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## Unit Seven: Solids and Fluids

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### GE253 Physics Unit Seven: Solids and Fluids John Elberfeld JElberfeld_at_itt-tech.edu 518 872 2082 Schedule Unit 1 Measurements and Problem Solving Unit 2 ... – PowerPoint PPT presentation

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Title: Unit Seven: Solids and Fluids

1
Unit SevenSolids and Fluids
GE253 Physics
• John Elberfeld
• JElberfeld_at_itt-tech.edu
• 518 872 2082

2
Schedule
• Unit 1 Measurements and Problem Solving
• Unit 2 Kinematics
• Unit 3 Motion in Two Dimensions
• Unit 4 Force and Motion
• Unit 5 Work and Energy
• Unit 6 Linear Momentum and Collisions
• Unit 7 Solids and Fluids
• Unit 8 Temperature and Kinetic Theory
• Unit 9 Sound
• Unit 10 Reflection and Refraction of Light
• Unit 11 Final

3
Chapter 7 Objectives
• Distinguish between stress and strain, and use
elastic moduli to compute dimensional changes.
• Explain the pressure-depth relationship and state
Pascal's principle and describe how it is used in
practical applications.
• Relate the buoyant force and Archimedes'
principle and tell whether an object will float
in a fluid, on the basis of relative densities.
• Identify the simplifications used in describing
ideal fluid flow and use the continuity equation
and Bernoulli's equation to explain common
effects of ideal fluid flow.
• Describe the source of surface tension and its
effect and discuss fluid viscosity.

4
• Read and study College Physics, by Wilson and
Buffa, Chapter 7, pages 219 to 250
• Be prepared for a quiz on this material

5
Written Assignments
• Do the homework on the handout.
• You must show all your work, and carry through
the units in all calculations
• Use the proper number of significant figures and,
when reasonable, scientific notation

6
Introduction
• Until now, we have beendealing with ideal
objects
• Now we will look at objects that can stretch,
bend, break, flow, and compress when forces are
applied

7
Introduction
• In this week, we will study real, macroscopic
objects, such as wires, blocks, and containers of
fluids.
• We will keep the concept of force and see what
happens to macroscopic objects when forces act on
them and see what forces macroscopic objects
exert.

8
Stress and Strain
• The stress of taking physics may cause a strain
• But in physics, these terms have different and
precise meanings.
• We will learn to use these terms as we study the
effects of forces on solids and fluids in this
unit, not to accelerate objects, but to deform
them.

9
Stress and Strain
• Stress (force/area) causes strain ( deformation
of some type)

10
Stress and Strain
• In physics, stress is related to the force
applied to an object
• Strain is related to how the object is deformed
as a result.
• Both also depend on the size of the object.

11
Stress
• The diagram shows a wire or rod of length Lo and
area A.
• When you apply a force F on the wire, it
stretches by a distance .
• When you apply a force F in the opposite
direction on a rod, the rod is compressed by a
distance .
• The greater the force F, the greater is the
amount of stretching or compressing.

A
F
L0
12
Stress
• It is clear that a thick wire is harder to
stretch than a thin one.
• For this reason, you can define the concept of
stress as
• Stress F / A
• The units of stress are N/m2.

13
Strain
• The longer the wire or rod, the greater is the
amount of stretching. For this reason, you can
define strain as
• Strain ?L / L
• The vertical lines stand for absolute value,
which means the same strain results from positive
?L due to stretching or negative ? L due to
compressing.

14
Strain
• A strain of 0.05 on a wire means that the wire
has been stretched to a length 5 greater than
its original length.

15
Youngs Modulus
• NOTE This graph shows Youngs Modulus how much
a wire will stretch if you apply different forces
on it.

