10 August 2012

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Why Does Ice float on water Archimedes' Law of Floatation Explained

Why Does Ice float on water Archimedes' Law of Floatation Explained
Everyone knows that ice floats on the water, size of the ice does not matter, big or small ice floats on the water.

Ice will not sink in the water.

Even icebergs which are big, huge in size keep on floating in the sea.

Archimedes (Greek) (c. 287 BC – 212 BC) was an ancient Greek mathematician, physicist, engineer, astronomer, and philosopher born in the seaport colony of Syracuse, Magna Graecia, what is now current day Sicily.

Archimedes was born in 287 B.C. in Syracuse on the eastern coast of Sicily.
Archimedes lived for 75 years.
Archimedes received his formal education in Alexandria, Egypt which at the time was considered to be the 'intellectual center' of the world.
When he completed his formal studies in Alexandria, he returned and stayed in Syracuse, where he spent most of the rest of his life, devoting his time to research and experimentation in many fields

He created mechanics by discovering screw, compound pulley, lever and center of gravity.

He used geometrical methods to measure curves and the areas and volume of solids.

He also calculated the value of ‘Pi’ with a remarkable accuracy at 3.1408 and 3.1429.

Archimedes is generally considered to be the greatest mathematician of antiquity and one of the greatest of all time.

He is known for the famous principle of floatation and the screw propeller.

His works in the field of math includes discovering infinitesimals, formulas for measuring a circle, spheres, parabolas, cylinders and cones.

The principle of floatation remains of his most recognized and popular invention till date.

How the Principle was invented?

Hiero of Syracuse wore a crown as a symbol of his authority. Over the years, Hiero was made aware that his Royal Goldsmith (who made his crown from Hiero’s treasury) was living a lifestyle that was beyond his means. Hiero suspected that the Royal Goldsmith was using royal gold, intended for the royal crown, to augment his personal wealth. Archimedes was asked to determine whether some silver had been substituted byte dishonest goldsmith. Archimedes knew that silver was less dense than gold, but did not know any way of determining the relative the density (mass/volume) of an irregularly shaped crown, Archimedes had to solve the problem without damaging the crown, so he could not melt it down into a regularly shaped body in order to calculate its density. While taking a bath, he noticed that the level of the water in the tub rose as he got in, and realized that this effect could be used to determine the volume of the crown. For practical purposes, water is incompressible, so the submerged crown would displace an amount of water equal to its own volume. By dividing the mass of the crown by the
Volume of water displaced, the density of the crown could be obtained. This density would be lower than that of gold if cheaper and less dense metals had been added. Archimedes so excited by his discovery that he had forgotten to dress; he leaped up and ran naked through the streets back to his laboratory screaming "Eureka!" (Greek: Meaning, "I have found it!").
The test was conducted successfully, proving that silver had indeed been mixed in. Later, Archimedes observation has been formalized into Archimedes Principle.

Archimedes’ principle states that a body, when it is completely or partially immersed in a fluid experiences a buoyant force, which is equal to the weight of the fluid it displaces.
Note that: 

When a body is totally immersed, it displaced its own volume of fluid. The term fluid covers liquids and gases.The buoyant force acts vertically upwards through the center of gravity of the fluid displaced.

Archimedes' Principle holds regardless of the shape of an object, for irregular as well as regular bodies and any liquids. Archimedes’ principle is a law that explains up thrust or buoyancy

Buoyant force is an up thrust or upward force exerted by a fluid on an object immersed in it resulting in the apparent loss of weight of the object.

 It can be observed that an object submerged in a fluid weighs less than when the object is outside the fluid. The magnitude of the buoyant force depends on the weight of the displaced fluid, and not on the object’s weight. If an object is submerged, it displaces its total volume of fluid. If it is partially submerged, it displaces the volume of fluid equal to its submerged volume. The weight of the fluid it displaces is the volume of fluid multiplied by the fluid’s specific weight.

The buoyant force on a body is vertical, and is equal and opposite to the weight of the fluid displaced by the body. Buoyant force acts through the center of buoyancy of a body, which is at the center of gravity of the fluid displaced. Besides, increase in buoyant force is said to be proportional to an increase in-depth. This explains why the buoyant force or pressure at the bottom of a particular object is greater than the force on top. This particular concept is clearly evident when one tries to hold a cork down a glass of water. If the hand holding down the cork on the bottom of the glass is removed, the cork will immediately float back up

Buoyancy is the ability of an object to float in a liquid, such as water. Whether or not a given object will float is determined by the buoyant force on the object. This concept helps to explain why some things float while other objects sink. Additionally, buoyancy is an important factor in the design of many objects and in a number of water-based activities, such as boating or scuba diving.

