Hot air displaces a balloon, producing upthrust. This upthrust is balanced by the weight of the balloon.
The balloon displaces a volume of air equal to its own volume. The air displaced is heavier than the air in the balloon as hot air is lighter than the cold air of same volume.
As the upthrust produced is the same as the weight of the air displaced, the force of the upthrust is greater than the weight of the balloon. Thus, the balloons keep rising till the upthrust is equal to the weight of the balloon acting downwards.
Objects like cork, wood etc. float while stones etc., sink when placed in water.
An object will float if the buoyant force of water is greater than the weight of the object itself.
Density of objects which float in water is less than the density of water.
On the other hand, when the buoyant force is less than the weight of the object, the object will sink. It will be noticed that if such objects are weighed while they are submerged in water the weight will be less than their actual weight. Density of these objects is more than the density of water.
Block A is floating: The upthrust of the water must be balancing the weight of the block. So the weight of the water displaced must be equal to the weight of the block.
Not whole of the block is under water. The volume of water displaced is less than the volume of the block. But the weight of the water displaced equals the weight of the block. So equal volumes of block and water cannot weigh the same. The block would be lighter. We say that the density of the block is less than the density of water.
Block B is just floating: The upthrust of the water must be just balancing the weight of the block. So the weight of the water displaced must be equal to the weight of the block.
All of the block is under water. The volume of water displaced is the same as the volume of the block. So both weight and volume, of the block and the displaced water are equal. The density of the block and the water are the same.
Block C has sunk: The upthrust from the water is not enough to make the block float. So the weight of the displaced water must be less than the weight of the block.
So equal volumes of water and the block do not weigh the same. The block is denser than water.
Activity :
Way of Experiencing More Upthrust
In the first case, when the can is pushed into water it has to displace less volume of water and experiences less upthrust. This is because the water is displaced by the curved surface of the cylindrical part of the can.
In the second case, when the can is pushed we experience more upthrust because the can has to displace a larger volume of water.Behaviour of Floating Objects
Let us place blocks of different kinds of low density material in water as shown in figure below. Each block is 20 cm x 10 cm x 5 cm. Thus, the volume of each block is 1000 cm3. The densities and weights of these blocks is mentioned below:
| Block | Destiny | Weight |
|---|---|---|
| A | 0.2 g/cm3 | 200 g |
| B | 0.4 g/cm3 | 400 g |
| C | 0.6 g/cm3 | 600 g |
The fractional part of these materials which is submerged in water is numerically equal to their density in grams per cubic centimeter.
As they float, some sink deeper than the others. Blocks which sink more displace more water than those that sink less.
When the heights of the blocks above and under the surface of water are measured, and volume of the blocks under water is calculated we get the following data:
| Block | Height above water | Height under water | Volume of the sub merged block |
|---|---|---|---|
| A | 4 cm | 1 cm | 200 cm3 |
| B | 3 cm | 2 cm | 400 cm3 |
| C | 2 cm | 2 cm | 600 cm3 |
Though the third column represents the volume of the submerged part of the block it also indirectly represents the volume of the water displaced by the submerged part of the block, i.e., the volume of the liquid displaced equals the volume of the block under the liquid surface.
In each case, as density of water is 1 g cm-3, you will notice that if the weight of water of the volume equal to the volume of the submerged part is calculated (the third column) it is equal to the weight of the respective block.
For example, the volume of the submerged part in case of block A is 200 cm3. Weight of 200 cm3 of water is equal to 200 g. This is the same as the weight of the block A. In case of the other blocks also we find the same thing.
When an object floats in water, or in any other liquid, the weight of the water, or the liquid, displaced by the submerged part of the object is equal to the weight of the object.
In case of ice, its density is 0.95 g/cm3. Thus in colder countries where there are icebergs in oceans, only about one-tenth of the ice is seen above water and the remaining nine-tenths remain submerged. Hence, there is danger of these icebergs to the ships sailing in these oceans.
Suppose we lower the block B into kerosene, which has a density of 0.8 gcm-3. It will sink deeper into the kerosene than in water because it displaces an amount of liquid equal to its own weight.
Weight of block is 400 g.
Therefore, weight of the kerosene that must be displaced by block B = 400 g.
Now density d of a substance is given by the following formula:
Therefore, W = d x V
Here,
400 g = 0.8 x V
= 500 cm3
Thus, volume of kerosene that must be displaced = 500 cm3
Now, the base area of the block is 20 x 10 = 200 cm3
Hence, the height of the submerged part of the block
= 2.5 cm
In case of water only 2 cm of the block was under water. In case of kerosene, it is 2.5 cm under water. In liquids which are less dense, the block submerges more and the liquids which are more dense, the block submerges less.
For liquids which are denser than water the case would be opposite. Thus, in a very dense liquid like mercury the blocks of aluminium, iron and lead will float.
The depth to which a metal sinks in mercury depends on the ratio of its density to that of mercury.
The fractional part submerged equals the ratio of the density of the material of the block to the density of the liquid, i.e.,
