AP Physics Rapid Learning Series - 11
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Mechanics of Solids ec a cs o So dsand Fluids
Physics Rapid Learning Series
Rapid Learning Centerwww.RapidLearningCenter.com/© Rapid Learning Inc. All rights reserved.
Wayne Huang, Ph.D.Keith Duda, M.Ed.
Peddi Prasad, Ph.D.Gary Zhou, Ph.D.
Michelle Wedemeyer, Ph.D.Sarah Hedges, Ph.D.
AP Physics Rapid Learning Series - 11
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Learning ObjectivesBy completing this tutorial, you will learn the properties of two basic states of matter – solids and fluids:
Classification of states of matter
Elasticity of solids
Pressure variation of fluids and buoyancy
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y y
Fluids in motion
Surface tension and viscosity.
Concept MapPrevious content
New content
States of Matter
Includes ViscousFlow
Solids Fluids
Elasticity
Pressure
Static fluids
Surface
Viscosity
Non viscous Non-viscous Flow
By
In motion
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Variation
Buoyancy and Buoyancy and Archimedes’
Principle
Leads to
Bernoulli’s Equation
Work and EnergyLaw of
Work and EnergyTension
YieldsCapillary Action
Leads to
Density
ExpansionThermal
Expansion
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States of Matter
Low temperature High temperature
Change of state with temperature
Solids GasesFluids (Liquid)
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Strong inter-molecular force
Loose inter-molecular force
Fixed molecule
Definite shape
Wandering molecule
Indefinite shape
Solids and Elasticity
Let’s start out by discussing solids.
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Classification of Solids - 1
Crystalline
Ordered atomic
Two categories:
Ordered atomic structure
Existence of melting point
Amorphous solid
Randomly arranged
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y gatomic structure
No melting pointExample:
Nature Crystal
Classification of Solids - 2
Crystalline
Ordered atomic
Two categories:
Ordered atomic structure
Existence of melting point
Amorphous solid
Randomly arranged
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y gatomic structure
No melting pointOrdered atomic structure
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Classification of Solids - 3
Crystalline
Ordered atomic
Two categories:
Ordered atomic structure
Existence of melting point
Amorphous solid
Randomly arranged
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y gatomic structure
No melting pointMelting curve
Classification of Solids - 4
Crystalline
Ordered atomic
Two categories
Ordered atomic structure
Existence of melting point
Amorphous solid
Randomly arranged
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y gatomic structure
No melting pointExample:Candle
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Classification of Solids - 5
Crystalline
Ordered atomic
Two categories:
Ordered atomic structure
Existence of melting point
Amorphous solid
Randomly arranged
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y gatomic structure
No melting point Randomly arranged structure
Classification of Solids - 6
Crystalline
Ordered atomic
Two categories:
Ordered atomic structure
Existence of melting point
Amorphous solid
Randomly arranged
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y gatomic structure
No melting point Melting curve
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Density and Thermal Expansion - 1
DensityMass per unit volume,i ld h hi hi.e. gold has a higher density than iron.Thermal expansion effect
Volume or length increases with temperature
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temperature.
Thermal expansion effect
Density and Thermal Expansion - 2
DensityMass per unit volume, Thermal
expansioni.e. gold has a higher density than iron.Thermal expansion effect
Volume or length increases with temperature
( )00 TTαLL −=−
High Temp.
Low
Length athigh Temp.
Length at
expansion coefficient
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Thermal expansion coefficients
LowTemp.
Length atlow temp.
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Density and Thermal Expansion - 3
DensityMass per unit volume,i e gold has a higher densityi.e. gold has a higher density than ironThermal expansion effect
Volume increases with temperature
Thermal expansion ffi i t
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coefficients
ApplicationsUsed in Thermostat
Bimetallic strips
Deformation of Solids
Stress Force causing deformation
StrainDegree of deformation
Elastic behavior
Proportional limit
Elastic limit
Proportional limitElastic
limit
Elastic behavior
Plastic behavior
Breakingpoint
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Elastic limit
Plastic behavior
Breaking pointStress-strain curve
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Three Types of Elastic Modulus - 1
Young’s modulus
Definitions:
stresstensileY ≡
AF
Force
Cross area
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straintensileY ≡
0L∆L
Length change
Original length
Three Types of Elastic Modulus - 2
Shear modulus
Definitions:
AF
Tangent force
Cross area
stressShearG =
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h∆x
area
Tangentdisplacement
Original thickness
strainShearG =
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Three Types of Elastic Modulus - 3
Bulk modulus
Definitions:
AF
Normal force
Normal areastressVolumeB =
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V∆V
Volume change
Original Volume
strainVolumeB −=
Example: Squeezing a SphereA sphere, with volume of 0.50 m3 and bulk modulus of 8 GPa, is immersed in water deeply. The pressure on it is 20 MPa. What is the change in volume of the sphere?
