Archimedes'
Principle
is an air parcel in equilibrium,
i.e., the net force on it is zero and it is therefore, in accordance with
Newton's 2nd Law, not
accelerating. The net force on it is the sum of the only two forces
which act upon it, the gravitational force,
W,
also known
as its weight, and the pressure gradient force,
PGF,
which is the sum of all the infinitesimal pressure forces acting upon its
surface and which is also known as the buoyant force.
is an object of exactly the same size and shape as the air parcel, at exactly
the same level in the atmosphere. Because all the
infinitesimal components of the pressure gradient force which acts upon it are
identical with the components of the pressure
gradient force on the air parcel so is the total pressure gradient force or
buoyant force, PGF.
But the magnitude of that pressure
gradient force equals the weight of the air parcel at the left and
therefore also equals the weight of the air parcel which the
object displaces. Thus we can state Archimedes' Principle:
The buoyant force on any object is equal
to the weight of the fluid
it
displaces. (We note
there is nothing special about air in this argument. The displaced fluid
could be air, water or any other
fluid. We also note that the apparent weight of the fluid-displacing
object, Wnet,
equals the true weight W',
minus that
buoyant
force, PGF.
Each class member registers an apparent weight on his/her
bathroom scales of one to two ounces less
than his/her true weight because of the buoyant force exerted on him/her by
the atmosphere. )
