ARCHIMEDES’ PRINCIPLEARCHIMEDES’ PRINCIPLE.BOUYANCY..BOUYANCY.

Name: Name: ArchimedesArchimedes Birth Date: Birth Date: c. 287 B.C.c. 287 B.C. Death Date: Death Date: 212 B.C.212 B.C. Place of Birth: Place of Birth: SyracuseSyracuse Place of Death: Place of Death: SyracuseSyracuse Nationality: Nationality: GreekGreek Occupations: Occupations:

mathematicianmathematician

Facts about ArchimedesFacts about Archimedes

The greatest mathematician of antiquity and one of the greatest of all time.

 a Greek mathematician, physicist, engineer , inventor and astronomer

DiscoveriesDiscoveries

The Golden CrownThe Golden Crown The Archimedes ScrewThe Archimedes Screw The Claw of ArchimedesThe Claw of Archimedes

Archimedes’ PrincipleArchimedes’ Principle BOUYANT FORCE BOUYANT FORCE

    - the upward force of the fluid on an - the upward force of the fluid on an objectobject

- depends on the weight of the - depends on the weight of the displaced fluid displaced fluid

- always upward or opposite to the - always upward or opposite to the gravity gravity

Archimedes’ principle states that the Archimedes’ principle states that the buoyant force on a submerged object is buoyant force on a submerged object is equal to the weight of the fluid that is equal to the weight of the fluid that is displaced by the object. displaced by the object.

Equation: Equation: F = mg or F = pVgF = mg or F = pVg where inwhere in : : m= mass of liquidm= mass of liquid g = gravitational accelerationg = gravitational acceleration V = object’s volumeV = object’s volume p = liquid’s density (p = liquid’s density (equal to equal to

the weight per unit of volume)the weight per unit of volume)

ExamplesExamples

1.1.

2.2.

A submarine can control it rising or            sinking through tanks that either let in       water or air. The air causes it to rise         while the water causes it to sink.              

3.3.

Fish have swim bladders which do work

    the same way a submerine's tanks do.

So when a boat is floating in static equilibrium, the following equation So when a boat is floating in static equilibrium, the following equation holds true:holds true:

B = Fg = MgB = Fg = Mg Where B is the buoyant force, Fg is the force of gravity, and Mg is the Where B is the buoyant force, Fg is the force of gravity, and Mg is the

weight of the object. More importantly, the total weight of the water weight of the object. More importantly, the total weight of the water displaced is equal to the total weight of the object displacing the water displaced is equal to the total weight of the object displacing the water (Archimedes's Principle). Therefore, “displacement” is what we call the (Archimedes's Principle). Therefore, “displacement” is what we call the volume of water that is moved aside by a floating boat. Displacement is volume of water that is moved aside by a floating boat. Displacement is recorded as the weight of the volume of water moved.recorded as the weight of the volume of water moved.

We can take this a step further and see that if B = Mg and M =pV, then B = pVg. Where We can take this a step further and see that if B = Mg and M =pV, then B = pVg. Where V is volume, p is density, M is mass, and g is the acceleration of gravity. So the buoyant V is volume, p is density, M is mass, and g is the acceleration of gravity. So the buoyant

force is a function of density and we can conclude that the density of an object force is a function of density and we can conclude that the density of an object determines whether or not it will float. So if a sailboat had an average density greater determines whether or not it will float. So if a sailboat had an average density greater

than saltwaterthan saltwater

it would not remain on the surface. However, if it would not remain on the surface. However, if the sailboat has an average density of 32 pounds the sailboat has an average density of 32 pounds per cubic foot, it will float on the surface of the per cubic foot, it will float on the surface of the water and be halfway submerged. This is why water and be halfway submerged. This is why ships that are constructed of materials possessing ships that are constructed of materials possessing much greater densities than that of water can still much greater densities than that of water can still float. The air inside the hull brings the average float. The air inside the hull brings the average density of the entire ship below the density of density of the entire ship below the density of water. Even a cement boat can float and they water. Even a cement boat can float and they have have