The word Buoyancy is derived from a Spanish word known as “Boyar”, which means float. The property of a fluid to push the submerged object in the upward direction is called Buoyancy. It has the floating tendency when an object is placed in a fluid. Buoyancy results from the variations in pressure present on opposite sides of an object or body submerged in a static liquid. So this phenomenon of buoyancy is caused because of Buoyant force. Factors that affect Buoyancy in the fluid are,
- Density (P)
- Volume (V)
- Acceleration due to gravity (g)
At the point when an item is immersed in water or some other liquid, we see that the item encounters a force from the downward direction inverse to the gravitational pull, which is answerable for the diminishing in its weight. This upward or vertical force applied by the liquid goes against the weight of an item immersed in a liquid. As we probably are aware, the pressure in a liquid state raises with depth. Hence, the pressure at the lower part of an item immersed in the liquid is more prominent than that at the top. The distinction in this pressure brings about a net upward force on the item which we characterize as buoyancy. It is because of buoyancy that human swimmers, fish, boats, and icebergs stay above water.
Buoyant Force
The net upward force exerted up on a body partially or completely submerged in a fluid is called Buoyant Force. It is also known as Upthrust. Because of buoyant force, an object immersed fully or partially in a fluid appears to be lighter in weight (loses its weight). The unit used to describe the buoyant force is Newton(N) which is also the unit of force (F).
The pressure applied by the liquid in which an object is submerged causes buoyancy. Additionally, the buoyant force experienced by the item is in every case upwards due to the pressure of the liquid increasing with the level of depth. Few applications in which buoyant force is applicable are Freight transport, Marine designing (eg. ships)
Buoyant force formula
As we know that density, volume, and the descending force, for example, gravity impact the buoyant force directly, utilizing this number of elements, the general formula of the buoyant force is derived by,
Buoyant force (Fb) = V × p × g
Where; V - Volume of the fluid
p- Density of the fluid
g - acceleration due to gravity
This formula gives the buoyant force of the liquid medium applied to the item following the Archimedes principle.
Archimedes Principle
It states that the upward buoyant force that is applied on an object submerged in a liquid, whether to some extent or completely lowered, is equivalent to the weight of the liquid that the object uproots and acts in the upward direction at the center of mass of the uprooted liquid.
Difference between Buoyancy and Buoyant force
|
Buoyancy is defined as the tendency of an object submerged in liquid to float. | It is the net upward force exerted up on a body partially or completely submerged in a fluid. |
| The Phenomenon of Buoyancy is caused because of Buoyant force. | It is also known as Upthrust. |
| It is caused due to the pressure applied by the liquid in which an object is submerged. | It is caused due to the pressure of the liquid increases with the level of depth. |
| It is a tendency of an object immersed in the fluid. | It is an upward acting force. |
| The main factor of buoyancy is the density of the fluid | The main factor of the buoyant force is the weight of an object. |
| Buoyancy is also affected by the Volume of the fluid displaced and Acceleration due to gravity. | It is not affected by the mass and density of the submerged object. |
| Pressure is low or nil | A created pressure at the lower bottom of an immersed object. |
| It doesn't have any upward force. | It always acts in an upward direction. |
| Buoyancy doesn't act against the weight of a body immersed in the fluid. | It acts against the weight of a body immersed in the fluid. |
Applications of Buoyancy are: - Submarines
- Hydrometers- To measure specific gravity
- To measure the density of the solids and liquids
| Applications of Buoyant force: - Marine designing
- Freight shipping
- In boats and huge ships
|
A few examples of buoyancy are: - Human Swimmers
- Icebergs
- Floating cork or a Leaf
| A few examples of buoyant force are: - Hot Air Balloon
- Cruise ships, Naval aircraft carriers
- Fish
|
Sample Problems
Question 1: What is the buoyant force of a block of wood placed in the water with dimensions of length = 3.5 m, width = 0.6 m, and height = 0.5 m? The density of water is 1000 kg/m3 and Acceleration due to gravity is 10 N/kg.
Solution:
From given information,
Volume of the block (V) = length × width × height = 3.5 × 0.6 × 0.5 = 1.05 m3
Density of water (ρ) = 1000 kg/m3
gravity (g) = 10 N/kg
Therefore buoyant is calculated as:
Formula of buoyant force
Fb = ρ g V
Fb is buoyant force, ρ is density of water, g is acceleration due to gravity and V is volume
Fb = (1000)×(10)×(1.05) = (1000)×(10.5) = 10500 Newton
Question 2: Calculate the density of an unknown material if a block of unknown material weighs 73 newtons in air and 52 newtons when submerged in water? The density of water is 1000 kg/m3
Solution:
Let's consider the block with unknown density pb.
