 ## Law of Flotation

Subject: Science

#### Overview

The body is immersed in a liquid when the two forces should act. The two forces are: the weight of the body acting vertically downward, and the upthrust on the body acting vertically upward. Depending on these two forces, there arise three cases. First, a body sinks in a liquid only if the density of the body (d1) is greater than the density of the liquid (d2) in which a body is kept. Second, a body just floats on a liquid when the density of the body (d1) is equal to the density of the liquid (d2) in which the body is kept. Third, a body floats keeping some parts of it out when its density (d1) is lesser than that of the liquid (d2) in which it is kept.

##### Law of Flotation

Law of Flotation

When a body is allowed to immerse in a liquid, the following forces act on it:

1. The weight of the body acting vertically downward and
2. The upthrust on the body acting vertically upward.

Depending on the magnitude of these forces, the following three cases can be studied:

Case I: When the weight of the body is greater than the upthrust acting on it, the resultant force will be vertically downwards. As a result, the body gets sunk in the liquid.

Mathematically,

weight of the body (w1) ˃ weight of the liquid displaced

or, m1g ˃ m2g [$\because$ w = m × g]

or, m1 ˃ m2

or, d1v1 ˃ d2v2 [$\because$ d = $\frac{m}{v}$ or m = d × v]

$\therefore$ d1 ˃ d2 [$\because$ v1 = v2] Thus, a body sinks in a liquid only if the density of the body (d1) is greater than the density of the liquid (d2) in which the body is kept. Due to this reason, a piece of iron, being denser than water, sinks completely in water.

Case II: When the weight of the body is just equal to the upthrust acting on it, the resultant force acting on it is zero. As a result, the body floats in the liquid.

Mathematically,

W1 = w2

or, m1g = m2g

or, m1 = m2 [$\because$ w = m × g]

or,  d1v1 = d2v2 [d = $\frac {m}{v}$ or m = d × v]

Since, the volume of body (v1) is equal to the volume of displaced liquid (v2) i.e., v1 = v2, d1 is also equal to d2.

$\therefore$ d1 = d2

Thus, a body just floats on a liquid when the density of the body (d1) is equal to the density of the liquid (d2) in which the body is kept.

Case III: When the weight of the body is less than the upthrust acting on it, the resultant force will be directed vertically upwards. As a result, a body will come at rest with its some part in air and some part in water. In this case, the weight of the body will be equal to the weight of the liquid displaced by the immersed portion of the body.

Mathematically,

Weight of the body (w1) = weight of the liquid displaced (w2)

or, m1g = m2g [$\because$ w = m × g]

or, m1 = m2

or, d1v1 ˂ d2v2 [$\because$ d = $\frac {m}{v}$ or m = d × v]

Since the body is partially immersed in the liquid, the volume of the body ˃ the volume of the liquid displaced i.e. v1 ˃ v2 and hence we have, d1 ˂ d2.

$\therefore$ d1 ˂ d2

Thus, when the density of the body (d1) is lesser than that of the liquid (d2), a body floats keeping some of its parts out from the liquid.

From the above discussion, we can conclude that:

A body sinks in a liquid if the density of the body is greater than that of the liquid. In this case, the weight of liquid displaced is lesser than the weight of the body. But, if we shape the body in such a way that the weight of the body is equal to the weight of the liquid displaced by the body, it floats on the liquid. For example: a floating ship.

The law of floatation states that “weight of a floating body is equal to the weight of the fluid displaced by the body”.

i.e. weight of floating body (w1) = weight of the displaced fluid (w2)

Experimental Verification of Law of Floatation

Verification:

Materials Needed:

• Eureka can
• Beaker
• Top Pan Balance
• Dry Wooden Block
• Water
• Tripod Stand

Process:

1. An overflow can is kept over a top pan balance.
2. The can is filled with water up to its spout and an empty beaker is kept below the spout of the can.
3. The weight of water with overflow can [Eureka can] is noted.
4. Now, a dry wooden block is kept in the water of the can.

Conclusion:

The water is displaced into the beaker but the top pan balance does not show any change. It proves that the weight of the displaced water is equal to the weight of the block. It verifies the law of floatation.

##### Things to remember
1. Law of floatation is a special condition of Archimedes’ Principle which states that the weight of a floating body is equal to the weight of the displaced liquid.
e. weight of floating body = weight of displaced fluid
2. A body sinks in a liquid only if the density of the body is greater than the density of the liquid in which the body is kept.
3. A body floats on a liquid when the density of the body is equal to the density of the liquid in which the body is kept.
4. A body floats keeping some part of it out when its density is lesser than that of the liquid.

• It includes every relationship which established among the people.
• There can be more than one community in a society. Community smaller than society.
• It is a network of social relationships which cannot see or touched.
• common interests and common objectives are not necessary for society.
##### Videos for Law of Flotation ##### Float or Sink : Why do things float? Why do things sink - Lesson for kids ##### Science 2074 02 23 Laws of flotation ##### Science 2074 02 23 Laws of flotation

Verification:

Materials Needed:

• Eureka can
• Beaker
• Top Pan Balance
• Dry Wooden Block
• Water
• Tripod Stand

Process:

1. An overflow can is kept over a top pan balance.
2. The can is filled with water up to its spout and an empty beaker is kept below the spout of the can.
3. The weight of water with overflow can [Eureka can] is noted.
4. Now, a dry wooden block is kept in the water of the can.

Conclusion:

The water is displaced into the beaker but the top pan balance does not show any change. It proves that the weight of the displaced water is equal to the weight of the block. It verifies the law of floatation.

Law of flotation is a special condition of Archimedes' principle which states that the weight of a floating body is equal to the weight of the displaced body, i.e. weight of floating body = weight of displaced fluid.