Solution:Step 1: By the definition of bulk modulus
Step 2: Finally we get
( )( )∆V/V
F/AB −=×B∆V
B∆V
×
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Step 2: Finally we get
( )BF/AV∆V −=
Step 3: Substituting the parameters, we get
Pressure
33m101.25∆V −×−=
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Melting process
Question: States of Solids
What are the physical differences between crystalline and amorphous?
Melting process
Definite shape and volume
Micro-structures
Transparency
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Transparency
Conductivity
Melting process
Answer: States of Solids
What are the physical differences between crystalline and amorphous?
Melting process
Definite shape and volume
Micro-structures
Transparency
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Transparency
Conductivity
Crystalline solids have a fixed melting point and defined micro-structures. Amorphous solids have neither.
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Static Fluids
The mechanical properties of static fluids
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Pressure in Fluids
Equilibrium equation for arbitrary portion in fluidsy p
Pressure in fluids
0APMgPA 0 =−−
ρAhM =
ρghPP 0 +=
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The forces on a water volume
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Pascal’s Principle
Pascal’s principle: The pressure at a depth of h below the surface of a fluid open to the atmosphere is greater than atmospheric pressure by the amount ρgh
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Same depth will have the same pressurePA = PB = PC = PD
Pressure is the same at all points that have the
same elevation
Pressure Transmission - 1Application of Pascal principle – Hydraulic jack
Fluid inside the jack is compressed through a pistol.
This pressure is transmitted to the larger output piston that creates a great force to
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Hydraulic jackcreates a great force to lift objects.
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Pressure Transmission -2
Pressure can be transmitted in fluid.
Application of Pascal principle – Hydraulic jack
Pressures at A1 and A2are the same.PA1 = F1/A1 = F2/A2 = PA2
Force can be amplified
If A1 <<A2, F2 >>F1
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Stroke is reduced by energy conservation law and continuity law
Illustration of operating Mechanism forhydraulic jack
Buoyancy - 1
What is buoyancy?
The lifting force for objects in fluids
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They are lifted by buoyancy
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Buoyancy - 2
What is buoyancy?The lifting force for objects in fluids
What causes buoyancy?Pressure difference on objects(1) Upper pressure(2) Lower pressure
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(2) Lower pressure(3) Resultant force
imρgVB =Buoyancy of an objectImmersed in fluids
Buoyant force, N
Archimedes’ Principle
Archimedes’ principle:Any body completely orAny body completely or partially submerged in a fluid is buoyed up by a force whose magnitude is equal to the weight of the fluid displaced by the body.
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imρgVB = Archimedes 287-212B.C.
Volume immersed m3
Acceleration of gravity 9.8m/s2
Density of material
Kg/m3
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Question: Hot Air BalloonWhy can a hot air balloon fly in the sky?
___________
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___________
Answer: Hot Air BalloonWhy can a hot air balloon fly in the sky?
Density of inner air ___________decreases
Buoyancy generated
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___________y y g
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Surface Tension
Questions:
Why insects can walk on water?
Why can razor blades float on water?
Why can water raise in
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Why can water raise in thin tubes?
Why does this happen?
Surface Tension- 2
Questions-Why can insects walk on water? -Why can razor blades float on water?-Why can water raise in thin tubes?
Surface tensionThe tendency for the Reason
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surface of a liquid to contract in area.
Why does this happen?
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Surface Tension- 3
Questions-Why can insects walk on water? Why can razor blades-Why can razor blades
float on water?-Why can water raise in thin tubes?
Surface tensionThe tendency for the surface of a liquid to
t t i
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Mathematical definition
2LFγ =
Apparatus for testing Surface tension
Inside edge and outside edge
contract in area.
Capillary Action - 1
Two types of fluid-surface interactions:
Mercury vs Glass
Water vs Glass
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Left: unwettableRight: wettable
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Capillary Action - 2
Two types of fluid-surface interactions:
Unwettable
WettableUnwettable
(water vs paraffin)
Contactangle
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Wettable(water vs glass)
Capillary Action - 3
Two types of fluid-surface interactions:
UnwettableUnwettable
Wettable
Water rise for wettable fluid-surface interaction
( )cosφr 2πγFv =Balanced by:
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hρgπrw 2=Balanced by:
Yields:
cos φρgr2γh =
Vertical component of surface forceWeight of
the watervolume
Water rise due to capillary action
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Question: Water Goes Up or Down?If a thin tube made of paraffin is inserted in water, the level of water inside the tube will be than the outside water. (water-paraffin is unwettable)
higher
lower
same
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uncertain
Answer: Water goes up or down?If a thin tube made of paraffin made is inserted in water, the level of water inside the tube will be than the outside water. (water-paraffin is unwettable)
higher
lower
same
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uncertain
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Fluids in Motion
Now we’ll study the properties of fluids that are moving
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fluids that are moving.
