Archimedes

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Archimedes Principle
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Important

• Class on Friday will be held in SUB Ballroom B!

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P2 P1 rgh
Patm
Patm 101 325 N/m2 Patm 101 325 Pa Patm 101
kPa Patm 14.7 lbs/in2
P2
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P2 P1 ?gh 2Patm Patm ?gh Patm ?gh h
Patm / ?g h (101325)/ (1000)(9.8) h 10.3 m
34 ft
hfresh water 10.3 m hsalt water 10.0
m hmercury 0.76 m
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THE BUOYANT FORCE
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HOW BIG IS THE BUOYANT FORCE?
Fbuoy
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THE CASPER BOX - no mass - just holds stuff
Fbuoy
10,000 N
WATER
How big is the buoyant force?
WE,W 10,000 N
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THE CASPER BOX - no mass - just holds stuff
Fbuoy
10,000 N
STEEL
How big is the buoyant force?
WE,S 78,000 N
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THE CASPER BOX - no mass - just holds stuff
Fbuoy
10,000 N
STYRO-FOAM
How big is the buoyant force?
WE,S 1,000 N
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(No Transcript)
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Archimedes Principle

• The buoyant force acting on an object is equal to
  the weight of the fluid
• displaced by the object, or
• that would fill the Casper Box
• If an object has greater density than the fluid
  it will sink.
• If an object has smaller density than the fluid
  it will float.

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How can a steel boat float?
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Where will they float?
Object A rA 0.8 g/cc
Object B rB 0.95 g/cc
oil r 0.9 g/cc
Object C rC 1.1 g/cc
Object D rD 1.3 g/cc
fresh water r 1.0 g/cc
Object E rE 4.0 g/cc
salt water r 1.2 g/cc
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The bouyant force is greatest on a ten ton ship
if it is floating in

• A) fresh water
• B) salt water
• C) mercury

a ? a 0

• D) all the same

What does change?
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THREE BLOCKS

• Which block has the greatest buoyant force?

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Which block experiences the largest buoyant force?
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What should I remember?

• Archimedes Principle always applies, whether an
  object sinks or floats.
• buoyant force is always equal to weight of fluid
  displaced.
• If an object floats, the buoyant force is also
  equal to the objects weight.(Newtons 2nd Law
  with a 0)

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Problem

• A cube of wood 20 cm on each side is placed in a
  tub of water and is found to sink so that only 6
  cm of the block is above the water. What is the
  density of the wood?

6 cm
20 cm
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6 cm
20 cm
a ? a 0
m g
F(buoy)W,b WE,b ?WVCB g ?b Vb g ?WVCB ?b
Vb
?b Vb g
?WVCB g
F(buoy)W,b W(water in Casper box)
?WVCB g
?b 700 kg/m3
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Hard problem
You are floating in a boat in your very own
swimming pool (you are rich). There are six gold
bricks sitting on the floor of the boat (you are
rich). You throw them into the pool. Does the
water level of the pool go up or down (or stay
the same)?