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Chapter 10 Lecture
Static Fluids
10.5 Buoyant Force
Example 10.5
• The bottom of a 4.0-m-tall diving bell is at an
unknown depth underwater. The pressure of the
air inside the bell is 2.0 atm (it was 1 atm before
the bell entered the water). The average density
of ocean water is slightly greater than the
density of fresh water, ρocean water = 1027 kg/m3.
How high is the water inside the bell and how
deep is the bottom of the bell under the water?
Prepared by
Dedra Demaree,
Georgetown University
© 2014 Pearson Education, Inc.
© 2014 Pearson Education, Inc.
WHITEBOARD
OBSERVATIONAL EXPERIMENTS
• 1. Divide your whiteboard in 4 sections.
• 1. Mr. Largo hangs a mass at the bottom of a
spring scale.
• 2. Mr. Largo is about to show you four experiments.
• 3. You must draw a FD for each experiment.
• 4. Include the magnitude of each force in each FD.
• 5. Let’s go . . . Everybody to the front of the room !
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• 2. Mr. Largo hangs a mass at the bottom of a
spring scale. Then he dips half of the mass in
water.
• 3. Mr. Largo hangs a mass at the bottom of a
spring scale. Then he dips the mass in water
(water barely covers the top of the mass).
• 4. Mr. Largo hangs a mass at the bottom of a
spring scale. Then he dips the mass completely in
water.
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THE MAGNITUDE OF THE FORCE OF FLUID
ON A SUBMERGED OBJECT
• The force exerted by the fluid pushing up on the
bottom is greater than the force exerted by the
fluid pushing down on the top of the block.
THE MAGNITUDE OF THE FORCE OF FLUID
ON A SUBMERGED OBJECT
• To calculate the magnitude of the upward
buoyant force exerted by the fluid on the
block, we start from Pascal’s second law
to determine the upward pressure of the
fluid on the bottom surface of the block,
compared to the downward pressure of
the fluid on the top surface of the block.
PB = PT + fluid(yT – yB)g
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ARCHIMEDES' PRINCIPLE:
THE BUOYANT FORCE
• A stationary fluid exert an upward
buoyant force on an object that is
totally or partially submerged in the
fluid. The magnitude of the force is
the product of the fluid density
FLUID, the volume VFLUID of the fluid
that is displaced by the object, and
the gravitational constant g:
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BUOYANT FORCE (FFonO)
FFonO = FLUIDVFLUIDg
FFonO = FFBonO - FFTonO
(Difference between the force of the fluid at bottom
and fluid at the top)
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NOTES:
• If the object is completely submerged in the fluid,
the volume VFLUID in the equation is just the
volume of the object.
• If the object floats, the volume VFLUID in the
equation equals the volume of the space taken
up by the object below the fluid’s surface.
© 2014 Pearson Education, Inc.
BUOYANT FORCE (FFonO)
• If OBJECT < FLUID, then the object floats partially
submerged.
• If OBJECT = FLUID, then the object remains wherever
it is placed totally submerged at any depth in the
fluid.
• If OBJECT > FLUID, then the object sinks at
increasing speed until it reaches the bottom of the
container.
© 2014 Pearson Education, Inc.
WHITEBOARD
• You have four objects at rest, each of the same
volume. Object A is partially submerged, and
objects B,C, and D are totally submerged in the
same container of liquid.
• A) Draw a FD for each object.
• B) Rank the densities of the objects from least to
greatest.
WHITEBOARD
• You stand on a bathroom scale. Suppose your
mass is 70.0 kg and your density is 970 kg/m3.
Determine the reduction of the scale reading
(FSonP) due to air.
• Density of air 1.29 kg/m3?
• rmi
• A) Force diagram.
• B) Find the magnitudes of:
• FEonYOU
• FAIRonYOU (Buoyant Force)
• FSonYOU
WHITEBOARD
• Pretend for a moment that you are Archimedes, who
needs to determine whether a crown made for the
king is pure gold or some less valuable metal.
You find that the force that a
string attached to a spring
scale exerts on the crown is
25.0 N when the crown hangs
in air and 22.6 N when the
crown
hangs
completely
submerged in water.
WHITEBOARD
• When analyzing a sample of ore, a geologist finds that
it weighs 2.00 N in air and 1.13 N when immersed in
water.
• Assume the ore sinks in water.
