Archimedes and Buoyant force help please?

There is more than one way of viewing the situation.  Archimedes saw that the buoyant force must be equal to the weight of the fluid displaced.  And the weight of the object cannot alter this.  The NET force on the other hand depends on the buoyant force + weight of object.

The object does not need to be less dense than the liquid it is immersed in, it can be immersed by physically pushing it in. So whether it's a hollow vessel full of air that would normally float or a solid lead object with the same displacement, the buoyant force on it will be the same when fully immersed.

The buoyant force is the weight of the fluid displaced or moved out of the way. Rocks sink in water because they have more mass in a smaller volume so don't push enough water out of the way to counter their weight. A piece of wood floats in water because wood has less mass in a larger volume and pushes water out of the way that weighs more than it weighs. Hope this helps.

Buoyant force is a function of the displacement of a fluid so, If the displacement of the fluid is the same then the buoyant force is the same.

If the volume is the same irrespective of masses then the buoyant force is the same.

Buoyant force is equal to the weight of the liquid displaced by the object.

For this to be true the volume of water must  not  beconstricted.

Sure...the buoyant force BF depends upon the immersed volume, whichever is its density !!

The bouyant force is equal to the weight of the volumen of fluid displaced. No matter the material, weight or shape of the object submerged. Comparing that bouyant force with the object weight is the result you can get:

-sinks to the fluid bottom,

-floats submerged 100% below the fluid level,

-floats partially submerged, 

-shoots out of the fluid (like a beach ball)

The definition of Archimedes  Principle is " The weight of a body immersed in a fluid is equal to the weight of the fluid displaced'.

So if it floats the weight of fluid displaced is greater than the body. 

If it sinks then the weight of the body is greater than the fluid displaced. 

The buoyancy force remains the same for the same fluid, say pure water.  It will be different for a different fluid say sea-water(salt water). because the density of pure water is less than  the density of sea/salt water.    

The buoyant force would be the same, if they are fully immersed.