Making use of archimedes’s principle, displacements, and buoyancy, explain why some objects float on water, but others do not.

Archimides' Principle states that any body immersed in a fluid receives a vertical pushing force upwards equal to the weight of the fluid displaced by the body.

Then, there are two forces acting on the body, its weight (vertical downwards) and the bouyancy (vertical push upwards).

There are three possibilities:

1) The buoyancy is greater than the weight of the body => the body will float (move upward, toward the surface if it is a liquid)

2) The buoyancy is equal than the weight of the boy => the body wll remain quite (also floating but not moving either upwards or downwards)

3) The buoyancy is less than the weight of the body => the body will sinkl.

So, a body will float on water when the buoyancy from the liquid is overcomes its weight.

Buoyancy is related with density because:

buoyancy = weight of the liquid displaced = mass o fliquid * g = density of the liquid * Volume of the liquid * g

Weight of the body = mass of the body * g = density of the body * Volumen of the body * g

When the body is completely immersed in the liquid its volume es equal to the volume of the liquid displaced =>

So we can compare the weight of the body and the buouancy force

density of liquid * volume of liquid * g    vs       density of body * volume of liquid * g

where the difference is the densities of liquid and body.

That is why it is deduced that the bodies float when their densities are smaller than the densities of the liquid where they are.