Mechanics

# Three important cases of thrust

Man floating on the surface of the pool

Archimedes’ principle says that, in the presence of gravity, a body immersed (partially or totally) in a fluid in equilibrium undergoes the action of a force, called buoyancy, of vertical direction and direction from the bottom up, whose intensity is equal to the volume of fluid displaced.

For the study of buoyancy we must consider three important cases . Let’s imagine that we abandon a body totally immersed inside a liquid in equilibrium. The forces acting on the body are the buoyancy E, of magnitude:

E= μ L .V F .g

and the weight P c , of intensity

c = m c .g or P c = μ c .V c .g

where μ c  is the density of the body.

As the body was left completely immersed in the liquid, we have V f = V c that we will simply denote by V. Thus, we have:

E= μ L .Vg
c = μ c .Vg

There are three possible situations:

1- μ c =μ L : : in this case, P c = E, and the body is in equilibrium in any position in which it is placed inside the liquid.

3- μ c < μ L : in this case, P c < E, and the body rises, under the action of the resultant force E – Pc, which is called ascension force : F asc = E – Pc. When the body reaches the free surface of the liquid, as it leaves the liquid, the displaced volume decreases and, consequently, the buoyancy intensity becomes smaller. Equilibrium occurs when the force of thrust becomes equal to the intensity of the body’s weight. Therefore, the body is in equilibrium, floating, partially immersed. Therefore, the condition of buoyancy of a body is that its density is less than that of the fluid in which it was placed.