What is Archimedes’ Principle?
The ancient Greek mathematician Archimedes brought a revolutionary concept of force shown by fluids. Archimedes’ principle notes the behavior of solids on fluids and states that the objects are either drifted or drowned by the fluid. According to him, fluids have their own kind of force in any objects. There are certain criteria to be floated or sunk. The objects having their density less than that of the fluid are sure to get floated and conversely those objects with greater density cannot be pushed upward by the fluid and hence they are drowned. This pushing force to the lifeline is termed as upthrust. So, the question arises “what happens to those having equal densities with that of the fluid?’. The answer is that they also keep floating, being submerged in the fluid. Buoyant force comes into action for fully submerging or partially submerged objects.
Now, we have to concentrate on the floating or sinking property and what other interesting facts lie besides those mechanisms. Of course, another factor arising here is the volume of fluid.Thus, Archimedes’ principle not only gives the mechanisms of fluid dynamics but also shows how nature keeps everything balanced.
Archimedes’ Principle Formula Explained (FB = ρ×g× V)
The upthrust force able to carry an object upward is given name as buoyant force and hence calculated as:
FB = ρ × g × V [Equation 1]
Where:
- FB = Buoyant force
- ρ = Density of the fluid
- g = Acceleration due to gravity
- V = Volume of the fluid displaced
Thus, the same object can show varied floating nature within different fluids of no same densities.
Blaise Archimedes and the Golden Crown Story
It is just to clarify that Blaise and Archimedes are not the same and Blaise Pascal is known for the Pascal’s law. So, it would be a huge mistake to call Blaise Archimedes.
Archimedes’ Principle is beautifully illustrated by the popular story of the golden crown. According to some tales, King Hiero II once asked Archimedes to figure out how it would behave if a pure 24 carat gold crown was impacted by silver. He also restricted any harm to the ground. Archimedes went for critical solutions. One instance when he submerged himself in the bathtub, his eyes kept fixating on the water driven out of the tub. It was the same moment he developed the theory for submerging objects. Watching displaced volume he thought of dipping the crown for two different cases and reasoning the King’s question. Folks say that he shouted “Eureka!” on the excitement of a discovery.
How Buoyancy Depends on Density and Displaced Volume
The property of buoyancy is stuck in two factors: density and the displaced volume.
- Density of the Fluid: As stated by equation [1], FB ∝ ⍴. Thus, the upward force will not be enough to push the higher density objects than that of it.
- Volume of Displaced Fluid: Another fact is that, the more volume of liquid displaced can also keep an object floating (FB ∝ V). This reveals that a heavier object can also enjoy drifting on water by displacing greater volume.
Floating vs. Sinking: Applying the Principle to Everyday Objects
We all are familiar with the terms floatation and sinking thanks to Archimedes’ principle. Some applications from daily circumstances to advanced activities are given below:
- Kitchen chores: We all have vegetables cooked in the kitchen. Before cooking we may have cut them and submerged them in water for cleaning. Thus, the dirt sinks in water which we spill out, picking the vegetables on top.
- Plastic bottle: A plastic bottle when placed in water with cap-closed, it floats. However an open-cap bottle drinks plenty of water raising its density and gets sunk.
- Ships: Ships through their internal designs of the base can displace more volume of water and hence float on it.
- Piece of Foam: As it is spongy, the wet foam is soaked and becomes dense so it sinks in water. However, a well dried piece floats due to its less density.
- Wooden log Vs a coin: Although being of large density, wooden log due to its large surface, expels more volume of water enough to float but the coin having high material density and smaller size, cannot displace enough water and goes down.
Applications of Archimedes’ Principle
- Icebergs and Glacial Floating: About 90% of icebergs float below the surface, and 10% do so above due to their density difference.
- Naval Engineering: Engineers design all the watercrafts, submarines and also airships with every safety step to ensure a smooth and lively float on water. Buoyancy control of submarines is also based on the same principle which the ballast tanks use to rise and go deep down.
- Floating Dry Docks: Giant docks are swooped in water and submerged to carry out a drowned ship to make it rise back and lift for repair.
- Measuring Volume of Irregular Objects and Comparing Density: The density comparison and purity testing can also be made based on the principle.
- Oil Spill Cleanup: Devices can be engineered to float and skim off oil, which is less dense than water.
- Scuba Diving: Scuba divers put on buoyancy tracking devices, or BCDs to change their depth. They have the ability to control how much they sink, float, or stay still by adjusting the amount of water they displace via inflating or deflating the jacket.
- Archaeology and Geology: In archeology or study of the rocks, Archimedes’ principle helps to research on the composition and porosity of the geological objects by putting it on water.
