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Archimedes was a Greek mathematician, physicist, and inventor. His developments on studying Density, the Buoyant Force and “Archimedes Principle” has been one of the most important contributions to scientific studies.

Archimedes and The Golden Crown :
Archimedes was asked to prove that a Kings golden crown was 100% pure gold. Archimedes knew the mass of the crown but could not determine the density. One day, in his bathtub, Archimedes realized that the volume of the water being displaced by his body was equal to his weight.

After his discovery, Archimedes ran across the streets yelling, “Eureka!”, the Greek word meaning “I found it!”

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The amount of mass located in a definite volume.

Equation:
ρ= m / v

A higher density means a higher mass and a lower volume.
A lower density means a lower mass and a higher volume.

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Understanding the basic principles of density allows us to understand its relationship to mass and volume.

If we know the mass and density of an object, we can find its volume

If we know the volume and density of a certain object, we can find its mass.

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A urine specific gravity test is a test performed by doctors in which they compare the density of water to a patient’s urine sample. The doctors check for the density of the patient’s urine.  A healthy urine sample has a specific gravity of about 1.002 to 1.035.

Doctors can analyze the results and see if a person falls below or above the average specific gravity, which they can then use to determine if that patient is healthy or at risk of illness.

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The upward force exerted by a fluid when an object is fully or partially submerged.

Equation:

•F(B )="ρ" x V x g

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Archimedes Principle states that any body completely or partially submerged in a fluid at rest is acted upon by an upward, or buoyant force ,  the magnitude of which is equal to the weight of the fluid displaced by the body

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Submarines:

Engineers design submarines based on measurements of mass, volume, and density. If the ballast tank on a submarine has a small amount of water, it will have less mass hence it will float.

Medical Field:

Doctors can use the Archimedes Principle to measure the volume of the cancellous bone. Researchers use these tests to conduct studies dealing with bone strength, osteoporosis, and bone stiffness

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What is the volume of a bar of gold that has a mass of 14.83 kg. The density of gold is 19.32
g/cm³.

Step 1: Convert kilograms to grams.

14.83 kg × 1000g1kg = 14 830 g

Step 2: Calculate the volume.

V = md = 14 830 g × 1cm³19.32g = 767.6 cm³

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Solid- firm and stable in shape; not liquid or fluid

Liquid-a substance that flows freely but is of constant volume, having a consistency like that of water or oil.

Gas-a substance or matter in a state in which it will expand freely to fill the whole of a container, having no fixed shape (unlike a solid) and no fixed volume (unlike a liquid).

Density- mass of a unit volume of a material substance
Pressure-continuous physical force exerted on or against an object by something in contact with it.

Bouyant Force-the upward force exerted by any fluid upon a body placed in it

Archimedes Principle- the law that a body immersed in a fluid is buoyed up by a force (buoyant force) equal to the weight of the fluid displaced by the body.

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https://www.youtube.com/watch?v=b5SqYuWT4-4
https://www.youtube.com/watch?v=16HDJNoXQII
https://www.youtube.com/watch?v=GnBQ6vIutDM