YoungsModulusRegion
16
Graph
• Engineers need to know the force need to stretch
material a certain distance
• What force cause the bridge to sag into the
waves?
• Graphs show strain on the X axis and stress on
the Y axis

17
Youngs Modulus
• Youngs Modulus works in the straight line part
of the graph only
• The ratio of stress to strain in a material is
known as Youngs modulus
• Y (F/A) / ( ?L / L)
• Where, F is force A is cross sectional area
perpendicular to the applied force and L is
length of the object being stressed.
• NOTE Youngs Modulus is an ELASTIC Modulus
because materials bounce back to their original
shape in that part of the graph.

18
Youngs Modulus
• The bigger the modulus, the stronger the
material, and the more force it takes to cause a
specific deformation.
• Because material bounce back to their original
shapes, moduli (plural) are elastic
• The units of Youngs modulus are the same as
those of stress, N/m2.
• Youngs modulus for steel is 20 x 1010 N/m2 and
for bone is 1.5 x 1010 N/m2 for example.

19
Practice
• The femur (upper leg bone) is the longest and
strongest bone in the body.
• Let us assume that a typical femur is circular
and has a radius of 2.0 cm.
• How much force is required to extend the bone by
0.010?

20
Calculations
• Y (F/A) / ( ?L / L)
• From the chart Ybone 1.5 x 1010N/m2
• R 2cm(1m/100cm) .02m
• A ?R2 ?(.02m)2 1.26 x 10-3m2
• ?L / L .01 .01/100 1 x 10-4
• Y ( ?L / L) (F/A)
• F A Y ( ?L / L)
• F 1.26 x 10-3m2 1.5 x 1010N/m2 1 x 10-4
• F 1.89 x 103 N (about 425 pounds)

21
Practice
• A mass of 16 kg is suspended from a steel wire of
0.10-cm-diameter.
• By what percentage does the length of the wire
increase?
• Youngs modulus for steel is 20 x 1010 N/m2.

22
Calculation
• Y (F/A) / ( ?L / L)
• F W mg 16kg 9.8m/s2 157 N
• R .1cm(1m/100cm)/2 .0005m
• A ? R2 ? (.0005m)2 7.85 x 10-7m2
• ( ?L / L) (F/A) / Y (F/ ? R2 ) / Y
• (?L/L) (157N/ 7.85 x 10-7m2) / 20x1010N/m2
• (?L/L) .001 0.1
• NOTE The change in length is inversely
proportional to the SQUARE of the radius!

23
Shear Modulus
• To distort a rectangular solid, apply a force on
one of its faces in a direction parallel to the
face.
• Simultaneously, you must also apply a force on
the opposite face in the opposite direction.
• The diagram on the screen shows how you can
distort an object by applying force.

24
Shear
• The diagram on the screen shows that the amount
of distortion can be measured by the new angle Ø
, which the faces make.
• Shearing stress is defined as F/A, where F is the
tangential force and A is the area of the surface
that the force acts on.
• Shearing strain is the angle Ø .
• Similar to linear distortions, shearing strain
is directly proportional to shearing stress.
• The constant of proportionality is called the
shear modulus (S)
• S (F/A) / F

25
Shear
• Shear modulus has the same units as Youngs
modulus, N/m2.
• For many substances, shear modulus is
approximately one-third of the Youngs modulus.

26
Bulk Modulus
• You can also distort a rectangular solid by
applying forces perpendicular to its surfaces.
• This stress causes the solid to become smaller
and is known as volume stress or pressure.
• Volume stress is defined as F/A, where F is the
force perpendicular to the surfaces, and A is the
area of the surface.

27
Bulk Modulus
• Volume strain is the change in volume divided by
the original volume.
• Similar to shearing stress and stress, strain is
directly proportional to volume stress.
• The constant of proportionality is called bulk
modulus (B) and is defined as
• B (F/A) / ( ?V / V)

28
Bulk Modulus
• Solids are usually surrounded by air that exerts
a compressing force on their surface.
• Pressure Force/Area
• Therefore, when you apply a force F, you increase
this force, or more precisely, the volume stress.
• Bulk modulus is usually written as
• B (F/A) / ( ?V / V)
• B ?p / ( ?V / V)
• ?p is the increase in pressure above normal air
pressure

