396
CHAPTE R 14 FLU I DS
When a body floats in a fluid, the magnitude F b of the buoyant force on the body
is equal to the magnitude F g of the gravitational force on the body.
When a body floats in a fluid, the magnitude F g of the gravitational force on the
body is equal to the weight m f g of the fluid that has been displaced by the body.
of the displaced water. Like the stone, the block is not in static equilibrium.
However, this time the gravitational force
is lesser in magnitude than the
buoyant force (as shown to the right of the pool), and so the block accelerates
upward, rising to the top surface of the water.
Our results with the sack, stone, and block apply to all fluids and are summarized
in Archimedes’ principle:
F
:
g
When a body is fully or partially submerged in a fluid, a buoyant force from the
surrounding fluid acts on the body. The force is directed upward and has a magnitude equal to the weight m f g of the fluid that has been displaced by the body.
F
:
b
The buoyant force on a body in a fluid has the magnitude
F b ϭ m f g (buoyant force),
( 1 4 - 1 6 )
where m f is the mass of the fluid that is displaced by the body.
Floating
When we release a block of lightweight wood just above the water in a pool, the block
moves into the water because the gravitational force on it pulls it downward. As the
block displaces more and more water, the magnitude F b of the upward buoyant force
acting on it increases. Eventually, F b is large enough to equal the magnitude F g of the
downward gravitational force on the block, and the block comes to rest. The block is
then in static equilibrium and is said to be floating in the water. In general,
We can write this statement as
F b ϭ F g (floating).
(14-17)
From Eq. 14-16, we know that F b ϭ m f g. Thus,
We can write this statement as
F g ϭ m f g (floating).
(14-18)
In other words, a floating body displaces its own weight of fluid.
Apparent Weight in a Fluid
If we place a stone on a scale that is calibrated to measure weight, then the
reading on the scale is the stone’s weight. However, if we do this underwater,
the upward buoyant force on the stone from the water decreases the reading.
That reading is then an apparent weight. In general, an apparent weight is related
to the actual weight of a body and the buoyant force on the body by
which we can write as
weight app ϭ weight Ϫ F b (apparent weight).
( 1 4 - 1 9 )
apparent
weight ϭ
actual
weight Ϫ
magnitude of
buoyant force ,
CHAPTE R 14 FLU I DS
When a body floats in a fluid, the magnitude F b of the buoyant force on the body
is equal to the magnitude F g of the gravitational force on the body.
When a body floats in a fluid, the magnitude F g of the gravitational force on the
body is equal to the weight m f g of the fluid that has been displaced by the body.
of the displaced water. Like the stone, the block is not in static equilibrium.
However, this time the gravitational force
is lesser in magnitude than the
buoyant force (as shown to the right of the pool), and so the block accelerates
upward, rising to the top surface of the water.
Our results with the sack, stone, and block apply to all fluids and are summarized
in Archimedes’ principle:
F
:
g
When a body is fully or partially submerged in a fluid, a buoyant force from the
surrounding fluid acts on the body. The force is directed upward and has a magnitude equal to the weight m f g of the fluid that has been displaced by the body.
F
:
b
The buoyant force on a body in a fluid has the magnitude
F b ϭ m f g (buoyant force),
( 1 4 - 1 6 )
where m f is the mass of the fluid that is displaced by the body.
Floating
When we release a block of lightweight wood just above the water in a pool, the block
moves into the water because the gravitational force on it pulls it downward. As the
block displaces more and more water, the magnitude F b of the upward buoyant force
acting on it increases. Eventually, F b is large enough to equal the magnitude F g of the
downward gravitational force on the block, and the block comes to rest. The block is
then in static equilibrium and is said to be floating in the water. In general,
We can write this statement as
F b ϭ F g (floating).
(14-17)
From Eq. 14-16, we know that F b ϭ m f g. Thus,
We can write this statement as
F g ϭ m f g (floating).
(14-18)
In other words, a floating body displaces its own weight of fluid.
Apparent Weight in a Fluid
If we place a stone on a scale that is calibrated to measure weight, then the
reading on the scale is the stone’s weight. However, if we do this underwater,
the upward buoyant force on the stone from the water decreases the reading.
That reading is then an apparent weight. In general, an apparent weight is related
to the actual weight of a body and the buoyant force on the body by
which we can write as
weight app ϭ weight Ϫ F b (apparent weight).
( 1 4 - 1 9 )
apparent
weight ϭ
actual
weight Ϫ
magnitude of
buoyant force ,