk of ice floating on the water. Let us assume it measures 10 cm on each side, which gives a volume of 1000 cm3 (1 liter). We could find its mass if we knew its density. The density of ice is 0.92 g/cm3. Let us round to 0.9 g/cm3 for simplicity. Given the definition of density (mass divided by volume) we can do the following calculation to find the mass:
mass = density * volume = 0.9 g/cm3 * 1000 cm3 = 900 g
Remember we need to check that the units match (read the journal of March 10 if you have not). Units match; cm3 are cancelled (cm3 / cm3 = 1) and we get grams, which is the unit of mass, and that is what we are after. This means the ice chunk weights 900 g.
The iceberg will sink in the water until the weight of the volume of water that it displaces is equal to 900 g. The density of fresh water is 1 g/cm3, how much fresh water weights 900 g?
volume = mass / density = (900 g) / (1 g/cm3) = 900 cm3
Units match and we get the right unit. The iceberg will have 900 cm3 under water, and the remaining 100 cm3 above water. And 100 cm3 is 10% of 1000 cm3!!
Icebergs are not made of solid ice. They have tons of air bubbles trapped, which makes them less dense than solid ice, like the air bubbles make Styrofoam less dense than the pure plastic (read journal of March 6). The density range for glacier ice is between 0.83 g/cm3 and 0.917 g/cm3 (I looked it up on a book from Palmer's library. Amazing! No google but yes books!).
Ocean water is denser than fresh water because of its salts, but it is not that much different for our purposes. We are measuring surface densities close to 1.03 g/cm3. We will round it to 1 g/cm3 for simplicity.
Let us take an iceberg with density of 0.8 g/cm3. Can you tell how much of the iceberg will be above water and how much below water?
If we want to use real size icebergs, we need to use density in kg/m3 instead of g/cm3. The water density is 1000 kg/m3 and that of the glacier ice we are using is 800 kg/m3. Imagine the iceberg with dimensions: 50 m high, 200 m on one side and 100 m on the other. This gives a volume of: 1000 000 m3.
To find the iceberg's mass:
m = d*v = 800 kg/m3 * 1000000 m3 = 800 000 000 kg (wow!)
How much fresh water weights that much? Let us find out:
v = m / d =( 800 000 000 kg) / (100 kg/m3) = 8 000 000 m3,
which is 80% of the iceberg's total volume.
Iceberg floating as explained by Archimedes
We discovered today that glacier ice icebergs have close to 20% to 10% of their volume sticking out of the water, the actual value depends on the density of the ice (how much air it contains).
** Check your knowledge: How much of an iceberg with density 830 kg/m3 would stick out if placed on oil? I have no idea of oil's density, and it will depend on the type and quality of the oil. We know it is less than water, because it floats on it. Let us assume it is 910 kg/m3 or 0.91 g/cm3 (check on google if you want, and let me know). Send me your answers. I will provide the answer two days after I receive three answer.