[Physics Class Notes] on Buoyancy Pdf for Exam

It is often observed that while swimming our body feels light or while taking out water from the well, the bucket feels lighter when it is partially or fully immersed in water. The reason behind this is that our body experiences forces from the downward direction or the opposite direction of the gravitational pull. This results in a decrease in weight. This is one of the reasons why the plastic balls float on the water instead of sinking in the water due to their weight.

The upward force exerted by a fluid opposes the weight of an object, immersed in the fluid. The pressure at the bottom of an object submerged in the fluid is always greater than at the top. The difference in the pressure of the fluid results in the net upward force on the object. This upward force is termed Buoyancy. It is necessary to understand density and relativity to completely understand the concept of Buoyancy.

The mass per unit volume of material is termed Density. The density is used to measure how tightly packed the matter is.

Density ρ = Mass/Volume=M/V

KG is the S.I unit or density, whereas, g is the C.G.S unit of density.

Relative Density: The ratio of the density of a substance to the ratio of the density of the water is termed the relative density or the specific gravity of a substance.

The relative density is measured as follows:

Relative Density = Density of a substance / Density of water

The relative density is the ratio of a substance having similar quantities; therefore, there is no unit for relative density.

Buoyancy is one of the main reasons why an object floats in water or fluid. The force exerted on fluid when an object is partly or fully immersed in the liquid can be termed Buoyancy. The differences in pressure on the opposite side of an object are the buoyant forces. 

Newton (N) is the unit used to describe the buoyant force.

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For example: When a body is in water some amount of water is displaced in the water due to its weight. This amount of water is determined based on the density of an object which is related to the volume as well.

The center of Buoyancy is the point where the force is applied to the object.

Buoyant Force/ Upthrust:

The upward force exerted by an object when an object is partly or fully immersed in a fluid is called the Buoyant Force. The buoyant force makes a body appear lighter when immersed in fluid partially or wholly.

An object tends to sink if the density of the object is greater than the density of the fluid it is submerged in. But if the density of the object is lower than the density of the liquid it is submerged in then the object will float. In other words, if the relative density of a substance is less than 1, the substance will float in water whereas, if the relative density of a substance is more than 1 then the substance will sink in the water.

The Buoyant Force Formula is as Follows:

Fbuoyant​ = ρVf​g

In this formula, pVg is the density of the displaced fluid multiplied by the volume of the displaced fluid. The density p -= m/V, therefore, m = pV. From this, we know that pVf is the mass of the displaced fluid.

We can also replace pVf with m.

Thus, Fbuoyant​ = mf​g

The buoyant force depends on two important factors:

1. The density of fluid it is placed in.

2. The volume of the body.

There are various applications of the buoyant force. Some of the applications are given below:

Submarine

The large ballast tank in the submarine is of great use to control its position and depth. The ballast tank allows the water to get into the submarine as it submerges in water and to make it weigh greater than the buoyant force.

Hot Air Balloon

The buoyant force is used to raise and float the hot air balloon. The air in the atmosphere exerts a buoyant force on the object. The hot air balloon descends when the weight of the balloon is greater than the buoyant force. It becomes stable when the buoyant force and the weight of the hot air balloon are the same.

Ship

The overall density of a ship is less than that of the sea, because of the hollow-like structure of the ship. The volume of the water displaced by the ship gives equal weight to the ship. The buoyant force is large to give support to the ship and make it float.

Fish

Most of the fishes use the Archimedes Principle to swim in the water. The fish go up and down in the water and fill its air sac or the swim bladder with gases. The gases diffuse from their body and make their body lighter in weight. This helps the fish to go up in the water.

Following are the Factors that Affect Buoyancy:

1. The volume of the fluid, the substance is placed in.

2. The density of the fluid.

3. Acceleration due to the gravitational force.

The mass of an immersed object and the density of an immersed object do not affect the buoyancy and the buoyant force. The overall depth of the object submerged does not affect the buoyant force. The deeper depth will not have any kind of effect on the buoyant force. The pressure at the top and bottom of the object will increase and decrease at the same rate when an object descends or ascends in the fluid. Therefore, the buoyant force remains unchanged even when the object goes deeper into the fluid. It is important to know the weight of the displaced fluid to find out the buoyant force of an object.

The buoyant force of an object = the weight of the fluid displaced by the object.

It is very essential to understand the buoyancy and the buoyant force to calculate and determine whether an object will sink or float when submerged in a fluid.

Example: A cubical shape large iceberg whose specific gravity is 0.9 is floating in the seawater. If the iceberg proportion above the sea level is 20 cm and the specific gravity of the seawater is 1.025, determine the volume of the iceberg.

Ans:

Let the side of the cubical iceberg be h.

The total volume of the iceberg =

The volume of the submerged portion is = (h -20) x

Now, For flotation, the weight of the iceberg = weight of the displaced water

The side of the iceberg is 164 cm.

Thus, the volume of the iceberg is 4.41

Answer: 4.41