Many swimmers know that there are easy ways to float at the surface, such as laying on a person's back or holding a full breath. When the weight of the water a swimmer displaces is more than its body weight, the swimmer will float. Because of buoyancy, we weigh very little in water. We can put most of energy into movement because we only need very little energy to carry ourselves

Law of floatation is a special case of Archimedes’ Principle.
The law of floatation explains that, "A floating body displaces its own weight of the fluid in which it floats". (
i.e. weight of floating body = weight of liquid displaced by the body) When a block of wood is placed in water it sinks until the weight of water displaced is just equal to its own weight

In determining whether a body will float in a given fluid, the relative density, or mass per unit of volume, of the body compared to the fluid determines the buoyant force. If the body is less dense than the fluid, it will float or, in the case of a balloon, it will rise. If the body is denser than the fluid, it will sink. Relative density also determines the proportion of a floating body that will be submerged in a fluid. If the body is two thirds as dense as the fluid, then two thirds of its volume will be submerged, displacing in the process a volume of fluid whose weight is equal to the entire weight of the body. A steel rowboat placed on end into the water will sink because the density of steel is much greater than that of water. However, in its normal, keel-down position, the effective volume of the boat includes all the air inside it, so that its average density is then less than that of water, and as a result, it will float

Thus, the Archimedes' law of floatation states that an object, whether wholly or partially submerged in liquid, experiences an upward thrust and the force is equal to the volume of the liquid displaced by the object.

It is interesting to note that for any object that is completely submerged in liquid, the amount of fluid displaced is equal to its volume.

And for an object that floats on a liquid surface, the volume of the displaced fluid is same as that of the object.

This object experiences an upward force known as the buoyant force.

During the Roman conquest of Sicily in 214 BC, Archimedes worked for the state, and several of his mechanical devices were employed in the defense of Syracuse. Among the war machines attributed to him are the catapult and - perhaps legendary - mirror system for focusing the sun's rays on the invaders' boats and igniting them. Nevertheless, despite Archimedes’ efforts, Syracuse eventually surrendered to the Romans. Archimedes was killed by a Roman soldier after the city was taken.

He is most famous for discovering the law of hydrostatics, sometimes known as 'Archimedes' principle', stating that a body immersed in fluid loses weight equal to the weight of the amount of fluid it displaces

Now question is - Why Ice floats on the water or in sea?

Water is different.
Water is a member of a very exclusive group of substances that are less dense as a solid than as a liquid.

Take alcohol for instance.
If we were to fill up a 1-liter container with pure alcohol at 30 degrees Celsius (86 Fahrenheit) and then take another 1-liter container and fill it with pure alcohol at 10 degrees Celsius (50 Fahrenheit) the cooler container of alcohol would weigh more.
This is because the cooler alcohol is more dense, so more alcohol molecules can fit in the same container.

This is true with freshwater too, up to a point. But at about 4 degrees Celsius (40 Fahrenheit), water reaches its densest point.
Amazingly, as water-cools further, it actually becomes less dense.

Water is different because of hydrogen bonding.

Water reaches its maximum density at 4°C (40°F).

As it cools further and freezes into ice, it actually becomes less dense.

On the other hand, most substances are most dense in their solid (frozen) state than in their liquid state.

A water molecule is made from one oxygen atom and two hydrogen atoms, strongly joined to each other with covalent bonds.

Water molecules are also attracted to each other by weaker chemical bonds (hydrogen bonds) between the positively charged hydrogen atoms and the negatively charged oxygen atoms of neighboring water molecules.

As water-cools below 4°C, the hydrogen bonds adjust to hold the negatively charged oxygen atoms apart.
This produces a crystal lattice, which is commonly known as 'ice'.

Greek scientist Archimedes gave the law of floatation of bodies.
According to this law, whenever a body is placed in water, it is acted upon by two forces—the weight of the body acting downwards and the buoyant force of water acting upwards.

If the weight of the body is equal to or less than the up-thrust of water, the body floats on water.

In other words, if the weight of the body is equal to or less than the weight of the water displaced by it, it will float on water.

On the other hand, if the weight of the body is more than the weight of the water displaced, the body will sink in water.

Hence, a body floats when its weight is equal to the weight of the water displaced.

A piece of wood floats on water, because its weight is less than the weight of the water displaced by it.
Since the weight of wood is nearly half of the weight of an equal volume of water, half of wood is under water, while the other half is above it.

Similarly, the weight of cork is nearly one-fifth of the weight of the water displaced by it, so approximately one-fifth of cork is under water while the rest remains above water.

We can understand the floatation of ice also on the basis of this law.

In general, when a liquid changes to solid, it contracts because its molecules come closer to each other.

Because of this, the volume of the substance decreases or its density increases.

Hence, a substance becomes heavier in ‘solid state than in the liquid, state.

But water is a peculiar liquid. When it becomes ice, instead of contracting, it expands. The volume of ice becomes more than that of the water.

The effect of the increase in the volume of ice is that its density becomes nine-tenth of water, that is, ice becomes lighter than water.