Fluid in Motion: A Preview
Properties of fluids:Density, gravity, viscosity
Continuity
Laminar and turbulent flow
Bernoulli’s Equation for steady ideal flow
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steady ideal flow
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Density and Gravity
Definition of densityMass per unit volume (fluids take indefinite shape but definite volume)p )GravityThe force between the earth and the matter. It is governed by Newton’s law of gravitation.
This force is pointing “downwards” (toward the earth) and is proportional to the mass
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) p pof the matter by the scaling factor of 9.8 m/s2, which is denoted by g.
For fluids, the force per volume is used instead of the force itself.
Viscosity
DefinitionInternal friction of a fluid; damping mechanism of fluids
Coefficient of viscosity
SvFl
ratestrainshearstressshearη ==
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Viscous flow
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Viscosity Applications
DefinitionInternal friction of a fluid; damping mechanism of fluids
Coefficient of viscosity
SvFl
ratestrainshearstressshearη ==
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ApplicationsDashpot or damper
Configuration and products
The Equation of Continuity
ContinuityThe net rate of flow of mass inward across any closed surface is equal to the rate of increase of the mass within the surface
Mathematical expression222111 vAρvAρ =
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For non-compression fluid222111
constantρρ 21 ≡=Yields:
2211 vAvA =
Flow into and out of a portion of a tube
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Laminar and Turbulent Flow - 1
Laminar or streamlineEvery particle y ppassing a particular point moves exactly along the smooth path followed by particles passing that point earlier.
Laminar(Streamline)
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Different streamlines cannot intercross.
Velocity is low.
Smoke from a cigarette
Cigarette
Laminar and Turbulent Flow - 2
Turbulent flowMotion is highly
Turbulent flow
g yirregular.
Vortices are developed within the fluid.
Resistance to the flow is increased
Laminar(Streamline)
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flow is increased.
Velocity is high.
Smoke from a cigarette
Cigarette
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Steady Ideal Flow
Ideal flow:Non-viscous & non-compressible
The work at lower end
The work at upper end
VP∆xFW 1111 ==
VPW 22 −=Ideal flow in a pipe
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Work and energy law
( )1221
2221 ρgVyρgVyρVv
21ρVv
21WW −+⎟
⎠⎞
⎜⎝⎛ −=+
Kinetic energy Potential energyWork
Bernoulli’s Equation
Mathematical expression
Bernoulli’s Equation
Physical meaning:
constantρgyvρ21P 2 =++
For an ideal flow, the sum of the pressure (P),
Ideal flow in a pipe
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, p ( ),
the kinetic energy per unit volume (1/2ρv2) ,
and the potential energy per unit volume(ρgy)
has the same value at all points along a stream line.
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Application for Bernoulli’s Equation
Velocity at “2” is zero
Velocity at “1” is to be measured
Pitot tube
Illustration of pitot tube
Velocity at 1 is to be measured
Heights of “1” and “2” are the same
By Bernoulli’s equation
12112
222 ρgyρv
21Pρgyρv
21P ++=++
=0
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111222 ρgyρ2
ρgyρ2
Same
3l1221 ghρPPρv
21
=−=
Density of the liquid in the tube
3l
1 ghρρ2v =
yields
Example: Speed at a Drain HoleConsider a tank with a drain hole at its bottom. The cross-sectional area of the tank is large relative to that of the hole. The water level drops slowly so that we assume V2=0. Find the speed at which the water leaves the hole 2 pwhen the water level is 0.5m above the hole.
Solution:Step 1: By Bernoulli’s Equation
Step 2: Finally we get
22201
210 ρgyvρ
21Pρgyvρ
21P ++=++
=0
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Step 2: Finally we get
Step 3: Substituting the parameters, we get
( )121 yy2gv −=
3.13m/sv 1 =
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Question: Aerodynamic Force on Wings
Why can a fixed-wing aircraft fly?Tip: Consider and apply Bernoulli’s equation
Air flow near the upper surface of the wing is moving faster than that near its lower surfaceAn air flow blowing toward the wing
The pressure on the upper surface of the wing is smaller than that near its lower surface
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Other mechanism
Answer: Aerodynamic Force on Wings
Why can a fixed-wing aircraft fly?Tip: Consider and apply Bernoulli’s equation
Air flow near the upper surface of the wing is moving faster than that near its lower surfaceAn air flow blowing toward the wing
The pressure on the upper surface of the wing is smaller than that near its lower surface
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Other mechanism
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Ideal flow: Bernoulli’sIdeal flow: Bernoulli’s
States of matter: Solid,
States of matter: Solid, Applications Applications
Learning Summary
Static behavior ofStatic behavior of
Bernoulli’s equation
Bernoulli’s equation
Liquid and Gas
Liquid and Gas
of fluid flowof fluid flow
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Static behavior of fluid: pressure, buoyancy, and surface tension
Static behavior of fluid: pressure, buoyancy, and surface tension
Solids and elasticity
Solids and elasticity
Congratulations
You have successfully completed the tutorial
Mechanics of Solids and FluidsFluids
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