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?

m

W

T=?

ropeIf I suspend a block on a

rope, what force do we need to pull with on the rope to make the block hang steady?

If I immerse the block in water, what happens to the tension in the rope?

BuoyancyA useful model:

Immersion of the block produces an upward buoyant force, which at least partly counteracts the weight.

W – T – FB = 0 T = W - FB

W

FB

T

+

Apply Newton’s 2nd Law

m

• 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

W

FB

T

Archimedes’ Principle

Water displaced

Hung

T = W

Weight

Tension

Weight

FB

T = W - FB

FloatingTension

weight

buoyant force

Floating:

Floating: fully submerged

Water displaced

Some fish can remain at a fixeddepth without moving by storinggas in their bladder.

Submarines take on or discharge water into their ballast tanks

equalsWater

displaced

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?

Volume of water displaced. This volume is not necessarily the volume present.

Weight of ship = weight of water displaced

The buoyant force is equal to the weight of the water displaced, not the water actually present. The missing water that would have filled the volume of the ship below the waterline is the displaced fluid.

hF

top

bottom

A

o

So buoyancy is a force. Can we explain in terms of a push or pull ?

F = (pbottom – ptop) A

F = (patm + F g h – patm) A

F = F g h A = F VF g

F = mF g = Weight of displaced fluid =Buoyant force

? ATwo cups are filled to the same level. One cup has ice cubes floating on it. Which weighs more?

BTwo 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?

? ATwo cups are filled to the same level. One cup has ice cubes floating on it. Which weighs more?

BTwo 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?

cups weigh the same

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?

FT + FB

FG

a = 0m

m = 470 kg

Vclam = 0.350 m3

g = 9.8 m.s-2

water = 1.0x103 kg.m-3

FT + FB = FG

FT = FG - FB

FT = m g - water g Vdisplaced

FT = m g - water g Vclam

FT = (470)(9.8) – (103)(9.8)(0.350) N

FT = 1.2103 N

FT = ? N F = 0

A ring weighs 6.32710-3 N in air and6.03310-3 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 FG FB

Archimedes’ PrincipleFB = weight of water displacedFB = F Vring g

weight of ring FG

Mass of ring mring

ring = mring / Vring

Vring = 3.0x10-8 m3 ring = 2.2x104 kg.m-3 maybe gold

know FTwater

calculate

A wooden raft has a density of 0.500103 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 2.0010-4 m2. The mass of the rod was 4.5010-2 kg. To calibrate the hydrometer it is placed into water that had a density of 1.000103 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?