29
Table
1.0 x 10 9 4.5 x 109 26 x 109 2.2 x 109
30
Compare Bulk Modulus
• NOTE
• B ?p / ( ?V / V)
• For a gas, it takes the smallest pressure to
create a change in volume, so gasses have the
smallest bulk modulus
• Solids require a big pressure to have a change in
volume, so they have the biggest bulk modulus
• Bigger modulus implies a stronger material

31
Practice
• By how much must you change the pressure on a
liter of water to compress it by 0.10?

32
Calculation
• B ?p / ( ?V / V)
• B 2.2 x 109N/m2
• ( ?V / V) .1 (1/100) .001
• ?p B ( ?V / V)
• ?p 2.2 x 109 N/m2 .001 2.2 x 106 N/m2
• Because there is always air pressure, this is the
INCREASE in pressure to cause the change in
volume

33
Pressure in a Fluid
• The molecules in a solid are tightly bound.
• In a liquid or a gas, however, the molecules are
in motion and free to move.
• The diagram shows a cubical container filled with
gas.
• The molecules of the gas are represented by the
red dots.
• The blue arrows show the direction they are
moving in.

34
Pressure
• When a gas molecule with momentum p hits the wall
and bounces back, it exerts an impulse equal to
2p on the wall.
• To calculate the force exerted by a single
molecule, you need to know how long the collision
lasted.
• The effect of a single molecule is very small,
but the effect of a room full, like in a tornado,
can be huge.

35
Measuring Pressure
• The diagram shows a device that measures the
pressure of a gas.
• Because gas molecules can move freely, the
pressure of a gas will be the same no matter
where you place the gauge.
• Furthermore, any changes in pressure applied to
the container will be transmitted throughout the
gas volume by the moving molecules.

36
Pascals Principle
• Because liquid molecules are also free to move,
the same principles also apply to liquids and
thus all fluids.
• Pascals principle states this effect
• Pressure applied to an enclosed fluid is
transmitted undiminished to every point in the
fluid and to the walls of the container.

37
Atmospheric Pressure
• When a gas is in a container, it exerts uniform
pressure throughout the container.
• In the case of atmosphere, however, the air stays
at the Earths surface because of the force of
gravity.
• Air pressure is greatest at sea-level and
decreases as the altitude increases.
• The pressure of our atmosphere at sea-level is
• This amount of pressure is defined as 1
atmosphere (atm).

38
Density
• A liquid is much more dense than a gas.
• As a result, the effect of gravity on a liquid is
much greater than that on a gas in the same sized
container on the earth.
• In ordinary sized containers, a gas exerts
uniform pressure throughout the container it is
in, but a liquid does not.
• To refresh your memory, density is the mass of an
object or system of particles divided by the
volume it occupies.
• ? m / V

39
Depth and Pressure in a Liquid
• The diagram explains the relationship between
pressure and depth in a liquid.
• It shows a container of water with an imaginary
rectangular column of water.
• The column of water has a surface area A, and a
weight mg.
• Hence, a person holding the column of water
experiences a force mg, and a pressure mg/A,
which is the pressure of the water at the bottom
of the container.

40
Demonstration
41
Pressure
• You can derive the equation for pressure using
the relationship between mass and density
• ? m/V gt m ? V
• V A h gt m ? Ah
• p F/A mg/A ? Ah g / A
• p ? g h
• The total pressure of the liquid at the bottom of
the container is
• p p0 ? g h where p0 normal air pressure

42
Density
43
Practice
• What is the total pressure exerted on the back of
a scuba diver in a lake at a depth of 8.00 m?

44
Total Pressure
• Pressing down on the divers back is all the water
above him, plus all the AIR above the water.
• pwater ? g h 1000kg/m3 x 9.8m/s2 x 8m
• pwater 7.84 x 104 N/m2 7.84 x 104 Pa
• pAir 1 Atmosphere 101kPa
• Ptotal 7.84 x 104 Pa 101kPa
• Ptotal 1.79 x 105 Pa

