Archimedes discovered the buoyancy principle, which is used in various applications, including ships. It allows them to float when the weight of the water displaced equals the weight of the ship. Anything shaped to displace its own weight of water before it reaches the point where it will submerge will surely float.
Today you’ll get to know the definition, applications, formula, derivation, experiments, example, and calculation of Archimedes principle.
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Let’s begin!
What is Archimedes’ Principle?
Archimedes’ principle deals with forces applied to an object by fluids surrounding it. This applied force reduces the net weight of the object submerged in a fluid. This principle can also be seen as the physical law of buoyancy, which helps us understand how ships float in water.
In other words, any object, totally or partially immersed in a fluid or liquid, is buoyed up by a force equal to the weight of the fluid displaced by the object. In this case, Archimedes’ principle allows the buoyancy of any floating object partially or fully immersed in a fluid to be calculated.
The downward force on the object is what we refer to as weight. The upward or buoyant force on the object is what Archimedes’ principle stated. So, the net force on the object is the difference between the magnitudes of the buoyant force and its weight.
If this net force is negative, the object surely sinks, and if positive, the object rises. If the object’s weight is zero, the object is neutrally buoyant; that is, it remains in place without either sinking or rising.
In simple terms, Archimedes’ principle states that when a body is completely or partially immersed in a fluid, it experiences an apparent loss in weight. This weight is equal to the weight of the fluid displaced by the immersed part of the body.
This principle can be stated as the upward buoyant force exerted on a body immersed in a fluid, whether partially or fully submerged, is equal to the weight of the fluid that the body displaces and acts in the upward direction at the center of mass of the displaced fluid.
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Applications of Archimedes Principle
Below is the application of Archimedes principle in various fields:
Submarine:
The applications of Archimedes in submarines are so common due to their relation with the sea. They were able to stay underwater because of a component called a ballast tank, which allows water to flow into it. This makes the submarine be in its position underwater, as the weight is greater than the buoyant force.
Hydrometer:
For the measurement of the relative density of liquids, a hydrometer is an instrument used. It is made of a lead shot that makes them float vertically on the liquid. When the hydrometer sinks lower, the density of the liquid will be less.
Hot-air balloon:
Hot-air balloons are able to float in mid-air because the buoyant force of the hot-air balloon is less than the surrounding air. So, the balloon will descend when the buoyant force is more. This is achieved by varying the quantity of hot air in the balloon.
The formula of Archimedes principle
Just as stated earlier, Archimedes law states that the buoyant force on an object is equal to the weight of the fluid displaced by the object. It is written mathematically as:
- Fb = ρ x g x V, where
- Fb is the buoyant force
- P is the density of a fluid
- V is the submerged volume
- g is the acceleration due to gravity.
Derivation of Archimedes principle
- The mass of the liquid displaced is.
- Mass = Density × Volume = ρ × V
- This is because density (ρ) is defined as
- Density, ρ = Mass/Volume = MV
- Thus, the weight of that displaced liquid is
- Weight = Mass × Acceleration due to gravity
- W = M × g = ρ × V × g
- Thus, from the Archimedes principle, we can write
- The apparent loss of weight = weight of water displaced = ρ×V×g
- Thus, the Thrust force is,
- Thrust = ρ × V × g
Where:
- ρ is the density of liquid
- V is the volume of liquid displaced
The thrust force is also known as a buoyant force because it is responsible for objects floating. Thus, this equation is also called the law of buoyancy.
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Solved Examples of Archimedes Principle
Q1. Calculate the resulting force if a steel ball of radius 6 cm is immersed in water.
- Ans: Given,
- Radius of steel ball = 6 cm = 0.06 m
- Volume of steel ball, V = 43πr³
- V = 43π(0.063)
- ∴V = 9.05 × 10 m³
- Density of water, ρ = 1000 kg.m⁻³
- Acceleration due to gravity, g = 9.8 m/s²-
- Formula from Archimedes principle
- Fb = ρ × g × V
- Fb = (1000 kg.m⁻³) (9.8 m.s⁻²) (9.05 × 10 m³)
- ∴ Fb = 8.87 N
Q2. Calculate the buoyant force if a floating body is 95% submerged in water. The density of water is 1000 kg.m-3.
Ans: Given,
- Density of water, p = 1000 kg.m-3
- formula from Archimedes principle
- Fb = ρ × g × V
or - Vb × ρb × g = ρ × g × V
Where:
- ρ,g, and V are the density, acceleration due to gravity, and volume of the water
- Vb, ρb, and g are the volume, density, and acceleration due to the gravity of the body immersed
- Rearranging the equation,
- ρb=VρVb
- Since 95% of the body is immersed,
- 0.95 × Vb = V
- ∴ρb = 950 kg.m-3
Conclusion
Archimedes’ principle deals with forces applied to an object by fluids surrounding it. This force applied reduces the net weight of the object submerged in a fluid. This principle can also be seen as the physical law of buoyancy, which helps us understand how ships float in water.