Exam 2 :
The average increased from 62 to 66 % !
Physics 101: Lecture 24, Pg 1
Physics 101: Lecture 24
Fluids: Pascal and Archimedes
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Today’s lecture will cover Textbook Sections 11.5-11.6
Î Archimedes Principle & Buoyancy
Î Pascal’s Principle
Note: Everything we do assumes fluid
is non-viscous and incompressible.
Physics 101: Lecture 24, Pg 2
Pascal’s Principle
Any change in pressure applied to a completely enclosed
fluid is transmitted undiminished to all parts of the fluid
and the enclosed walls.
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Example: hydraulic lift
Consider two pistons with area A1 and A2 at the same
height at different ends of an enclosed fluid. Am external
Force F1 is applied to piston 1. Consequently the fluid
exerts a force on piston 2 which is related to F1 as
follows
F2 = F1 (A2 / A1)
Physics 101: Lecture 24, Pg 3
Archimedes Principle
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An object fully or partially immersed in water
experiences an upward force due to the difference in
fluid pressure at different depths. This net force
exerted on the object by the fluid is called the buoyant
force :
FB = P2 A – P1 A = (P2-P1) A = ρ g h A
Using that h A=V is the volume of the fluid and
that ρ V=m is the mass of the fluid one finds that
FB = weight of fluid displaced by the object
Physics 101: Lecture 24, Pg 4
Archimedes Principle cont.
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When does an object float ?
An object floats when the upward acting buoyant force
is balanced by the downward acting weight of the object:
Also
FB = weight of object
FB= weight of displaced water
=> For a floating object: Wobject = Wdisplaced fluid
Physics 101: Lecture 24, Pg 5
Archimedes Principle (summary)
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Buoyant Force (FB)
ÎBuoyant force = weight of fluid displaced
ÎFB = ρfluid x Vdispl g
ÎW = Mg = ρobject Vobject g
If object floats….
ÎFB=W
ÎTherefore ρfluid g Vdispl. = ρobject g Vobject
ÎTherefore Vdispl./Vobject = ρobject / ρfluid
Physics 101: Lecture 24, Pg 6
Concept Question
Which weighs more:
1. A large bathtub filled to the brim with water.
2. A large bathtub filled to the brim with water with a battle-ship
floating in it.
3. They will weigh the same.
CORRECT
Tub of water + ship
Tub of water
Weight of ship = Buoyant force =
Overflowed water
Weight of displaced water
Physics 101: Lecture 24, Pg 7