45
Barometers
• A barometer is a device that measures atmospheric
pressure.
• To make a barometer at home, turn a glass upside
down under water.
• When you lift it straight up, it will remain
filled with water.
• Air pressure holdsthe water up

46
Barametric Pressure
• At the surface of the Earth, the mercury in a
barometer rises to a height of 760 mm.
• This means atmospheric pressure is
•
• The density of mercury is taken from the density
table shown previously.
• Here we have introduced another unit of pressure
called the torr, named after a famous scientist,
and representing the pressure corresponding to 1
mm of mercury.

47
Pascals Principle
• The pressure of a gas in a container is the same
at every point in the gas and on the walls of the
container.
• Pressure in a liquid varies with depth
• The diagram on the screen shows a piston that
exerts a force F over an area A on a body of
water.
• This creates a pressure p that can be experienced
throughout the fluid.

48
Pressure
• Total pressure is the sum of the pressure from
the weight of the fluid AND the added pressure
from the piston

49
Hydraulic Lift
• Two pistons are connected to a hydraulic lift.
• When you press the input piston, the output
piston rises.
• The pressure on the input piston is the same as
that on the output piston.
• Keep in mind that the force is given by the
pressure times the area. F P A
• The output piston has a much larger area than the
input piston.
• Therefore, the output piston exerts a much larger
force than the input piston, and you can easily
lift an automobile. F P A

50
Lift a Car
• p1 p2
• F1/A1 F0/A0
• F0 F1 (A0 /A1 )

51
Practice
• The input and lift (output) pistons of a garage
lift have diameters of 10 cm and 30 cm,
respectively. The lift raises a car with a weight
of 1.4 x 104 N.
• (a) What is the force on the input piston?
• (b) What is the pressure to the input piston?

52
Calculations
• p1 p2
• F1/A1 F0/A0
• R1 10cm (1m/100cm)/2 .05m
• R2 30cm (1m/100cm)/2 .15m
• A1 ? R12 ?(.05m)2 7.85x10-3m2
• A2 ? R22 ?(.15m)2 7.07x10-2m2
• F1 F0(A1/A0)
• F1 1.4 x 104 N (7.85x10-3m2/ 7.07x10-2m2)
• F1 1,550N
• p1 F1/A1 1,554N / 7.85x10-3m2 2.0x105N/m2
• p2 F2/A2 1.4 x 104 N / 7.07x10-2m2
• p2 2.0x105N/m2 checks!

53
Thought Experiment
• If the output piston of a hydraulic lift has a
very large area, a two-year-old can lift the
Empire State Building.
• Does this make sense?
• Is energy conserved?

54
Results
• Yes, it does make sense.
• Simple machines, such as levers, transform small
input forces into large output forces.
• Energy is the ability to do work.
• It is the product of force and distance.
• Machines transform small forces applied over
large distances to large forces applied over
small distances.

55
Practice
• A 60-kg athlete does a single-hand handstand.
• If the area of the hand in contact with the floor
is 100 cm2, what pressure is exerted on the
floor?

56
Calculation
• p F/A
• A 100 cm2 (1m/100cm)2 1.00x10-2m2
• p mg/A 60kg 9.8m/s2/ 1.00x10-2m2
• p 5.88x104N/m2

57
Practice
• An oak barrel with a lid of area 0.20 m2 is
filled with water. A long, thin tube of
cross-sectional area 5.0 X 10-5 m2 is inserted
into a hole at the center of the lid, and water
is poured into the tube.
• When the water reaches 12 m high, the barrel
bursts.
• What was the weight of the water in the tube?
• What was the pressure of the water on the lid of
the barrel?
• What was the net force on the lid due to the
water pressure?

58
Calculations
• W m g ? V g ? Ah g
• A 5.0 X 10-5 m2 , h 12 m
• W1000kg/m3 5.0 X 10-5 m2 12 m 9.8m/s2
• W 5.88 N
• p F/A 5.88 N / 5.0 X 10-5 m2
• p 1.18x105N/m2
• OR
• p ?gh 1000kg/m3 9.8m/s2 12m 1.18x105N/m2
• Checks!

