Sect. 14.4: Buoyant Forces Archimedes’ Principle. Experimental facts: 1. Objects submerged (or partially submerged) in a fluid APPEAR to “weigh” less than in air. 2. When placed in a fluid, many objects float! Both are examples of BUOYANCY.
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1.Objects submerged (or partially submerged) in a fluid APPEARto “weigh” less than in air.
2.When placed in a fluid, many objects float!
Both are examples ofBUOYANCY
∑Fy = 0, is satisfied.
P = ρg h (fluid atREST!!)
Mg is the weight of the FLUID displaced by the object!
The total (upward) buoyant force Bon an objectof volume Vcompletely or partially submerged in a fluid with density ρfluid:
B= ρfluidVg (1)
ρfluidV M Mass of fluid which would take up same volume as object, if object were not there. (Mass of fluid that used to be where object is!)
Upward buoyant force
B= Mg (2)
B= weight of fluid displaced by the object!
(1) or (2) Archimedes Principle
Proved for cylinder. Can show valid for any shape
if an object of volume Vobj is
totally submerged in a fluid of
B = ρfluidgVobj
Fg = Mg = ρobjgVobj
∑Fy = 0, the net vertical force must be zero:
B - Fg = (ρfluid – ρobj)gVobj = 0
or, ρfluid = ρobj. That is, the object & the fluid must have the same density!
The direction of the motion of an object in a fluid is determined only by the densities of the fluid and the object
Free body diagram
density ρobj floating (partially
submerged) at top of a fluid of
density ρfluid. See figure:
B - Fg = ρfluidgVfluid- ρobjgVobj= 0 or ρfluidVfluid= ρobjVobj
the volume of the object beneath the fluid
level. The last relation can be rewritten as:
equilibrium: ∑Fy = B - Fg = 0
Gives: ρfluidVfluid= ρobjVobj
f Fraction of the volume of floating object which is submerged.
Archimedes’ Principle: The fraction of a floating object which is submerged is equal to the ratio of the density of the object to the density of the fluid.