Contents
Physics Topics are often described using mathematical equations, making them precise and quantifiable.
Applications of Principle of Flotation
Why Objects Float Or Sink In A Liquid
When a piece of wood is placed in water, it floats but when a piece of iron is put in the same water, it sinks to the bottom. We will now discuss why some objects float and others sink in the same liquid. When an object is put in a liquid, then two forces act on it:
- Weight of the object acting downwards (which tends to pull down the object), and
- Buoyant force (or upthrust) acting upwards (which tends to push up the object).
Now, whether an object will float or sink in a liquid will depend on the relative magnitudes of these two forces (weight and buoyant force) acting on the object in opposite directions. Three cases arise :
(a) If the buoyant force (or upthrust) exerted by the liquid is less than the weight of the object, the object will sink in the liquid.
(b) If the buoyant force (or upthrust) exerted by the liquid is equal to the weight of the object, then the object will float in the liquid.
(c) If the buoyant force (or upthrust) exerted by the liquid is more than the weight of the object, the
object will rise in the liquid and then float.
From the above discussion we conclude that an object will float in a liquid if the upward buoyant force it receives from the liquid is great enough to overcome the downward force of its weight. We will now discuss the principle of flotation of objects (or bodies).
The Principle of Flotation
When the weight of an object acting downwards is equal to the upward buoyant force exerted by the liquid, the buoyant force will balance the weight of object due to which the object will float in the liquid. So, for an object to float in a liquid, the weight of object should be equal to buoyant force acting on it (see Figure 60). But by Archimedes’ principle, the buoyant force acting on an object is equal to the weight of liquid displaced by it. So, we can say that the condition for an object to float in a liquid is that the weight of object should be equal to the weight of liquid displaced by it. This condition gives us the principle of flotation which can be stated as follows.
According to the principle of flotation : An object will float in a liquid if the weight of object is equal to the weight of liquid displaced by it. That is, for flotation :
Weight of object = Weight of liquid displaced by it
A floating object may be partly or totally submerged in the liquid. The liquid is displaced by that portion of the object which is submerged under liquid.
How Does a Boat Float in Water
A boat is kept afloat by an upward force from the water. This upward force is called buoyant force (or upthrust) and it is caused by the pressure of water ‘pushing up’ on the bottom of the boat. When a boat is gradually lowered into water (in a river or sea), it displaces more and more water due to which the upward ‘buoyant force’ on it increases. The boat stops sinking down into water when the buoyant force acting on it
is just enough to support the weight of boat (see Figure). Now, Archimedes’ principle says that the buoyant force is equal to the weight of liquid displaced by the boat. So, when a boat is floating, the weight of water displaced by the submerged part of the boat is equal to the weight of the boat.
As more and more people get into the boat, the boat becomes lower and lower in water. When the boat becomes lower in water, it displaces more water. Due to greater weight of water displaced, the buoyant force on the boat increases. And this greater buoyant force enables the extra weight of the people in the boat to be supported. If, however, the water level reaches the upper edge of boat, no further increase in buoyant force is possible because the boat cannot displace any more water. If any more people get into the boat in this condition, the boat will sink.
The Density of Floating Objects
We have just learnt that for an object to float in a liquid, the weight of liquid displaced by it should be equal to its own weight. This can happen if the object has a lower density (or lower average density) than the liquid. If, however, the object has a higher density than the liquid, then the weight of liquid displaced will be less than the weight of the object and the object will not float, it will sink.
We can tell whether an object will float (or sink) in a liquid by comparing its density (or average density) with that of the liquid.
1. An object will float in a liquid if its density (or average density) is less than that of the liquid (see Figure). This point will become more clear from the following examples :
- The density of cork is less than that of water, so cork floats in water.
- The density of wood is less than that of water, therefore, wood floats in water.
- The density of ice is less than that of water, so ice floats in water.
- The density of glass is less than that of mercury, so a piece of glass floats in mercury.
- The density of iron is less than that of mercury, therefore, a nail of iron floats in mercury.
Please note that if the density of an object is less than that of the liquid, then the object floats in the liquid in such a way that a portion of the object is inside the liquid (or submerged in the liquid) and the remaining portion is above the surface of liquid (as shown in Figure).
2. An object will also float in a liquid if its density is equal to that of the liquid (see Figure). For example, tar has the same density as water, so tar just floats in water. Please note that when the density of an object is equal to that of the liquid, then the object floats in the liquid in such a way that all of it remains submerged in water (as shown in Figure). No part of it remains above the surface of water.
3. An object will sink in a liquid if its density is more than that of the liquid (see Figure). This point will become more clear from the following examples :
- Iron (or steel) has more density than water, so a nail of iron (or steel) will sink in water. This is why when a nail of iron (or steel) is placed on the surface of water in a trough, it immediately sinks to the bottom.
- Glass has more density than water, so a piece of glass will sink in water.
- Aluminium as well as gold have higher densities than water, therefore, a solid piece of aluminium or of gold will sink in water.
- Mercury is a liquid metal having higher density than water, so mercury also sinks in water.
Why Ships Float
When we put a piece of iron in water, it sinks immediately because iron is denser than water. Why should then ships made from iron and steel float in water ? This can be explained on the basis of ‘average density’ as follows.
Ship is not a solid block of iron and steel. A ship is a hollow object made of iron and steel which contains a lot of air in it. Air has a very low density. Due to the presence of a lot of air in it, the average density of the ship becomes less than the density of water. And since the average density of ship is less than that of water, therefore, a ship floats in water. Thus, a ship made of iron and steel floats in water because its average density is less than that of water (due to the presence of a lot of air space in it). In fact, all the hollow objects made of dense materials (like metals) float in water because due to the presence
of a lot of air in them, their average density becomes less than the density of water. The floating of ships can also be explained in another way as follows.
When a ship is placed in water it sinks to a certain level such that the weight of water displaced by its submerged portion is equal to the whole weight of the ship. Since the ship fulfils this condition of flotation, it floats in water. Thus, a heavy ship floats because it displaces a large weight of water (which provides a great buoyant force to keep it afloat).