Unlocking Archimedes’ Wisdom: A Journey Through Theory and Practice

by Johnny Jacks
In the 8th-grade physics curriculum, one encounters a fascinating concept known as diametrical repulsion, which has numerous real-world applications. In this article, Goodheathplan.com aims to provide you with a comprehensive synthesis of the theories surrounding Archimedes’ repulsion, its practical implications, and its relevance in our daily lives. Join us on this journey of exploration.

Understanding Diametrical Repulsion

Diametrical repulsion, often referred to as Archimedes’ thrust, is a fundamental force that frequently manifests in various human activities and everyday scenarios.

Defining the Term

Before delving into the specifics of diametrical repulsion, let’s take a moment to learn about the brilliant mind behind its discovery – Archimedes. Archimedes, a Greek polymath, was a mathematician, physicist, inventor, engineer, and astronomer. Although historical records provide limited details about his life, he remains one of the most prominent scientists of antiquity.

Archimedes made a groundbreaking observation: the greater the immersion of an object in water, the stronger the repulsive force it experiences. In essence, the force exerted on an immersed object by the surrounding fluid is directly proportional to the volume of water displaced by that object. This insight led to the formulation of the concept of thrust.

Archimedes’ repulsion, also known as Archimedes’ principle, is the force exerted by a fluid (whether liquid or gas) on an object submerged within it, under the influence of external forces such as gravity or inertial forces.

This physical force is equal in magnitude but opposite in direction to the total force exerted by the external force field on the fluid volume equivalent to the volume of the submerged object. Archimedes’ principle finds practical application in various scenarios, such as the buoyancy of boats and airships, the mechanics of submarine submersion and fish swimming, and the phenomenon of fluid convection.

The Greek scientist Archimedes.

The Greek scientist Archimedes.

Symbol and Measurement Unit of Diametrical Thrust Force

The symbol representing diametrical thrust is denoted as FA.

The standard unit of measurement for repulsion force is the newton, abbreviated as N.

Characteristics of Diametrical Thrust

Diametrical repulsion occurs when an object is immersed in a fluid, be it gas or liquid, within the influence of an external force field of physics, which may involve gravitational or inertial forces.

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Diametrical repulsion acts both in the same direction as gravity and in the opposite direction.

The presence or absence of diametrical repulsion plays a crucial role in determining whether an object will sink or float.

Magnitude of Repulsion Force

Predicting the Magnitude of Diametrical Thrust

As per the findings of the Greek scientist Archimedes, the greater the volume of water displaced by an object submerged in it, the stronger the repulsion force exerted by the water on that object.

=> We can predict that the magnitude of the repulsion force on an object immersed in a liquid will be equal to the weight of the liquid displaced by the object.

Experimental Verification

Experiment Setup:

Two cups, labeled A and B

Overflow bottle

Dynamometer

Heavy objects

Conducting the Experiment:

  1. Record the dynamometer reading when attaching the weight to cup A, resulting in a reading of P.
  2. Immerse the heavy object into the overflow bottle, causing water to overflow into cup B. Record the dynamometer reading at this point as P1.
  3. Pour the water from cup B into cup A and record the dynamometer reading as P.

Observations:

P1 value < P: This difference is due to the presence of Archimedes’ thrust acting on the heavy object.

The value of the diametrical thrust (Archimedes repulsion) can be calculated as follows:

FA = P – P1 (1)

When we transfer the water from cup B to cup A, we have:

P1 + FA = P (2)

=> The weight of the water in cup B corresponds to the value of Archimedes’ repulsion.

Therefore, our earlier prediction about the magnitude of the diametrical thrust is indeed correct based on equations (1) and (2).

Conclusion on the Magnitude of Diametrical Thrust

The magnitude of the repulsion force is determined by the density of the liquid and the volume of the liquid displaced by the object.

The magnitude of the thrust force is always equivalent to the weight of the object.

Buoyancy

When an object is immersed in a liquid, there are three possible scenarios:

FA < P: The object sinks when the diametrical thrust is less than its weight.

FA > P: The object will float and remain buoyant until FA = P.

FA = P: The object remains suspended in the liquid (or on the liquid’s surface).

In simpler terms, when an object’s overall density is less than that of the liquid it’s placed in, it will float. This explains why, despite being much larger and heavier than individual metal components, ships can float on water.

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Even though metal is dense, its water displacement volume is small, resulting in a higher overall density. Conversely, ships have a substantial water displacement, leading to a lower overall density, allowing them to float.