Using Archimedes’ Principle to Measure Density and Specific Gravity
Archimedes’ principle notes every drop of expelled fluid measures it and beautifully interprets the submerging body. By measuring the volume of displaced fluid and a measuring balance to obtain the mass, one can easily calculate the density of an unknown object.
Similarly, as the density of the substance can be obtained easily by the above procedure, we can now measure the density of water at 4°C and their ratio which will provide us with the specific gravity.
Hydrometers, Spring Balances, and Other Buoyancy Experiments
Hydrometers made up of low dense materials can float in liquids and reveal the unknown density or specific gravity of the liquid. Two different density liquids can be brought up for the test. The hydrometer dipped goes a little lower and floats which can speak the two differing densities.
One can take weight measurement at two different instances using spring balance and calculate the differentials. This helps to calculate the buoyant force with the help of actual weight measured in air and the apparent weight seen in the liquid and their ratio taken gives the specific gravity. These experiments are straightforward to demonstrate and very effective to grasp Archimedes’ Principle.
Limitations and Assumptions of Archimedes’ Principle
Though broadly applicable, Archimedes’ Principle has some restrictions which are very essential to remember.
- Applies only for fluids: The principle accepts only for uniform pressure of true fluids like liquid and gas. Solids or semi-solids are also turned down by it.
- Ideal Fluids: The law is in accurate account with only incompressible fluids.
- Neglects Surface Tension: Surface tension can also put some effects on the fluids in small-scale experiments. However, it is neglected.
- Only calculates Buoyant force: The principle is only able to calculate the buoyant force for fully or partially submerged objects so the force that carries an object completely up still remains a big question. Thus other effects like drag force, resistance etc. are not accounted for by the principle.
- No Fluid Motion: It considers only those fluids in motion and immediately breaks down for dynamic fluids.
- Shape Effects: Drag and flow patterns can affect how objects float, particularly in dynamic systems.
- Temperature Effects on density: Real fluids’ density is affected by the temperature and also differs by salinity. So, density is also not uniform every time.
- Not sure for porous objects: An object engulfing water brings change in its effective volume, density or composition which may hamper the exact calculation.
Common Misconceptions about Buoyant Force Clarified
Some confusion is to be sorted out while clarifying the principle. Some major wrong concepts are given below:
- Heavy objects always get drowned: Weight has nothing to do with Archimedes principle as it only cares about the density. So, large objects with greater surface can also float depending on their internal design.
- Objects displace their own volume in fluid: This applies to those being fully submerged. Floating objects drive out less volume.
- Buoyant force equals weight of the object: The statement of equality is only for fully or partially submerged objects and fails for sinking or fully floating objects.
Practice Problems: Calculating Buoyant Force Step-by-Step
Problem 1: Wooden Block in Water
What would be the buoyant force for an iceberg of volume 0.01 m³ floating in water?
Solution:
- Volume = 0.001 m³
- Water density = 1000 kg/m³
- g = 9.81 m/s²
FB = ρ × g × V = 1000 × 9.81 × 0.001 = 9.81 N
Problem 2: Iron Object in Oil
An iron rod weighing 200 N accidentally gets submerged in oil (density = 900 kg/m³). If 0.02 m³ of oil overflows, will the object float or sink?
Solution:
- FB = 900 × 9.81 × 0.02 = 176.58 N
Net force = Weight – Buoyant force = 200 – 176.58 = 23.42 N (downward)
So, the object will sink.
Conclusion
Archimedes’ Principle remains as a flawless and timeless theory that has practical and real-world implications. It provides invaluable insights into the behavior of solids in fluids or even two differing density fluids. Thus, every droplet of static fluid has a physical meaning that characterizes any dipped object. Thus, it is an important natural phenomenon that emerged as a mathematical theory due to the critical thinking of Archimedes.
With its strikingly simple yet profound nature one can grasp why things float or sink. Archimedes’ Principle remains a cornerstone of classical physics and a practical tool in many scientific and industrial fields.
References
Kireš, M. (2007). Archimedes’ principle in action. Physics education, 42(5), 484.
Mohazzab, P. (2017). Archimedes’ principle revisited. Journal of Applied Mathematics and Physics, 5(04), 836.
Urone, P. P., & Hinrichs, R. (2012). Archimedes’ Principle. Intro to Physics for Non-Majors.
Ožvoldová, M., Špiláková, P., & Tkáč, L. (2014). Archimedes’ principle-internet accessible remote experiment. International Journal of Interactive Mobile Technologies.
https://byjus.com/physics/archimedes-principle/
https://www.britannica.com/science/Archimedes-principle
Archimedes’ Principle
