http://www.physics.usyd.edu.au/teach_res/jp/fluids09
lect3.ppt
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BUOYANCY - FLOATING AND SINKING
Why do ice cubes float on water?
Why does a hot air balloon rise?
What is wrong with the picture of the ship
on the left?
If I suspend a block on a rope,
what force do we need to
pull with on the rope to
make the block hang
steady?
rope
T=?
m
If I immerse the block in water, what
happens to the tension in the rope?
W
Buoyancy
A useful model:
Immersion of the block
produces an upward
buoyant force, which
at least partly
counteracts the
weight.
T
FB
Apply Newton’s 2nd Law
W – T – FB = 0
T = W - FB
+
W
Archimedes’ Principle
• When an object is immersed in a
fluid, there is an upward buoyant
force equal to the weight of the
volume of fluid displaced by the
object.
• This applies to either full or partial
immersion (i.e. a “sinking” or
“floating” object)
T = W - FB
T
FB
m
W
Hung
Tension
T=W
Weight
Floating
Tension
FB
T = W - FB
Water
displaced
Weight
Floating:
buoyant
force
equals
Water
displaced
weight
Floating: fully submerged
Some fish can remain at a fixed
depth without moving by storing
gas in their bladder.
Water
displaced Submarines take on or discharge
water into their ballast tanks
Why can ships float?
A 200 tonne ship enters a lock of a canal.
The fit between the sides of the lock is so
tight that the weight of the water left in the
lock after it closes is much less than the
ship's weight. Can the ship float?
T h e b u o ya n t fo rce is e q u a l to th e w e ig h t o f th e w a te r d isp la ce d , n o t
th e w a te r a ctu a lly p re se n t. T h e m issin g w a te r th a t w o u ld h a ve fille d
th e vo lu m e o f th e sh ip b e lo w th e w a te rlin e is th e d isp la ce d flu i d .
V o lu m e o f w a te r d isp la ce d . T h is
vo lu m e is n o t n e ce ssa rily th e
vo lu m e p re se n t.
W e ig h t o f sh ip = w e ig h t o f w a te r d isp la ce d
So buoyancy is a force.
Can we explain in terms of a push or pull ?
top
A
rF
h
ro
bottom
F = (pbottom – ptop) A
F = (patm + rF g h – patm) A
F = rF g h A = rF VF g
F = mF g = Weight of displaced fluid =Buoyant force
?
A
Two cups are filled to the same level.
One cup has ice cubes floating on it.
Which weighs more?
B
Two cups are filled to the same level.
One of the cups has ice cubes floating
in it. When the ice melts, in which cup
is the level higher?
?
A
Two cups are filled to the same level.
One cup has ice cubes floating on it.
Which weighs more?
cups weigh the same
B
Two cups are filled to the same level.
One of the cups has ice cubes floating
in it. When the ice melts, in which cup
is the level higher?
the level is the same
A Cartesian diver can be made by completely filling an empty soft drink
bottle with water. A medicine dropper is then placed in the bottle so that
a small air pocket is trapped at the top of the dropper. When the bottle
is squeezed, the medicine dropper sinks. When the bottle is release,
the diver rises.
Why does the dropper sink when the bottle is squeezed?
Your answer should include a list of the important physical quantities
involved, the names and descriptions of the physical principles
involved.
?
A giant clam has a
mass of 470 kg and
a volume of 0.350
m3 lies at the bottom
of a freshwater lake.
How much force is
needed to lift it at
constant velocity?
m = 470 kg
FT + FB = FG
Vclam = 0.350 m3
g = 9.8 m.s-2
FT = ? N
m
FT + FB
F = 0
a=0
rwater = 1.0x103 kg.m-3
FG
FT = FG - FB
FT = m g - rwater g Vdisplaced
FT = m g - rwater g Vclam
FT = (470)(9.8) – (103)(9.8)(0.350) N
FT = 1.2103 N
A ring weighs 6.32710-3 N in air and
6.03310-3 N when submerged in water.
What is the volume of the ring?
What is the density of the ring?
What is the ring made of?
air
water
Volume? density? What is the ring made of?
air
water
FTair = FG
FTwater + FB = FG
know FTair
know FTwater
weight of ring FG
know FG
Mass of ring mring
rring = mring / Vring
calculate
FB
Archimedes’ Principle
FB = weight of water displaced
FB = rF Vring g
Vring = 3.0x10-8 m3 rring = 2.2x104 kg.m-3 maybe gold
A wooden raft has a density of 0.500103 kg.m-3 and
dimensions of 3.05 m  6.10 m  0.305 m. How deep does it
sink into the water when unloaded? What is the maximum
number of 70 kg people can the raft carry before it sinks?
A hydrometer is a simple instrument used to measure
the density of a liquid by measuring how deep it sinks
in a liquid.
A particular hydrometer was made of a uniform
cylindrical rod that could float vertically in a liquid. The
length of the rod was 0.250 m and its cross sectional
area was 2.0010-4 m2. The mass of the rod was
4.5010-2 kg. To calibrate the hydrometer it is placed
into water that had a density of 1.000103 kg.m-3.
How far from the bottom end of the rod should a mark
of 1.000 be placed to indicate the relative density of the
water?
The hydrometer sinks to a depth of 0.229 m when
placed into an alcohol solution. What is the density of
the alcohol solution?