Buoyancy and Archimedes Principle
buoyancy – objects in a fluid appear to weigh less than when outside the fluid. Fg acts downward while Fb acts upward
For fish and divers Fg ≈ Fb
occurs because P in a fluid increases with depth
Consider a cylinder of height, h, whose top and bottom ends have an area A & which is completely submerged in a fluid of density ρF
The fluid exerts a pressure P1 = ρFgh1 at the top surface of the cylinder
The force due to this pressure on the top of the cylinder is F1 = P1A = ρFgh1A
and is directed downward
The fluid exerts and upward force on the bottom of the cylinder
equal to F2 = P2A = ρFgh2 A
THE NET FORCE due to fluid pressure is the buoyant force, Fb
Fb = ρFgV
ρFgV = mFg ∴ Fb = weight of fluid displaced by the cylinder
Archimedes (287?–212 B.C.) Principle–the buoyant force on a body immersed in a fluid is equal to the weight of the fluid displaced by that object.
The rock D is acted upon by Fw downward and Fb upward.
We want to determine Fb
Consider a “rock” composed of the fluid D’ with the same
size and shape as the original rock in (a)
Since the fluid is at rest, Fb on D = Fb on D’ since the
surrounding fluid is in EXACTLY the same configuration
Therefore, Fb = W’ so Fb = weight of the body of the fluid whose volume = volume of D
Archimedes’s Principle applies to objects that float as well
An object floats if less dense than surrounding fluid
At equilibrium, i.e. when floating, mg = Fb