Floatation | Archimedes’ Principle & Buoyancy

Pressure and Fluids

All liquids and gases are called as fluids. A solid exerts pressure on a surface due to its weight.

Similarly, fluids have weight, and they also exert pressure on the base and walls of the container in which they are enclosed. A fluid exerts pressure in all directions even upwards.

Buoyancy

To understand the term Buoyancy let us perform and activity.

Take an empty plastic bottle. Close the mouth of the bottle with an air tight stopper. Put it is a bucket filled with water.

· We will see that the bottle floats.

· Now push the bottle into the water. We will feel an upward push. If we push it further down, we will find it difficult to push deeper and deeper.

· This indicates that water exerts a force on the bottle in the upward direction.

· This upward force exerted by the water goes on increasing as the bottle is pushed deeper till it is completely immersed.

· If we release the bottle, it bounces back to the surface.

Explanation

The force due to the gravitational attraction of the earth acts on the bottle in the downward direction. So the bottle is pulled downwards. But the water exerts an upward force on the bottle. Thus, the bottle is pushed upwards.

The weight of an object is the force due to gravitational attraction of the earth. When the bottle is immersed, the upward force exerted y the water on the bottle is greater than its weight therefore it rises up when released.

To keep the bottle completely immerse the upward force on the bottle due to water must be balanced. This can be achieved by an externally applied force acting downwards. This force must at least be equal to the difference the upwards force and the weight of the bottle.

The upward force acting on an object immersed in a liquid Buoyant force or upthrust.

Factors affecting Buoyant force

The magnitude of buoyant force acting on an object immersed in a liquid depends on two factors.

(i) volume of object immersed in the liquid.

(ii) density of the liquid.

The buoyant force exerted by a liquid depends on the vol. Of the solid object immersed in the liquid. As the volume of solid object immersed inside the liquid increases, the upward buoyant force also increases. And when the object is completely immersed in the liquid, the buoyant force becomes the maximum and remain constant. Also, the magnitude of buoyant force acting in a solid object does not depend on the nature of the solid object.

It depends only on its volume. For e.g. If two balls made of different metals having different weights but equal volumes are fully immersed is a liquid, they will experience an equal upward ‘buoyant force’ i.e. equal loss in weight.

The buoyant force exerted by a liquid depends on the density of the liquid in which the object is immersed. As the density of liquid increases, the buoyant force exerted by it also increases, for e.g. Sea water has higher density then fresh water therefore sea water will exert more buoyant force on an object immersed in it than the fresh water. Therefore it is easier to swim is sea water because sea water exerts a greater buoyant force on the swimmer due to its higher density.

Even a very heavy material like an iron block floats in mercury because mercury exerts a very high buoyant force on iron block due it its very high density.

Archimede’s principle

Introduction:

Archimedes was a greek scientist. He discovered the principle, subsequently named after him, after noticing that the water in a both tub overflowed when he stepped into it. He raw through the streets shoaling “Eureka”! which means “I have got it”. This knowledge helped him to determine the purity of the gold in the crown made for the king. This work in the field of Geometry and Mechanics made him famous. His understanding of levers, pulleys, wheels – axle helped the greek army is its war with roman army.

“Archimedes’ principle states that when a body is partially or wholly immersed is a liquid, it experiences an upward force that is equal to the weight of the fluid displaced by it.

Activity of understand Archimede’s Principle

(a) Take a piece of stone and tie it to one end of a rubber string or a spring balance.

(b) Suspend the stone by holding the balance or the string as shown in figure.

(d) Now slowly dip the stone in the water is a container. You will find that the elongation of the string or the reading of the balance decreases as the stone is gradually lowered is the water.

(e) However no further change is observed once the stone gets fully immersed is the water.

Explanation:

The elongation is produced is the string or the spring balance due to the weight of the stone. Since the extension decreases once the stone is lowered is water, it weans that same force acts on the stone in upward direction. As a result, the net force on the string decreases and hence the elongation also decreases. This upward force exerted by water is known as the force of buoyancy.

Add figure 10.6 (N.C.E.R.T)

Applications of Archimede’s Principle

(a) Archemede’s principle is used in determing the relative density of a substance.

(b) The hydrometers used for determing the density of liquids are baded on Archimede’s principle.

(d) Archimede’s principle is used is designing ships and submarines.

Why objects float or sink is a liquid

Then an object is put is a liquid, then two forces act on it.

Weight of the object acting downwards due to the gravitational pull of the earth on the object.

Buoyant force acting upwards which tends to push up the object.

Sinking of an object in Water

If we place an Iron nail on the surface of water in a beaker then the nail sinks. The force due to the gravitational attraction of the earth on the iron nail pulls it downwards. There is an upthrust of water on the nail, which pushes it upwards. But the downward force acting on the nail is greater than the upthrest of water on the nail, so it sinks.

An object will sink is a liquid if its density is more than that of the liquid.

Floating of an object in Water

If we place a piece of cork on the surface of water in a beaker than the cork floats. This happens because of the difference is their densities. The density of a cork is less than the density of water. This means that the upthrust of water on the cork is greater than the weight of the cork. So it floats.

Therefore objects of density less than that of a liquid float on the liquid. The objects of density greater than that of a liquid sink in the liquid.

Question: When an aluminim object is immersed in water it displaces 5 kg of water. How much is the buoyant force acting on the aluminim object is Newtons? $\displaystyle (g=10\,\mathbf{m/}{{\mathbf{s}}^{\mathbf{2}}})$

Solution: According to Archimede’s principle the buoyant force acting on the aluminim object will be equal to the weight of water displaced by this aluminim object.

Now, $\displaystyle W=m\times g$