A vessel can float on water because its total specific gravity is lower than that of water.

A vessel can float on water because its total specific gravity is lower than that of water.

However, a ship’s weight can change, affecting its overall density. Loading cargo onto a ship gradually causes it to sink, following the formula mentioned earlier. Overloading can result in the ship sinking beyond the point where water enters hollow compartments or tanks within the hull.

This increases the ship’s weight and decreases the volume of water displaced, leading to a higher overall density than that of the water, causing the ship to sink. It’s important to note that these principles apply when the ship is stable and not tilting.

The formula for calculating the azimuth repulsion force

The formula for calculating the diametrical repulsion force is as follows:

FA = dV

Where:

  • FA: Diametrical thrust (N)
  • D: Specific gravity of the liquid (N/m^2)
  • V: Volume of the liquid displaced by the object (m^3)

Note:

V represents the volume of the liquid displaced by the object, which corresponds to the submerged part of the object. It should not be confused with the total volume of the object.

To calculate the sinking of an object, you can consider the following scenarios:

If the problem states Vfloat, then Vsink = Object – Vfloat.

If the problem mentions a height h indicating the submerged part of the object (especially for objects with irregular shapes), then Vsink = Base Area x h.

If the problem specifies that the object is fully submerged in the liquid, then Vsink = Object.

Utilizing diametrical thrust in real life

Applications of diametrical thrust in everyday life are as follows:

  1. Ship and Boat Design: One of the most notable applications of diametrical thrust is in the design of ships and boats. When constructing vessels, designers create spacious hulls to increase the volume of the ship. This design principle allows boats to float effortlessly on the water’s surface. It explains why even enormous ships with significant tonnage do not sink when placed in water.
  2. Hot Air Balloon Manufacturing: Diametrical thrust is also applied in the production of hot air balloons, particularly in an aerial environment. To enable hot air balloons to ascend to great heights, heat is used to expand the air inside the balloon, increasing its volume and, consequently, the thrust. This expansion reduces the balloon’s overall density, facilitating its ascent. In some cases, helium is used instead of heated air to achieve the same effect.
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These practical applications demonstrate how an understanding of diametrical thrust plays a crucial role in various real-life situations.

Application of archimedes thrust in the production of hot air balloons.

Application of archimedes thrust in the production of hot air balloons.

  • Buoyancy in Fish due to Diametrical Thrust

In their natural habitat, fish can regulate their buoyancy, allowing them to either sink or rise in the water. This ability is attributed to a part of their body structure that contains a large bubble, operating on the principles of diametrical thrust.

When a fish intends to float, this bubble inflates, increasing its volume and consequently enhancing the thrust. This assists the fish in effortlessly floating higher in the water. Conversely, when the fish wants to dive, the bubble contracts, reducing its volume and diminishing the thrust, causing the fish to sink.

The air bubble within the fish adjusts when the fish intends to dive or rise.

The air bubble within the fish adjusts when the fish intends to dive or rise.

Solving Physics Problems on Diametrical Thrust

Question 1: What factors does Archimedes thrust depend on?

A. Specific gravity of liquids and objects.

B. The specific gravity of the liquid and the volume of the liquid displaced by the object.

C. Specific gravity and of the object.

D. The weight of the object and the volume of the liquid displaced by the object.

Question 2: Which of the following statements is correct?

A. The thrust force is in the same direction as gravity.

B. The Archimedes thrust acts in all directions because the liquid exerts pressure in all directions.

C. Archimedes repulsion has a set point in the object.

D. Acceleration force is always equal to the weight of the object.

Question 3: An aluminum ingot and a steel ingot of equal volume are submerged in water. Which of the following statements is true?

A. The deeper the ingot, the greater the Archimedes thrust on that ingot.

B. Steel has a larger specific gravity than aluminum, so the steel ingot is subjected to a larger Archimedes thrust force.

C. Both aluminum and steel ingots are both subjected to the same Archimedes repulsion because they have the same mass.

D. Both aluminum and steel ingots are subjected to the same Archimedes repulsion because they occupy the same volume in the water.

Question 4: The repulsive force acting on an object immersed in a liquid is equal to:

A. Weight of the object

B. Weight of liquid

C. Weight of the part below the surface of the liquid

D. Weight of liquid displaced by the object

ANSWERS:

Question 1: B

Question 2: B

Question 3: B

Question 4: D

Hopefully, through this article, you have gained an understanding of the concept of diametrical thrust, its calculation, and its practical applications in daily life. Thank you for reading this article.

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