•
•
•
•
•
A) Sketch
B) Force Diagram
C) Buoyant Force
D) Volume of water displaced
E) Density of ore
• Find the volume of the crown and then determine its
density (compare to density of gold GOLD = 19,300
kg/m3).
• Is the crown made of gold?
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WHITEBOARD
• You hold on your hand a 50 kg rock of
density 2200 kg/m3 that is completely
submerged in water of density 1000
kg/m3 .
• A) Sketch
• B) Force Diagram
• C) Find the magnitudes of:
• FEonR
• FWonR
• FHonR
WHITEBOARD
• A 3.6 goose floats on a lake with 40% of its body
below the 1000 kg/m3 water level..
• A) FD
• B) Write an expression for the buoyant force
exerted on the goose (Note, the volume of water
displaced is 40% the volume of the goose).
• C) Find the density the goose.
WHITEBOARD
• A person of density 1 floats in seawater of
density 2. What fraction ( f ) of the person’s
body is submerged?
• A) FD
• B) Write an expression for the buoyant force
exerted on the person (Note: the volume of
water displaced is a fraction of the volume of the
person)
• C) What fraction ( f ) of the person’s body is
submerged?
WHITEBOARD
• An empty life raft of cross-sectional area
2.0 m x 3.0 m has its top edge 0.36 m above the
waterline. How many 75-kg passengers can the
raft hold before water starts to flow over its
edges? The raft is in seawater of density 1025
kg/m3.
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WHITEBOARD
• A 3.0m x 1.0m rectangular plastic container that
is 1.0 m high, has a mass of 1500 kg. The
container floats in fresh water (density 1000
kg/m3), partially submerged.
• A) FD
• B) Write an expression for the buoyant force
exerted on the container.
• C) Write an expression for the depth of the
container submerged in water.
• D) Find the depth of the container submerged in
water.
HOW DO SUBMARINES MANAGE TO SINK
AND THEN RISE IN THE WATER?
• A submarine's density increases when water fills
its compartments.
– With enough water in the compartments, the
submarine's density is greater than that of the
water outside, and it sinks.
• When the water is pumped out, the submarine's
density decreases.
– With enough air in the compartments, its
density is less than that of the outside water,
and the submarine rises toward the surface.
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STABILITY OF SHIPS
• A
challenge
watercraft
is
to
building
to
maintain
stable equilibrium for the
ship, allowing it to right itself
if it tilts to one side due to
wind or rough seas.
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BALLOONING
• Using hot air, balloonists can adjust the average
density of the balloon (e.g., the balloon's
material, people, equipment) to match the
density of air so that the balloon can float at any
location in the atmosphere (up to certain limits).
– A burner under the opening of the balloon
regulates the temperature of the air inside the
balloon and hence its volume and density.
– This allows control over the buoyant force
that the outside cold air exerts on the balloon.
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EFFECTS OF ALTITUDE ON HUMANS
Effects of altitude on humans
• The pressure of atmospheric air decreases as
one moves higher and higher in altitude.
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– Between 4600 m and 6000 m, heart and
breathing rates increase dramatically, and
cognitive and sensory function and muscle
control decline.
– Between 6000 m and 8000 m, climbers
undergo critical hypoxia, characterized by
rapid loss of muscular control and loss of
consciousness.
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Scuba diving
• Scuba divers breathe compressed air.
– While moving slowly downward, a diver
adjusts the pressure outlet from the
compressed-air tank to accumulate gas from
the cylinder into her lungs, increasing the
internal pressure to balance the increasing
external pressure.
– If a diver returns too quickly to the surface,
the great gas pressure in the lungs can force
bubbles of gas into the bloodstream.
– This
gradual
process
is
called
decompression.
HOMEWORK
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ALG
ALG
ALG
ALG
ALG
10.3.4 page 10-6
10.3.5 page 10-6
10.3.6 page 10-7
10.3.7 page 10-8
10.3.10 page 10-9
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YOU MUST WORK ON
ALG 10.4.1 page 10-9
ALG 10.4.2 page 10-10
ALG 10.4.3 page 10-10
ALG 10.4.4 page 10-10
ALG 10.4.5 page 10-11
ALG 10.4.6 page 10-11
ALG 10.4.7 page 10-12
SUGGESTED PROBLEMS
• Section 10.5
• 54, 55, 56, 60, 61, 62, 67,
68, 69, 70, 77, 78
COME FOR EXTRA HELP
IF NEEDED !
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