59
Calculations
• p F / A
• F p A
• F 1.18x105N/m2 0.20 m2
• F 2.36 x 104N (More than 5000 pounds!)

60
Archimedes
• Have you ever yelled, 'Eureka!' when you figured
out how to solve a challenging problem?
• Well the story goes that when Archimedes figured
out the principle named after him, he was so
excited that he not only yelled, 'Eureka,' but
also went running through town from the public
bath naked!
• You may not get that excited over Archimedes
principle, but you will learn some useful and
interesting things about fluid buoyancy and fluid
flow in this lesson.

61
Archimedes' Principle
• The upward force experienced by an object when it
is immersed in a liquid or a gas is called
buoyant force.
• Buoyant force is equal in magnitude to the weight
of the volume of fluid displaced.
• This rule is called Archimedes' principle.
• BF mg ? V g

62
Archimedes Principle
• The diagrams on the screen illustrate Archimedes
principle.
• Part (a) shows buoyant force as the force that
pushes up when you hold a piece of wood under
water.
• Part (b) shows buoyant force as the force that
reduces the weight of an object weighing 10 N
to 8 N.

63
Practice
• A spherical helium balloon has a radius of 30 cm.
What is the buoyant force acting on it in air?

64
Calculations
• Find the volume if R 30 cm .3 m
• V (4/3) ? R3 .113 m3
• BF mg ? V g 1.29kg/m3 .113 m3 9.8m/s2
• BF 1.43 N (about 1/3 of a pound)
• If the balloon and the air in the balloon has
weight less then 1.43 N, it will float if more,
it will sink

65
Practice
• The diagram shows a partially submerged iceberg
at rest.
• It is in equilibrium because its buoyant force is
equal to the weight of the iceberg.
• Suppose a uniform solid cube of material 10 cm on
each side has a mass of 700 g. Will the cube
float? If it will float, how much of the cube
will be submerged?

66
Calculations
• Suppose the cube were completely SUBMERGED!
• LSide 10 cm .1m
• V LWH (.1m)(.1m)(.1m) 10-3 m3
• BF ? V g 1x103Kg/m3 10-3 m3 9.8m/s2
• BF 9.8N
• Weight of the object mg
• W 700 g (1kg/1000g) 9.8m/s2 6.86 N
• The buoyant force is greater than the weight!
• The object will be pushed up to the surface and
will rise above the surface until the weight of
the fluid displaced just balances the weight of
the object

67
Floating Object
• V LWH (.1m)(.1m)(.1m) 10-3 m3
• W 700 g (1kg/1000g) 9.8m/s2 6.86 N
• BF 6.86 N ? V g 1x103Kg/m3 V 9.8m/s2
• V 6.86 N / (1x103Kg/m3 9.8m/s2 )
• V 7 x 10-4 m3
• 7 x 10-4 m3 is the volume of the cube below the
surface
• The remainder
• 10-3 m3 - 7 x 10-4 m3 3 x 10-4 m3 is above the
surface
• It is 70 submerged

68
Ideal Fluid Flow
• To mathematically describe fluid flow like we
have projectile motion, for example can be very
difficult in real cases.
• Consider the upper portion of the rising smoke
it looks almost random!
• In order to obtain a basic description of fluid
flow, we will make some simplifications and
consider ideal fluid flow, so the flow looks more
like the lower part of the rising smoke stream.
• The conditions for an ideal fluid are that its
flow is

69
Ideal Fluid Flow
• Steady The flow is not turbulent particles in
the fluid do not collide, and their paths do not
cross. The flow looks smooth.
• Irrotational There is no rotational motion in
small volumes of the fluid, so there are no
embedded in the stream does not rotate.
• Nonviscous Viscosity is negligible. This means
the fluid flows easily, without significant
friction or resistance to the flow.
• Incompressible The density is constant
throughout the fluid.
• When a fluid's flow has these four
characteristics, we say it is an ideal fluid.
Unless specified otherwise, we will consider
these four conditions to be true in the fluids we
consider.