In air,
Fair = pb V g
When the block is fully submerged in water then calculated weight reduces because of buoyant force,
F water=pb V g - F buoyant
Here buoyant force is,
F buoyant = p V g
Since the block is fully immersed, lets arrange second equation,
F water + p V g = pb V g
Now calculating Volume in first equation,
V= Fair / pb g
Hence,
(Fwater + Fair) × p/pb = Fair
Solving density,
pb = Fair / ( Fair - F water ) × p
Now with the numeric values,
pb = 73 N / (73 N - 52 N) × 1000 kg/m3 = 3476.19 kg/m3.
Therefore the density of the material identified is 3476.19 kg/m3
Question 3: What will be the buoyant force, for a floating body of 85% submerged in water? The water density is 1000 kg.m3.
Solution:
Given,
Density of water, p = 1000 kg.m3
According to Archimedes' principle formula,
Fb = ρ × g × V
or on the other hand
ρ × g × V = Vb × ρb × g
Where,
ρ, g, and V are the density, speed increase because of gravity, and volume of the water
Vb, ρb, and g are the volume, density and speed increase because of gravity of body immersed.
Pb= V / p × Vb
Since 85% of the body is submerged,
0.85 × Vb = V
∴ρb = 850 kg.m3
Question 4: What is the buoyant force of a steel ball of a radius of 5 cm submerged in water? Assuming acceleration due to gravity is 9.8 m.s2 and density of water is 1000 kg.m3
Solution:
Radius of steel ball is 5 cm = 0.05 m
Volume of steel ball, V = 4/3πr3
V = 4/3π × 0.053
Value of pie = 3.14
∴V = 1.33 × 3.14 × 0.000125
Density of water ρ = 1000 kg. m3
Acceleration due to gravity, g = 9.8 m. s2
From Archimedes’ principle formula,
Fb = ρ × g × V
Fb = 1000 kg.m3 × 9.8 m.s2 × (1.33 × 3.14 × 0.000125)
∴Fb = 5.11 N
Question 5: An object of mass 130 kg and density 700kg/m3 floats in water. How much additional mass needs to be added to the object to avoid sinking from below the given options?
(a) 15 kg (b) 55 kg (c) 95 kg (d) 100 kg
Answer:
Let's assume the maximum mass be 'm' which needs to be added to the object to stop sinking:
As we know,
Weight of water (displaced) = Weight of object + maximum mass to be added
pw V g = m × g
pw V = m
pw V = 130 + m
pw = 1000 kg.m3
V = 130 / 700 = 0.185 m3
Presenting the values we get:
1000 × 0.185 = 130 + m
m = 185 - 130 = 55 kg
Hence if we add 55 kg mass or above to the object it will start sinking.
Therefore by adding 15 kg to the object it will float.
Question 6: If a cylinder of mass 20g weights 14g in water and if the area of cross-section is 0.65 square cm, what would be the length?
Solution:
Given area of cross section is 0.65cm2
L = ?
When weight of solid is fully immersed in water then the formula derived is,
V( ps - pw )g = Weight calculated in water
Here p is density ( s indicates solid, w is water) and V is volume.
Buoyant force is V pw g - (weight calculated in water)
V pw g = ( 20- 14) g
As V ps g weight calculated in air given as 20g
As we know pw= 1,
V= 6 cm3
Therefore the length can be calculated by dividing volume with cross-section
L = 6 / 0.65
Hence the length L= 9.23 cm.
Question 7: If a ball of mass 20 kg and volume 0.4m3 is submerged in water, what is the net force on the ball? Where g = 10 m/s2 and density of water 1.0 g/ml
Answer:
Given mass m = 20 kg
Volume V = 0.4 m3
g= 10 m/s2
p water = 1000 kg/m3
The weight of water displaced by ball is simply the buoyant force:
Fb = V ball × p water × g
= 0.4 × 1000 kg/m3 × 10 m/s2
= 4000 N
Now force of gravity on ball is,
Fg = m × g = 20 × 10 = 200 N
Since these forces are opposed each other we can now say,
Fnet = Fb - Fg
= 4000N - 200N
Therefore Fnet = 3800 N
Frequently Asked Questions
Question 1: What is the significance of buoyant force in swimming?
Answer:
Buoyancy is significant in swimming since it assists the swimmer to stay nearer to the surface. This is on the grounds that the pressure experienced by the swimmer under the water is more than the pressure experienced above. This is additionally the justification for why swimmers can float on the outer layer of the water.
Question 2: What are the various types of buoyancy?
Answer:
The three kinds of buoyancy are Neutral, positive, negative buoyancy,
- Positive buoyancy is the point at which the submerged object is lighter than the liquid uprooted and this is the reason behind why the item floats.
- Negative buoyancy is the point at which the drenched object is denser than the liquid uprooted which brings about the sinking of the item.
- Neutral buoyancy happens when the weight of submerged object is equivalent to the liquid uprooted. Sea diving by the scuba diver is an optimal model for neutral buoyancy.
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