So we get about 10 liters of ice made out of 9 liters of water. And as you know, ‘liter’ is a measure of volume.

That is why nearly nine-tenth of ice is submerged in water, while only one-tenth is above water.

The ice under water (9/10 of the whole) displaces water whose weight equals that of the whole ice.

This law of floatation is derived from Archimedes principle.

This also explains how the maximum portion of the giant icebergs remains sub-merged in water while only a tip (1/10 part) is above water.

Bursting of water pipes in cold regions is due to the volume of ice being greater than that of water.

As soon as water freezes, the volume is increased which produces strong force due to which pipes burst?

In Finland, this property is utilized in breaking rocks.
Water is filled in empty spaces available between rocks.
When water freezes, it expands and, generates enough pressure to cause cracks in the rocks.

A substance floats if it is less dense, or has less mass per unit volume, than other components in a mixture.

For example, if you toss a handful of rocks into a bucket of water, the rocks, which are dense compared to the water, will sink.

The water, which is less dense than the rocks, will float.
Basically, the rocks push the water out of the way, or displace it.
For an object to be able to float, it has to displace a weight of fluid equal to its own weight.

This property of ice is very important since the top of a lake can freeze without sinking. If the ice sunk, then the entire lake would fill up with ice and all the fish would be frozen."

A hydrogen-filled balloon rises in air for precisely the same reason

The density of air is about 14 times that of hydrogen.

The total weight of a balloon consisting of fabric and hydrogen is thus much less than the weight of air it displaces.

The difference between the two represents the useful lifting power of the balloon.

A piece of solid steel sinks, but a ship made of steel floats.

Because a ship is hollow and contains air, its average density is less than that of water.


Take a spring balance, a piece of stone, a measuring cylinder and water. Measure the weight of stone in air by tying the string around in a loop, and hanging it from the spring balance. Take water in a measuring cylinder and note its volume level. Then dip the stone in the water while it is still hanging from the spring balance. You will see that the stone is weighing less!! If you see the water level now, you will see it has risen. Now from the volume of the water displaced, calculate the weight of water from the following equation for density:

Density of water = Mass of water [in gm] / Volume of water [in cubic cm]

A submarine has a large ballast tank, which is used to control its position and depth from the surface of the sea. A submarine floats in the sea because the buoyant force acting on the submarine is the same as the weight of the submarine. When water enters the ballast tank of a submarine, the weight of the submarine becomes greater than the buoyant force. Thus, the submarine dives into the sea. When compressed air forces water out of the submarine, its weight is less than the buoyant force. Thus, the submarine rises

The operation of a hot-air balloon or gas balloon is based on Archimedes’ principle. The air in the balloon is heated up by gas burner to over 100C.
The air expands and a large volume of air is displaced. Hot air has a lower density than the surrounding air.
When the buoyant force is greater than the weight of the balloon, the balloon starts rising up.

 As the height increases, the density of air decreases. Thus, the buoyant force will decrease. The balloon descends when the buoyant force is less than the weight of the balloon. It remains stationary in the air when the buoyant force is equal to the weight of the balloon. By varying the temperature of the air in the envelope, the balloon’s altitude can be controlled.

Ship –
Although a ship is constructed of metal, which is very heavy and hence has a greater density than water, but it can float in the sea. This is because the volume of the water displaced by the ship is sufficiently large to have a weight equal to the weight of the ship. A ship must displace more water to obtain sufficient buoyant force to support its weight. The shape of the ship is hollow so that the overall density of the ship is less than the sea water. As a result, the buoyant force acting on the ship is large enough to support its weight. Since the density of sea water varies with location the
line marked on the body of the ship act as a guide to ensure that a ship is loaded within safety limits. A ship will submerge deeper in the fresh water because the density of fresh water is less than sea water. A ship can also float higher in cold seasons because of the higher density of cold water.

A hydrometer is an instrument used to measure the relative density of liquids. It consists of a tube with a bulb at one end. Lead shots are placed in the bulb to weight it down and enable the hydrometer to float vertically in a liquid. In a liquid of lower density, a greater volume of liquid must be displaced for buoyant force to equal the weight of the hydrometer and so it sinks lower. However, the hydrometer floats higher in a liquid of higher density. On the basis of the above mentioned law of flotation, the scale on the stem can be calibrated to give readings for density in units of g cm-3.

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Friday, August 10, 2012

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General Knowledge Ice Float Water Archimedes' Law of Floatation 


virendra sharma August 10, 2012  

Very lucid explanation of A'S Pr and the laws of floatation . and a battery of related Qns.Thanks for excellent details their in .The scope of A'S Pr makes the article more meaningful .

MEcoy August 10, 2012  

that makes a lot of sense thanks for sharing

Anonymous,  August 10, 2012  

Very informative post- nice explanation of this phenomena of Ice floating.

Unknown August 28, 2013  

simple and well informative