70
Equation of Continuity
• When a liquid flows through a tube, the amount of
liquid entering the tube must equal the amount of
liquid coming out of it.
• If the cross-sectional area of the tube varies
across its length, then the speed of the liquid
must vary too.
• The diagram on the screen shows what happens to
the speed of water when the nozzle has a
smaller cross-sectional area than the tube.

71
Equation of continuity
• If the liquid is incompressible, the density of
the liquid remains the same throughout the tube.
If the liquid is incompressible, the density of
the liquid remains the same throughout the tube.
• Hence, as the above equation simplifies to
• Av constant
• Area x velocity constant
• Volume/time constant
• Equation of continuity is an equation that
describes the fact that the amount of fluid
entering a tube is equal to the amount of fluid
leaving the tube.

72
Equation of Continuity
• High cholesterol in the blood can cause fatty
deposits called plaques to form on the walls of
blood vessels.
• Suppose plaque reduces the effective radius of an
artery by 25.
• Because the area is smaller, what must happen to
the velocity?

73
Bernoullis Equation
• Bernoulli's equation states that when a liquid is
moving fast, its pressure is reduced.
• The diagram below shows a tube of varying
cross-sectional areas.
• The pressure indicators show that the pressure is
lower in the middle region, where the smaller
cross sectional area results in the flow rate
being greater.

74
Bernoulli's Equation
• To observe Bernoulli's equation, conduct the
following experiment.
• Hold two corners of a sheet of paper with both
hands.
• Rotate your hands so that the paper takes the
shape of the wing of an airplane.
• Blow over the top of the paper.
• You will observe that the sheet of paper rises.
• It lifts up because air flows on one side of the
paper, but is stationary on the other.
• This is the principle behind the lifting of air
planes the orientation and shape of the wing of
an airplane causes the air flowing over it to
flow faster than the air under it.

75
Wing Design
76
Surface Tension
• When there is a boundary between a liquid and a
gas, some remarkable phenomena occur.
• The figures on the screen show two water/air
phenomena and one soap solution/air boundary
phenomena.

77
Surface Tension
• 1) An insect is able to walk on water. 2) Water
in air forms circular droplets.3) Soap solutions
form bubbles.
• In the phenomenon where bubbles are made, there
are two surfaces the inside and the outside of
the bubble.
• Although the bubble is thin compared to a piece
of paper, it is very thick compared to the size
of a molecule.
• The surface in an air-liquid boundary is only two
or three molecules thick.

78
Surface Tension
• The forces of attraction between the molecules of
a liquid are lower than those of a solid.
• All the same, they do exist because otherwise the
molecules of a liquid would escape into the
atmosphere.
• In a liquid, a molecule, which is at a distance
from the surface, is surrounded by other
molecules.
• A molecule on the surface, however, is not
entirely surrounded by molecules.
• The molecules on the surface are held together by
a horizontal force between them, which is called
surface tension.

79
Viscosity
• You must have noticed that in January, molasses
flows slower than water or kerosene.
• This happens because of viscosity.
• Viscosity is a fluids internal resistance to
flow.
• It can be measured with a device called a
viscosimeter.
• There are various types of viscosimeters.

80
Flow Rate
• When fluid is flowing in a pipe, as a result of
viscosity, the speed of the fluid near the
surface of the pipe is less than that at the
center.
• The flow rate is the average volume of a fluid
that flows beyond a given point during a time
interval
• The diagram on the screen shows that is not easy
to calculate the average flow rate.
• Flow rate has the unit of m3/s.

81
Summary
• What are the elastic modulie?
• What is the relationship between pressure and
depth in a fluid?
• What is Archimedes principle?
• What are the essential principles of fluid flow?
• What causes surface tension and what is
viscosity?